Power Analyses - Workshop
Daniel J. Schad, Maximilian M. Rabe, Reinhold Kliegl
22/2/2021
library(lmerTest)
library(afex)
library(ggplot2)
library(dplyr)
library(designr)
library(gridExtra)
library(MASS)
What is statistical power?
- Given the H1 is true
- Given we assume some effect size
- –> Power = probability to obtain a significant result; i.e., to correctly recover the true H1
We can compute power by
- assuming the H1 is true
- assuming some effect size (e.g., difference in DV between 2 conditions)
How to obtain the probability of a significant result?
- simulate data based on the assumed model + effect size
- do this many times (e.g., nsim = 1000)
- run the statistical model on each simulated data set
- determine how many times we find a significant effect –> this probability is = power
An easy example: 2-sample t-test
# a) assume effect size + simulate data
x <- rep(c("x1","x2"), each=30)
y <- rep(c( 200, 220), each=30) + rnorm(60,0,50)
ggplot(data.frame(x,y), aes(x=x,y=y)) + geom_boxplot()
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)
# b) run statistical model & get p-value
t.test(y ~ x)$p.value
## [1] 0.03388535
# c) do this many times
nsim <- 1000
pVal <- c()
for (i in 1:nsim) {
x <- rep(c("x1","x2"), each=30)
y <- rep(c( 200, 220), each=30) + rnorm(60,0,50)
# b) run statistical model & get p-value
pVal[i] <- t.test(y ~ x)$p.value
}
# d) check how often it is significant
(power <- mean( pVal < 0.05 ))
## [1] 0.337
# e)
# We could do this for different numbers of subjects and see when power is ~80%
# We could change the difference in means/residual standard deviations
What we usually want to achieve is a power of 80%. That’s the standard. We should plan our analysis, with the number of subjects and items to achieve this power value of 80%. That is, if the effect that we want to test really exists, we want to have an 80% chance of actually detecting the effect with our analysis. In the power analysis, we can then vary the number of subjects or items, or make different assumptions about the effect size to see what we need to achieve 80% power. This should be the basis for planing an experimental study. Note that in the simulation studies below, we will sometimes use power thresholds of lower than 80%. This should normally not be done when running empirical studies.
One more point about power: if an experimental design has low power, then this can have severe negative consequences for statistical analysis. In an extreme case where power is only 10%, then if we find a significant result, there is a very high chance that the effect is actually due to chance and that the H0 is true. Moreover, when we have low power, then the effect size estimates from significant results are guaranteed to be too large (type M = magnitude error), and there is a danger finding effects in the wrong direction (type S = sign error).
Therefore, it is important to plan studies such that they have a good power, ideally = 80%. If you want to provide evidence for the null hypothesis, then even a higher power of e.g., 95% can be beneficial.
Linear model formulation
This is the formula for a simple linear model: \(y_i = b_0 + b_1 * x_i + e_i\), where \(y_i\) is the dependent variable for subject \(i\), \(b_0\) is the intercept, \(b_1\) is the slope, \(x_i\) is the value of the predictor for subject \(i\), and \(e_i\) is the random error term for subject \(i\). We can use this to simulate data.
The predictor term: This could be a continuous variable in a linear regression analysis (e.g., \(x_i\) could indicate the age of subject \(i\)). However, we can also use this formulation if the predictor is a factor, e.g., if we have two groups of subjects “x1” and “x2”. In this case, we have to use contrasts to code factors into numbers (for contrasts see Schad et al., 2020, JML). One example is the sum contrast. Here, the predictor variable is \(-1\) for one group (e.g., for x1) and \(+1\) for the other group (e.g., for x2).
# previous formulation
x <- rep(c("x1","x2"), each=30)
y <- rep(c( 200, 220), each=30) + rnorm(60,0,50)
# new:
x <- rep(c(-1,+1), each=30) # define predictor term: here, sum contrast coding (-1, +1)
y <- 210 + 10*x + rnorm(60,0,50) # simulate data
# run linear model
lm(y ~ x)
##
## Call:
## lm(formula = y ~ x)
##
## Coefficients:
## (Intercept) x
## 207.735 -1.415
##
## Call:
## lm(formula = y ~ x)
##
## Residuals:
## Min 1Q Median 3Q Max
## -98.808 -30.032 3.904 37.831 70.513
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 207.735 5.649 36.77 <2e-16 ***
## x -1.415 5.649 -0.25 0.803
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 43.76 on 58 degrees of freedom
## Multiple R-squared: 0.00108, Adjusted R-squared: -0.01614
## F-statistic: 0.06273 on 1 and 58 DF, p-value: 0.8031
ggplot(data.frame(x,y), aes(x=factor(x),y=y)) + geom_boxplot()
![](data:image/png;base64,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)
Content
- ANOVA + LMM: Random effects for subjects only, 1 within-subject factor
- ANOVA + LMM: Random effects for subjects only, 2x3 within-subject design
- LMM: Crossed random effects for subjects and items
- Vary effect size
- Based on a previous data set: latin square design
- LMM: continuous covariate
- logistic GLMM
Steps of a power analysis
- Create experimental design (designr)
- Simulate data (simLMM)
- Run statistical model (lmer, aov_car)
- Do this many times and compute power
Other statistical software: R-packages simr and faux
a) Create experimental design (desinr)
The R-package designr
has been written by us to create factorial experimental designs.
library(designr)
# one within-subject factor
# create design
design <-
fixed.factor("X", levels=c("X1", "X2")) + # fixed effect
random.factor("Subj", instances=5) # random effect
dat <- design.codes(design) # create data frame (tibble) from experimental design
length(unique(dat$Subj)) # number of subjets
## [1] 5
data.frame(dat) # look at data
## Subj X
## 1 Subj1 X1
## 2 Subj1 X2
## 3 Subj2 X1
## 4 Subj2 X2
## 5 Subj3 X1
## 6 Subj3 X2
## 7 Subj4 X1
## 8 Subj4 X2
## 9 Subj5 X1
## 10 Subj5 X2
# one between-subject factor
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", groups="X", instances=5)
dat <- design.codes(design)
length(unique(dat$Subj))
## [1] 10
## Subj X
## 1 Subj01 X1
## 2 Subj02 X1
## 3 Subj03 X1
## 4 Subj04 X1
## 5 Subj05 X1
## 6 Subj06 X2
## 7 Subj07 X2
## 8 Subj08 X2
## 9 Subj09 X2
## 10 Subj10 X2
# 2 (A: within-subjects) x 2 (B: between-subjects) design
design <-
fixed.factor("A", levels=c("A1", "A2")) +
fixed.factor("B", levels=c("B1", "B2")) +
random.factor("Subj", groups="B", instances=5)
dat <- design.codes(design)
length(unique(dat$Subj))
## [1] 10
## Subj A B
## 1 Subj01 A1 B1
## 2 Subj01 A2 B1
## 3 Subj02 A1 B1
## 4 Subj02 A2 B1
## 5 Subj03 A1 B1
## 6 Subj03 A2 B1
## 7 Subj04 A1 B1
## 8 Subj04 A2 B1
## 9 Subj05 A1 B1
## 10 Subj05 A2 B1
## 11 Subj06 A1 B2
## 12 Subj06 A2 B2
## 13 Subj07 A1 B2
## 14 Subj07 A2 B2
## 15 Subj08 A1 B2
## 16 Subj08 A2 B2
## 17 Subj09 A1 B2
## 18 Subj09 A2 B2
## 19 Subj10 A1 B2
## 20 Subj10 A2 B2
# 1 factor, 2 (crossed) random effects, within-subject, between-item factor
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=5) +
random.factor("Item", groups="X", instances=2)
dat <- design.codes(design)
length(unique(dat$Subj))
## [1] 5
## [1] 4
## Subj Item X
## 1 Subj1 Item1 X1
## 2 Subj1 Item2 X1
## 3 Subj1 Item3 X2
## 4 Subj1 Item4 X2
## 5 Subj2 Item1 X1
## 6 Subj2 Item2 X1
## 7 Subj2 Item3 X2
## 8 Subj2 Item4 X2
## 9 Subj3 Item1 X1
## 10 Subj3 Item2 X1
## 11 Subj3 Item3 X2
## 12 Subj3 Item4 X2
## 13 Subj4 Item1 X1
## 14 Subj4 Item2 X1
## 15 Subj4 Item3 X2
## 16 Subj4 Item4 X2
## 17 Subj5 Item1 X1
## 18 Subj5 Item2 X1
## 19 Subj5 Item3 X2
## 20 Subj5 Item4 X2
# within-subject, within-item factor
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=5) +
random.factor("Item", instances=2)
dat <- design.codes(design)
length(unique(dat$Subj))
## [1] 5
## [1] 2
## Subj Item X
## 1 Subj1 Item1 X1
## 2 Subj1 Item1 X2
## 3 Subj1 Item2 X1
## 4 Subj1 Item2 X2
## 5 Subj2 Item1 X1
## 6 Subj2 Item1 X2
## 7 Subj2 Item2 X1
## 8 Subj2 Item2 X2
## 9 Subj3 Item1 X1
## 10 Subj3 Item1 X2
## 11 Subj3 Item2 X1
## 12 Subj3 Item2 X2
## 13 Subj4 Item1 X1
## 14 Subj4 Item1 X2
## 15 Subj4 Item2 X1
## 16 Subj4 Item2 X2
## 17 Subj5 Item1 X1
## 18 Subj5 Item1 X2
## 19 Subj5 Item2 X1
## 20 Subj5 Item2 X2
# within-subject, within-item factor, latin square design
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=5) +
random.factor("Item", instances=2) +
random.factor(c("Subj", "Item"), groups=c("X"))
dat <- design.codes(design)
length(unique(dat$Subj))
## [1] 10
## [1] 4
## Subj Item X
## 1 Subj01 Item1 X1
## 2 Subj01 Item2 X2
## 3 Subj01 Item3 X1
## 4 Subj01 Item4 X2
## 5 Subj02 Item1 X2
## 6 Subj02 Item2 X1
## 7 Subj02 Item3 X2
## 8 Subj02 Item4 X1
## 9 Subj03 Item1 X1
## 10 Subj03 Item2 X2
## 11 Subj03 Item3 X1
## 12 Subj03 Item4 X2
## 13 Subj04 Item1 X2
## 14 Subj04 Item2 X1
## 15 Subj04 Item3 X2
## 16 Subj04 Item4 X1
## 17 Subj05 Item1 X1
## 18 Subj05 Item2 X2
## 19 Subj05 Item3 X1
## 20 Subj05 Item4 X2
## 21 Subj06 Item1 X2
## 22 Subj06 Item2 X1
## 23 Subj06 Item3 X2
## 24 Subj06 Item4 X1
## 25 Subj07 Item1 X1
## 26 Subj07 Item2 X2
## 27 Subj07 Item3 X1
## 28 Subj07 Item4 X2
## 29 Subj08 Item1 X2
## 30 Subj08 Item2 X1
## 31 Subj08 Item3 X2
## 32 Subj08 Item4 X1
## 33 Subj09 Item1 X1
## 34 Subj09 Item2 X2
## 35 Subj09 Item3 X1
## 36 Subj09 Item4 X2
## 37 Subj10 Item1 X2
## 38 Subj10 Item2 X1
## 39 Subj10 Item3 X2
## 40 Subj10 Item4 X1
ANOVA + LMM: Random effects for subjects only, 1 within-subject factor
Ok, let’s run a power analysis for a simple example: one within-subject factor with subject random effects.
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=30)
dat <- design.codes(design)
length(unique(dat$Subj))
## [1] 30
(contrasts(dat$X) <- c(-1, +1)) # define a sum contrast
## [1] -1 1
dat$Xn <- model.matrix(~X, dat)[,2] # convert this it a numeric variable
Next, we will use the R-function simLMM()
to simulate data for a linear mixed-effects model. simLMM()
is currently under development. If you find any errors, please write them into a script that reproduces the error and send it to us (e.g., to danieljschad@gmail.com). This would be very important feedback! Thank you for your help.
How does the function work? The most important function arguments are the following:
simLMM(formula, data, Fixef, VC_sd, CP)
Formula is a standard formula used in the lmer
function. For the present example, the formula would be form = ~ 1 + X + (1 + X | Subj)
. Since simLMM
is a simulation function, we do not have to specify a dependent variable. This example indicates an intercept 1
and a fixed effect for factor X
. For the random effects, we see random effects for subjects Subj
; these specify a random intercept and random slopes for factor X
. Since there is only one pipe |
, we know that the random intercepts and slopes are assumed to be correlated.
The next argument is the data data
, which is a data frame containing all the variables - this is just the same as in the lmer
function. Here, our data frame was termed dat
, i.e., data=dat
.
The next argument Fixef
specifies the fixed effects. This is a vector of numbers that specify the regression coefficients / fixed effects for each term in the formula. In our example, we have two fixed effects, an intercept and a slope. Thus, we enter two numbers, e.g., Fixef = c(200, 10)
, which specifies an intercept of \(200\) and a slope of \(10\).
The next argument VC_sd
specifies the standard deviations for the random effects. It is entered as a list. In the present example, we have only two random effects: subjects and the residual noise. These are assumed to be normally distributed with mean zero and some standard deviation. For subjects we have two random effects terms, the intercept and the random slopes. Let’s assume the intercept varies across subjects with a standard deviation of \(30\) and the slope varies across subjects with a standard deviation of \(10\). We combine these two terms in one vector sd_Subj <- c(30, 10)
. The second random effects term is the residual standard deviation. We here assume the residual noise is normally distributed with a mean of \(0\) and some standard deviation, which we assume here is \(50\). We now combine these standard deviations into a list VC_sd = list( c(30, 10), 50)
: we first enter the standard deviations for the subject random effects as a vector, and then we enter the standard deviation for the residual noise.
The next argument CP
specifies the random effects correlations. Here, we have different options for how to specify this. One option is to simply specify a single number, e.g., CP=0.3
. This will set all random effects correlations in the model to the value \(0.3\). If we have several random effects terms, e.g., for subjects and for items, we can enter a vector of length two, where the first number would specify all random effects correlations for subjects, and the second would specify all random effects correlations for items. Last, we can also enter a list of correlation matrices. E.g., when we have subjects and items, we would have a list of length two. And the first entry would contain a correlation matrix for the subject random effects and the second entry would contain a correlation matrix for item random effects. Here, because we have only one random effects correlation in the model, we simply use the specification CP=0.3
.
Taken together, this gives the following call of the simLMM
function: simLMM(~ X + (X | Subj), data=dat, Fixef=fix, VC_sd=list(sd_Subj, sd_Res), CP=0.3)
.
One additional argument that we can use is empirical
. By default this is set to empirical=FALSE
. If we set this to empirical=TRUE
, then the fixed effects estimates in the simulated data will exactly correspond to the numbers that we specify. However, the random effects will not be exact. We will demonstrate this below. If we use the default empirical=FALSE
, then the numbers (fixed-effects + random effects) that we specify are the “true” population parameters, from which we draw a random sample in the simulation. Note that empirical=TRUE
does not work for data from a logistic GLMM and it does not work when you have continuous predictors, i.e., covariates, instead of/in addition to factors.
With this background, let’s simulate data for our within-subject design. We use empirical=TRUE
.
# simulate data
fix <- c(200,10) # set fixed effects
sd_Subj <- c(30, 10) # set random effects standard deviations for subjects
sd_Res <- 50 # set residual standard deviation
dat$ysim <- simLMM(form = ~ 1 + X + (1 + X | Subj),
data = dat,
Fixef = fix,
VC_sd = list(sd_Subj, sd_Res),
CP = 0.3,
empirical = TRUE)
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 1 + X1 + ( 1 + X1 | Subj )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev. Corr
## Subj (Intercept) 30.0
## X1 10.0 0.30
## Residual 50.0
## Number of obs: 60, groups: Subj, 30
## Fixed effects:
## (Intercept) X1
## 200 10
We see that the simLMM
function produces some output that looks very similar to the output from a fitted lmer
object. In this output, we can check whether our specification of fixed and random effects is what we intended, or whether we made some mistake in our specification. We can turn this output off by specifying verbose=FALSE
. This will be useful in power simulations where we simulate data many many times.
Next, let’s check the simulated data.
# check group means
dat %>% group_by(X) %>% summarize(M=mean(ysim)) # the group means are EXACTLY 190 and 210. This is due to empirical=TRUE.
## # A tibble: 2 x 2
## X M
## * <fct> <dbl>
## 1 X1 190
## 2 X2 210
# check fixed effects + random effects
(m1 <- lmer(ysim ~ Xn + (Xn || Subj), data=dat, control=lmerControl(calc.derivs=FALSE))) # The fixed effects are EXACTLY as indicated. This is due to empirical=TRUE.
## Warning in as_lmerModLT(model, devfun): Model may not have converged with 1
## eigenvalue close to zero: 1.7e-09
## Linear mixed model fit by REML ['lmerModLmerTest']
## Formula: ysim ~ Xn + (Xn || Subj)
## Data: dat
## REML criterion at convergence: 646.0295
## Random effects:
## Groups Name Std.Dev.
## Subj (Intercept) 38.20
## Subj.1 Xn 28.89
## Residual 35.46
## Number of obs: 60, groups: Subj, 30
## Fixed Effects:
## (Intercept) Xn
## 200 10
aov_car(ysim ~ 1 + Error(Subj/X), data=dat) # We can also run an ANOVA
## Anova Table (Type 3 tests)
##
## Response: ysim
## Effect df MSE F ges p.value
## 1 X 1, 29 2926.46 2.05 .028 .163
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
We can see that because the setting empirical=TRUE
, the fixed effects were estimated exactly to the numbers that we set in the specification. This suggests that the simulation process was implemented as intended. However, the random effects terms are not exact.
VERY IMPORTANT: In order to perform a power analysis, we have to use empirical=FALSE
. In a power analysis, we are assuming that we randomly sample from the population parameters. This is what would happen in a “real” experiment. And we want to know how often an effect is significant.
Next, we perform a power analysis. We want to find out how many subjects are needed to run this study. We assume the fixed and random effects specified above. We simulate data from the model for different numbers of subjects. And we then fit lmer
models to the simulated data to see how often the effect of factor X
is significant given that there is a true effect of X
in the data.
nsubj <- seq(10,100,1) # we vary the number of subjects from 10 to 100 in steps of 1
nsim <- length(nsubj) # number of simulations
COF <- COFaov <- data.frame()
warn <- c()
for (i in 1:nsim) { # i <- 1
#print(paste0(i,"/",nsim))
# create experimental design
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=nsubj[i])
dat <- design.codes(design)
nsj <- length(unique(dat$Subj))
# create contrast and store as numeric variable
contrasts(dat$X) <- c(-1, +1)
dat$Xn <- model.matrix(~X,dat)[,2]
# for each number of subjects, we run 10 simulations to obtain more stable results
for (j in 1:10) { # j <- 1
# simulate data
dat$ysim <- simLMM(~ X + (X | Subj), data=dat, Fixef=fix, VC_sd=list(sd_Subj, sd_Res), CP=0.3, empirical=FALSE, verbose=FALSE)
# ANOVA
AOV <- aov_car(ysim ~ 1 + Error(Subj/X), data=dat)
AOVcof <- summary(AOV)$univariate.tests[2,]
COFaov <- rbind(COFaov,c(nsj,AOVcof))
# LMM
#LMM <- lmer(ysim ~ Xn + (Xn || Subj), data=dat,
# REML=FALSE, control=lmerControl(calc.derivs=FALSE))
# run lmer and capture any warnings
ww <- ""
suppressMessages(suppressWarnings(
LMM <- withCallingHandlers({
lmer(ysim ~ Xn + (Xn || Subj), data=dat, REML=FALSE,
control=lmerControl(calc.derivs=FALSE))
},
warning = function(w) { ww <<- w$message }
)
))
LMMcof <- coef(summary(LMM))[2,]
COF <- rbind(COF,c(nsj,LMMcof,isSingular(LMM)))
warn[i] <- ww
}
}
#load(file="data/Power0.rda")
# Results for LMMs
names(COF) <- c("nsj","Estimate","SE","df","t","p","singular")
COF$warning <- warn
COF$noWarning <- warn==""
COF$sign <- as.numeric(COF$p < .05 & COF$Estimate>0) # determine significant results
COF$nsjF <- gtools::quantcut(COF$nsj, q=seq(0,1,length=10))
COF$nsjFL <- plyr::ddply(COF,"nsjF",transform,nsjFL=mean(nsj))$nsjFL
# Results for ANOVAs
names(COFaov) <- c("nsj","SS","numDF","ErrorSS","denDF","F","p")
COFaov$sign <- as.numeric(COFaov$p < .05) # determine significant results
COFaov$nsjF <- gtools::quantcut(COFaov$nsj, q=seq(0,1,length=10))
COFaov$nsjFL <- plyr::ddply(COFaov,"nsjF",transform,nsjFL=mean(nsj))$nsjFL
#save(COF, COFaov, file="data/Power0.rda")
Note that in a standard LMM analysis, we would be interested to fit a parsimonious LMM (Matuschek et al., 2017, JML). This involves careful selection of the random effects. Unless one has an automatized selection of the parsimonious LMM, this is not possible when performing a power analysis and fitting hundreds of models. An alternative possibility is to fit a model with all random slopes, but with no random effects correlations. The problem with random effects correlation is that they are often very hard to estimate from the data. When trying to estimate them, there are often failures in model fit. However, removing the random effects correlations from the fit presumably does not affect power and alpha error much (Barr et al., 2013, JML). Therefore, for power analyses, it is recommended to not estimate random effects correlations. However, normally all random slopes should be estimated, since neglecting random slopes in the estimation can sometimes heavily inflate the alpha error and lead to false positive results (i.e., if there is strong true variation in the effect; Barr et al., 2013, JML).
First, we should check whether the models were singular fits. Singular fits are cases where some of the parameter values were estimated on their boundary. For example, a random effects standard deviation can be estimated to be exactly \(0\), or a correlation parameter can be estimated to be exactly \(+1\) or \(-1\). Normally, this should be avoided in LMMs, usually by excluding the respective term from the model. However, this is not possible in power analyses due to the large number of model fits. Therefore, we here check in how many cases there are singular fits.
load(file=system.file("power-analyses", "Power0.rda", package = "designr"))
mean(COF$singular)
## [1] 0
The mean of zero indicates that none of the models were singular fits. This supports the results from the analysis.
Moreover, we can check whether there were any warning messages, i.e., whether the optimizer has converged for the models.
## [1] 0.4945055
This shows that 50% of fits showed no warning message, which also means that 50% of model fits did exhibit a warning message. This is very bad news. It probably means that we cannot use this power analysis. Indeed, if we would run a study, there would be a high chance that there is a problem with convergence.
## [1] ""
## [2] "Model may not have converged with 1 eigenvalue close to zero: 6.7e-10"
## [3] ""
## [4] ""
## [5] "Model failed to converge with 1 negative eigenvalue: -1.5e-06"
## [6] ""
## [7] ""
## [8] "Model may not have converged with 1 eigenvalue close to zero: -1.3e-09"
## [9] "Model failed to converge with 1 negative eigenvalue: -4.2e-07"
## [10] ""
## [11] ""
## [12] ""
## [13] "Model failed to converge with 1 negative eigenvalue: -6.0e-08"
## [14] ""
## [15] "Model may not have converged with 1 eigenvalue close to zero: -6.3e-09"
## [16] ""
## [17] "Model failed to converge with 1 negative eigenvalue: -1.8e-07"
## [18] ""
## [19] "Model failed to converge with 1 negative eigenvalue: -1.8e-07"
## [20] ""
Notice that we haven’t yet implemented the detection of warning messages for the other example analyses (see below). But this should be done when conducting a power analysis. There is a paper that argues that warning messages can be largely ignored (https://debruine.github.io/lmem_sim/articles/paper.html): “as long as there are not too many of these non-convergence warnings relative to the number of runs, you can probably ignore them because the won’t affect the overall estimates”. However, with 50% warnings, we definitely have a problem. One possible option could be to see whether the average effect estimate (e.g. for the fixed effects) is the same for fits with versus without convergence warning. One reason why we have many warnings here is because we used a small number of data points to speed up the fitting algorithm.
Advice:
(This advice is off the top of the head; not based on evidence.)
- If there are more than 1% singular fits, warnings about eigenvalues, model crashes, etc. then don’t use this design and respecify the model with more subjects and / or items or simplify the random-effect structure (e.g., remove VCs which you expect to be small).
If a simulation passes (1),
Ignore the <=1% problem cases
Determine power for critical effects, VCs, and CPs — assuming that you want to determine the number of Subj and number of Item for 80% power for the effect sizes you expect.
Because this is an artificial example, we now proceed to plot the percentage of significant results as a function of the number of subjects.
p1 <- ggplot(data=COF)+
geom_smooth(aes(x=nsj, y=sign))+
geom_point( stat="summary", aes(x=nsjFL, y=sign))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign))+
geom_line( stat="summary", aes(x=nsjFL, y=sign))
p2 <- ggplot(data=COFaov)+
geom_smooth(aes(x=nsj, y=sign))+
geom_point( stat="summary", aes(x=nsjFL, y=sign))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign))+
geom_line( stat="summary", aes(x=nsjFL, y=sign))
grid.arrange(p1,p2, nrow=1)
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)
We can also run a local regression analysis (i.e., the smoothed regression line) manually and determine the number of subjects that we need to obtain a power of 60%.
# determine number of subjects needed for a power of 60%
m0 <- loess(sign ~ nsj, data=COF)
COF$pred <- predict(m0)
idx <- COF$pred>0.6
min(COF$nsj[idx])
## [1] 71
ANOVA + LMM: Random effects for subjects only, 2x3 within-subject design
We now create a 2 x 3 within-subject design with random effects for subjects.
design <-
fixed.factor("A", levels=c("A1", "A2")) +
fixed.factor("B", levels=c("B1", "B2", "B3")) +
random.factor("Subj", instances=60) #+
#random.factor("Items", instances=5)
dat <- design.codes(design)
nrow(dat)
## [1] 360
## [1] 60
## # A tibble: 12 x 3
## Subj A B
## <fct> <fct> <fct>
## 1 Subj01 A1 B1
## 2 Subj01 A2 B1
## 3 Subj01 A1 B2
## 4 Subj01 A2 B2
## 5 Subj01 A1 B3
## 6 Subj01 A2 B3
## 7 Subj02 A1 B1
## 8 Subj02 A2 B1
## 9 Subj02 A1 B2
## 10 Subj02 A2 B2
## 11 Subj02 A1 B3
## 12 Subj02 A2 B3
# set contrasts
(contrasts(dat$A) <- c(-1, +1))
## [1] -1 1
(contrasts(dat$B) <- contr.sdif(3))
## 2-1 3-2
## 1 -0.6666667 -0.3333333
## 2 0.3333333 -0.3333333
## 3 0.3333333 0.6666667
# Recommendation: hypr-package for contrasts + Schad et al. (2020) JML
dat$An <- model.matrix(~A,dat)[,2]
dat[,c("Bn1","Bn2")] <- model.matrix(~B,dat)[,2:3]
Note that we use a sliding difference contrast (contr.sdif
) for the 3-level factor B. The first of these contrasts tests the difference between B2 and B1, the second contrast tests the difference between B3 and B2.
One option would now be to specify the relevant fixed and random effects that relate to the set contrasts. This would imply defining a fixed effect for the intercept, one for the effect of factor A, two for the effect of factor B (which is coded via two contrasts), and two effects for the interaction of A x B. The fixed-effects part of the formula would look like this: ~ An + Bn1 + Bn2 + An:Bn1 + An:Bn2
, and we could specify fixed effects as Fixef=c(200,0,0,0,-1,-1)
. A similar specification would be needed for the random effects part. This would be a good approach.
One issue here might be that we might find it difficult to specify our expectations in terms of these fixed effects. Maybe we find it easier to specify the expected group means. We can use a trick to specify the group means instead of the fixed effects written down above. We create one large factor that has each design cell as a separate factor level: dat$F <- factor(paste0(dat$A, ".", dat$B))
.
Now, in the specification of the model formula, we can remove the intercept term (i.e., via -1
or 0 +
). If we would do so in a call to lmer
(or equivalently to lm
), then the fixed effects would simply provide estimates of the condition means, i.e., the mean responses for each factor level. We can take a look at how this factor is coded in the design matrix by using the function model.matrix()
.
# create one factor
dat$F <- factor(paste0(dat$A, ".", dat$B))
levels(dat$F)
## [1] "A1.B1" "A1.B2" "A1.B3" "A2.B1" "A2.B2" "A2.B3"
mm <- model.matrix(~ -1 + F, data=dat)
head(mm)
## FA1.B1 FA1.B2 FA1.B3 FA2.B1 FA2.B2 FA2.B3
## 1 1 0 0 0 0 0
## 2 0 0 0 1 0 0
## 3 0 1 0 0 0 0
## 4 0 0 0 0 1 0
## 5 0 0 1 0 0 0
## 6 0 0 0 0 0 1
We can see that in each row all columns are coded as \(0\), except for one column, which is coded as \(1\) - this column indicates the factor level that this row corresponds to. For example, the first data point is from the design cell A1
and B1
. The data point in the second row is from design cell A2
and B1
. This way, when we specify the fixed-effects, we can specify the condition means, i.e., the means of the dependent variable for each factor level.
We look at the levels of factor F
to make sure we consider the correct order of levels. Then, we specify that the first design cell (A1
and B1
) should have a mean of \(190\) (e.g., ms). The second design cell (A1
and B2
) should have a mean of \(200\). And so forth. Based on this reasoning, we can define the 6 means for each cell in the 2 x 3 design: fix <- c(190,200,210,210,200,190)
.
Next, we also have to specify the random effects standard deviations. Let’s assume we don’t have a lot of specific information. We can use the same coding as in the fixed effects term, by again removing the intercept: (-1 + F | Subj)
. This way, we can specify the standard deviation of each cell mean across subjects. Then we could simply assume that the standard deviation in each design cell is \(30\): sd_Subj <- c( 30, 30, 30, 30, 30, 30)
.
We again set the standard deviation of the random noise to \(50\).
An important aspect in this coding is the random effects correlation. This now specifies how strongly responses in the different design cells are correlated with each other across subjects. Note that this is very different from the usual specification, where the random effects correlations assess the correlation between effects, e.g., intercepts and slopes. I guess that the random effects correlations in the present setting should be relatively high, and set it to CP=0.85
. Of course, it would make sense to investigate this in real data to see what a realistic value would be.
# simulate data
levels(dat$F)
## [1] "A1.B1" "A1.B2" "A1.B3" "A2.B1" "A2.B2" "A2.B3"
fix <- c(190,200,210,210,200,190) # set fixed effects
sd_Subj <- c( 30, 30, 30, 30, 30, 30) # set random effects standard deviations for subjects
sd_Res <- 50 # set residual standard deviation
form <- ~ -1 + F + (-1 + F | Subj)
dat$ysim <- simLMM(form, data=dat, Fixef=fix, VC_sd=list(sd_Subj, sd_Res), CP=0.85, empirical=TRUE)
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 0 + FA1.B1 + FA1.B2 + FA1.B3 + FA2.B1 + FA2.B2 + FA2.B3 + ( 0 + FA1.B1 + FA1.B2 + FA1.B3 + FA2.B1 + FA2.B2 + FA2.B3 | Subj )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev. Corr
## Subj FA1.B1 30.0
## FA1.B2 30.0 0.85
## FA1.B3 30.0 0.85 0.85
## FA2.B1 30.0 0.85 0.85 0.85
## FA2.B2 30.0 0.85 0.85 0.85 0.85
## FA2.B3 30.0 0.85 0.85 0.85 0.85 0.85
## Residual 50.0
## Number of obs: 360, groups: Subj, 60
## Fixed effects:
## FA1.B1 FA1.B2 FA1.B3 FA2.B1 FA2.B2 FA2.B3
## 190 200 210 210 200 190
# check group means
dat %>% group_by(A) %>% summarize(M=mean(ysim)) # the data show no main effect of A
## # A tibble: 2 x 2
## A M
## * <fct> <dbl>
## 1 A1 200
## 2 A2 200
dat %>% group_by(B) %>% summarize(M=mean(ysim)) # the data show no main effect of B
## # A tibble: 3 x 2
## B M
## * <fct> <dbl>
## 1 B1 200
## 2 B2 200
## 3 B3 200
(tmp <- dat %>% group_by(A, B) %>% summarize(M=mean(ysim))) # there is an interaction
## `summarise()` has grouped output by 'A'. You can override using the `.groups` argument.
## # A tibble: 6 x 3
## # Groups: A [2]
## A B M
## <fct> <fct> <dbl>
## 1 A1 B1 190
## 2 A1 B2 200
## 3 A1 B3 210
## 4 A2 B1 210
## 5 A2 B2 200
## 6 A2 B3 190
ggplot(data=tmp, aes(x=B, y=M, group=A, colour=A)) + geom_point() + geom_line()
![](data:image/png;base64,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)
# check fixed effects + random effects
#summary(lmer(ysim ~ -1 + F + (-1 + F | Subj), data=dat))
summary(lmer(ysim ~ An*(Bn1+Bn2) + (An*(Bn1+Bn2) || Subj), data=dat, control=lmerControl(calc.derivs=FALSE)))
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ysim ~ An * (Bn1 + Bn2) + (An * (Bn1 + Bn2) || Subj)
## Data: dat
## Control: lmerControl(calc.derivs = FALSE)
##
## REML criterion at convergence: 3878.9
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.9981 -0.5290 -0.0416 0.5510 2.4357
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subj (Intercept) 1030.5065 32.1015
## Subj.1 An 110.2573 10.5003
## Subj.2 Bn1 802.6614 28.3313
## Subj.3 Bn2 414.2810 20.3539
## Subj.4 An:Bn1 450.3471 21.2214
## Subj.5 An:Bn2 0.3149 0.5611
## Residual 2006.3239 44.7920
## Number of obs: 360, groups: Subj, 60
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.000e+02 4.770e+00 5.900e+01 41.933 <2e-16 ***
## An 4.518e-16 2.722e+00 5.900e+01 0.000 1.0000
## Bn1 -1.416e-14 6.842e+00 7.703e+01 0.000 1.0000
## Bn2 6.642e-15 6.352e+00 7.703e+01 0.000 1.0000
## An:Bn1 -1.000e+01 6.399e+00 8.530e+01 -1.563 0.1218
## An:Bn2 -1.000e+01 5.783e+00 6.547e+01 -1.729 0.0885 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) An Bn1 Bn2 An:Bn1
## An 0.000
## Bn1 0.000 0.000
## Bn2 0.000 0.000 -0.385
## An:Bn1 0.000 0.000 0.000 0.000
## An:Bn2 0.000 0.000 0.000 0.000 -0.452
aov_car(ysim ~ 1 + Error(Subj/(A*B)), data=dat)
## Anova Table (Type 3 tests)
##
## Response: ysim
## Effect df MSE F ges p.value
## 1 A 1, 59 2667.85 0.00 <.001 >.999
## 2 B 1.99, 117.12 2931.07 0.00 <.001 >.999
## 3 A:B 1.92, 113.04 2300.65 5.44 ** .019 .006
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '+' 0.1 ' ' 1
##
## Sphericity correction method: GG
Now, that we saw that our model specification works, we can perform a power analysis. Let’s assume we are mainly interested in the interaction A:B. Because this involves two fixed effects, we perform a model comparison to evaluate their common effect. If you are interested in the specific effect of each of these terms, or in the main effects, similar analyses are possible.
nsubj <- seq(10,100,1) # again, we run from 10 to 100 subjects
nsim <- length(nsubj)
COF <- COFaov <- data.frame()
for (i in 1:nsim) { # i <- 1
#print(paste0(i,"/",nsim))
# create experimental design
design <-
fixed.factor("A", levels=c("A1", "A2")) +
fixed.factor("B", levels=c("B1", "B2", "B3")) +
random.factor("Subj", instances=nsubj[i]) # set number of subjects
dat <- design.codes(design)
nsj <- length(unique(dat$Subj))
# set contrasts & compute numeric predictor variables
contrasts(dat$A) <- c(-1, +1)
contrasts(dat$B) <- contr.sdif(3)
dat$An <- model.matrix(~A,dat)[,2]
dat[,c("Bn1","Bn2")] <- model.matrix(~B,dat)[,2:3]
# compute factor F
dat$F <- factor(paste0(dat$A, ".", dat$B))
for (j in 1:4) { # j <- 1 # run 4 models for each number of subjects
# simulate data
dat$ysim <- simLMM(form, data=dat, Fixef=fix, VC_sd=list(sd_Subj, sd_Res), CP=0.85, empirical=FALSE, verbose=FALSE)
# ANOVA
AOV <- aov_car(ysim ~ 1 + Error(Subj/(A*B)), data=dat)
AOVcof <- summary(AOV)$univariate.tests[4,]
COFaov <- rbind(COFaov,c(nsj,AOVcof))
# LMM: perform model comparison
LMM1 <- lmer(ysim ~ An*(Bn1+Bn2) + (An*(Bn1+Bn2) || Subj), data=dat, REML=FALSE, control=lmerControl(calc.derivs=FALSE))
LMM0 <- lmer(ysim ~ An+(Bn1+Bn2) + (An*(Bn1+Bn2) || Subj), data=dat, REML=FALSE, control=lmerControl(calc.derivs=FALSE))
LMMcof <- c(coef(summary(LMM1))[5:6,5],
as.numeric(data.frame(anova(LMM1,LMM0))[2,6:8]))
COF <- rbind(COF,c(nsj,LMMcof,isSingular(LMM1) & isSingular(LMM0)))
}
}
# results from LMMs
names(COF) <- c("nsj","p_An:Bn1","p_An:Bn2","Chisq","Df","p","singular")
COF$sign <- as.numeric(COF$p < .05)
COF$nsjF <- gtools::quantcut(COF$nsj, q=seq(0,1,length=10))
COF$nsjFL <- plyr::ddply(COF, "nsjF", transform, nsjFL=mean(nsj))$nsjFL
# results for ANOVA
names(COFaov) <- c("nsj","SS","numDF","ErrorSS","denDF","F","p")
COFaov$sign <- as.numeric(COFaov$p < .05)
COFaov$nsjF <- gtools::quantcut(COFaov$nsj, q=seq(0,1,length=10))
COFaov$nsjFL <- plyr::ddply(COFaov,"nsjF",transform,nsjFL=mean(nsj))$nsjFL
#save(COF, COFaov, file="data/Power1.rda")
Note that we here compute power only for the interaction term A:B. We actually assumed in the simulations that the main effects are exactly zero. However, equivalent power analyses are also possible for main effects.
Again, we first check how many fits were singular:
load(file=system.file("power-analyses", "Power1.rda", package = "designr"))
mean(COF$singular)
## [1] 0.6703297
Here, we see that there is a large number of singular fits: roughly 70% of all model fits were singular suggesting that the random effects structure used in the model was not fully supported by the data. Opinions differ on whether this is a problem and how to deal with this. This paper, for example argues that singular fits can be ignored (https://debruine.github.io/lmem_sim/articles/paper.html). However, we would argue that sometimes singular fits can be problematic (in particular when one is interested in the random effects). Of course, convergence problems should also be monitored in addition.
p1 <- ggplot(data=COF)+
geom_smooth(aes(x=nsj, y=sign))+
geom_point( stat="summary", aes(x=nsjFL, y=sign))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign))+
geom_line( stat="summary", aes(x=nsjFL, y=sign))
p2 <- ggplot(data=COFaov)+
geom_smooth(aes(x=nsj, y=sign))+
geom_point( stat="summary", aes(x=nsjFL, y=sign))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign))+
geom_line( stat="summary", aes(x=nsjFL, y=sign))
gridExtra::grid.arrange(p1,p2, nrow=1)
![](data:image/png;base64,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)
Determine number of subjects needed for a power of 80%.
m0 <- loess(sign ~ nsj, data=COF)
COF$pred <- predict(m0)
idx <- COF$pred>0.8
min(COF$nsj[idx])
## [1] 67
LMM: Crossed random effects for subjects and items
Let’s examine a design with only one factor X, but with crossed random effects for subjects and items, where factor X is a within-subject and between-item factor.
The computations are quite straightforward. Note that we now assume 3 random effects terms, one for subjects, one for items, and one residual noise term.
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=15) +
random.factor("Item", groups="X", instances=2)
dat <- design.codes(design)
(contrasts(dat$X) <- c(-1, +1))
## [1] -1 1
dat$Xn <- model.matrix(~X,dat)[,2]
# simulate data
fix <- c(200, 5) # set fixed effects
sd_Subj <- c(30, 10) # set random effects standard deviations for subjects
sd_Item <- c(10) # set random effects standard deviations for items
sd_Res <- 50 # set residual standard deviation
dat$ysim <- simLMM(form=~ X + (X | Subj) + (1 | Item), data=dat,
Fixef=fix, VC_sd=list(sd_Subj, sd_Item, sd_Res), CP=0.3,
empirical=TRUE)
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 1 + X1 + ( 1 + X1 | Subj ) + ( 1 | Item )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev. Corr
## Subj (Intercept) 30.0
## X1 10.0 0.30
## Item (Intercept) 10.0
## Residual 50.0
## Number of obs: 60, groups: Subj, 15; Item, 4
## Fixed effects:
## (Intercept) X1
## 200 5
# check group means
dat %>% group_by(X) %>% summarize(M=mean(ysim))
## # A tibble: 2 x 2
## X M
## * <fct> <dbl>
## 1 X1 195
## 2 X2 205
# check fixed effects + random effects
summary(lmer(ysim ~ Xn + (Xn || Subj) + (1 | Item), data=dat, control=lmerControl(calc.derivs=FALSE)))
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ysim ~ Xn + (Xn || Subj) + (1 | Item)
## Data: dat
## Control: lmerControl(calc.derivs = FALSE)
##
## REML criterion at convergence: 644.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.4539 -0.6250 -0.1323 0.6764 1.8460
##
## Random effects:
## Groups Name Variance Std.Dev.
## Subj (Intercept) 1171.4 34.23
## Subj.1 Xn 246.3 15.69
## Item (Intercept) 0.0 0.00
## Residual 2406.2 49.05
## Number of obs: 60, groups: Subj, 15; Item, 4
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 200.000 10.872 14.000 18.396 3.33e-11 ***
## Xn 5.000 7.518 14.000 0.665 0.517
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## Xn 0.000
In the power analysis, we again continuously increase the number of subjects. An alternative or additional analysis could involve continuously increasing the number of items and testing how many items are needed to achieve a certain power.
nsubj <- seq(10,100,4)
nsimSj <- length(nsubj)
nitem <- seq(2,30,4)
nsimIt <- length(nitem)
COF <- data.frame()
for (i in 1:nsimSj) { # i <- 1
#print(paste0(i,"/",nsimSj))
for (j in 1:nsimIt) { # j <- 1
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=nsubj[i]) +
random.factor("Item", groups="X", instances=nitem[j])
dat <- design.codes(design)
nsj <- length(unique(dat$Subj))
nit <- length(unique(dat$Item))
contrasts(dat$X) <- c(-1, +1)
dat$Xn <- model.matrix(~X,dat)[,2]
for (j in 1:5) { # j <- 1
dat$ysim <- simLMM(~ X + (X | Subj) + (1 | Item), data=dat,
Fixef=fix, VC_sd=list(sd_Subj, sd_Item, sd_Res), CP=0.3,
empirical=FALSE, verbose=FALSE)
LMM <- lmer(ysim ~ Xn + (Xn || Subj) + (1 | Item), data=dat, REML=FALSE,
control=lmerControl(calc.derivs=FALSE))
LMMcof <- coef(summary(LMM))[2,]
COF <- rbind(COF,c(nsj,nit,LMMcof, isSingular(LMM)))
}
}
}
# results for LMM
names(COF)<- c("nsj","nit","Estimate","SE","df","t","p","singular")
COF$sign <- as.numeric(COF$p < .05 & COF$Estimate>0)
COF$nsjF <- gtools::quantcut(COF$nsj, q=seq(0,1,length=10))
COF$nsjFL <- plyr::ddply(COF,"nsjF",transform,nsjFL=mean(nsj))$nsjFL
COF$nitF <- gtools::quantcut(COF$nit, q=seq(0,1,length=5))
COF$nitFL <- plyr::ddply(COF,"nitF",transform,nitFL=mean(nsj))$nitFL
#save(COF, file="data/Power2.rda")
Again, we plot the power as a function of the number of subjects. We see that power increases with increasing numbers of subjects and with increasing the numbers of items.
load(file=system.file("power-analyses", "Power2.rda", package = "designr"))
ggplot(data=COF) +
geom_smooth(aes(x=nsj, y=sign, colour=factor(nitF)), se=FALSE)+
geom_point( stat="summary", aes(x=nsjFL, y=sign, colour=factor(nitF)))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign, colour=factor(nitF)))+
geom_line( stat="summary", aes(x=nsjFL, y=sign, colour=factor(nitF)))
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)
# determine number of subjects needed for a power of 60%
idx <- which(COF$nit>46)
m0 <- loess(sign ~ nsj, data=COF[idx,])
COF$pred <- NA
COF$pred[idx] <- predict(m0)
min(COF$nsj[COF$pred>0.5], na.rm=TRUE)
## [1] 38
Vary effect size
One important aspect in power analyses is that we have to assume the true effect is known. However, we are usually unsure about its true value. Therefore, it can make sense to assume different values for the effect size and to look at how this impacts on power.
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=15) +
random.factor("Item", groups="X", instances=4)
dat <- design.codes(design)
length(unique(dat$Subj))
## [1] 15
## [1] 8
(contrasts(dat$X) <- c(-1, +1))
## [1] -1 1
dat$Xn <- model.matrix(~X,dat)[,2]
fix <- c(200,10)
sd_Subj <- c(30, 10)
sd_Item <- c(10)
sd_Res <- 50
dat$ysim <- simLMM(~ X + (X | Subj) + (1 | Item), data=dat, Fixef=fix, VC_sd=list(sd_Subj, sd_Item, sd_Res), CP=0.3, empirical=TRUE)
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 1 + X1 + ( 1 + X1 | Subj ) + ( 1 | Item )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev. Corr
## Subj (Intercept) 30.0
## X1 10.0 0.30
## Item (Intercept) 10.0
## Residual 50.0
## Number of obs: 120, groups: Subj, 15; Item, 8
## Fixed effects:
## (Intercept) X1
## 200 10
dat %>% group_by(X) %>% summarize(M=mean(ysim))
## # A tibble: 2 x 2
## X M
## * <fct> <dbl>
## 1 X1 190
## 2 X2 210
lmer(ysim ~ Xn + (Xn || Subj) + (1 | Item), data=dat, control=lmerControl(calc.derivs=FALSE))
## Linear mixed model fit by REML ['lmerModLmerTest']
## Formula: ysim ~ Xn + (Xn || Subj) + (1 | Item)
## Data: dat
## REML criterion at convergence: 1288.898
## Random effects:
## Groups Name Std.Dev.
## Subj (Intercept) 26.37
## Subj.1 Xn 16.81
## Item (Intercept) 14.08
## Residual 47.78
## Number of obs: 120, groups: Subj, 15; Item, 8
## Fixed Effects:
## (Intercept) Xn
## 200 10
The data simulations look good. We next go to the power simulations.
nsubj <- seq(10,100,1)
nsim <- length(nsubj)
COF <- data.frame()
for (i in 1:nsim) {
#print(paste0(i,"/",nsim))
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=nsubj[i]) +
random.factor("Item", groups="X", instances=4)
dat <- design.codes(design)
nsj <- length(unique(dat$Subj))
contrasts(dat$X) <- c(-1, +1)
dat$Xn <- model.matrix(~X,dat)[,2]
for (j in 1:18) {
# assume three different effect sizes for the fixed effect: 5, 10, or 15
FIX <- c(5,10,15)
fix <- c(200,FIX[(j%%3)+1])
dat$ysim <- simLMM(~ X + (X | Subj) + (1 | Item), data=dat, Fixef=fix, VC_sd=list(sd_Subj, sd_Item, sd_Res), CP=0.3, empirical=FALSE, verbose=FALSE)
LMM <- lmer(ysim ~ Xn + (Xn || Subj) + (1 | Item), data=dat, control=lmerControl(calc.derivs=FALSE))
LMMcof <- coef(summary(LMM))[2,]
COF <- rbind(COF,c(nsj,fix[2],LMMcof)) # store effect size
}
}
# results for LMM
names(COF) <- c("nsj","EffectSize","Estimate","SE","df","t","p")
COF$sign <- as.numeric(COF$p < .05 & COF$Estimate>0)
COF$nsjF <- gtools::quantcut(COF$nsj, q=seq(0,1,length=10))
COF$nsjFL <- plyr::ddply(COF,"nsjF",transform,nsjFL=mean(nsj))$nsjFL
#save(COF, file="data/Power3.rda")
load(file=system.file("power-analyses", "Power3.rda", package = "designr"))
ggplot(data=COF) +
geom_smooth(aes(x=nsj, y=sign, colour=factor(EffectSize)))+
geom_point(stat="summary", aes(x=nsjFL, y=sign, colour=factor(EffectSize)))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign, colour=factor(EffectSize)))+
geom_line(stat="summary", aes(x=nsjFL, y=sign, colour=factor(EffectSize)))
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)
The results show that power strongly varies as a function of the assumed effect size. This is something important to consider: maybe we are not really sure about the power of our experiment.
Determine number of subjects needed for a power of 50% under the assumption of an effect size of middle size (i.e., fixed effect of 10).
m0 <- loess(sign ~ nsj, data=subset(COF,EffectSize==10))
COF$pred <- NA
COF$pred[COF$EffectSize==10] <- predict(m0)
idx <- COF$pred>0.5
min(COF$nsj[idx], na.rm=TRUE) # 70
## [1] 88
Based on a previous data set: latin square design
Now let’s consider the case that we want to use results from a prior experiment as the assumption about effect sizes in our power analysis. First we load the data from the prior study.
# load empirical data
data(gibsonwu2013) # the Gibson & Wu (2013) dataset is included in the designr package
gw1 <- subset(gibsonwu2013, region=="headnoun") # subset critical region
gw1$so <- ifelse(gw1$type %in% c("subj-ext"),-1,1) # sum-coding for predictor
dat2 <- gw1[,c("subj","item","so","type2","rt")] # extract experimental design
datE <- dplyr::arrange(dat2, subj, item)
length(unique(datE$subj)) # 37
## [1] 37
length(unique(datE$item)) # 15
## [1] 15
# we re-create the empirical design from the experiment using designr
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("subj", instances=18) +
random.factor("item", instances= 8) +
random.factor(c("subj", "item"), groups=c("X"))
dat <- dplyr::arrange(design.codes(design), subj, item)
(contrasts(dat$X) <- c(+1, -1))
## [1] 1 -1
dat$so <- model.matrix(~X,dat)[,2]
length(unique(dat$subj)) # 36
## [1] 36
length(unique(dat$item)) # 16
## [1] 16
# compare designs
head(datE,20)
## subj item so type2 rt
## 2001 1 1 1 object relative 246
## 1192 1 2 -1 subject relative 542
## 1591 1 3 1 object relative 406
## 753 1 4 -1 subject relative 286
## 341 1 5 1 object relative 582
## 221 1 6 -1 subject relative 959
## 1471 1 7 1 object relative 270
## 922 1 8 -1 subject relative 438
## 461 1 9 1 object relative 294
## 1054 1 10 -1 subject relative 278
## 1342 1 11 1 object relative 494
## 94 1 13 1 object relative 1561
## 621 1 14 -1 subject relative 438
## 1891 1 15 1 object relative 286
## 1761 1 16 -1 subject relative 374
## 20371 2 1 -1 subject relative 286
## 19801 2 2 1 object relative 278
## 19501 2 3 -1 subject relative 254
## 20521 2 4 1 object relative 734
## 18991 2 5 -1 subject relative 390
## subj item X so
## 1 subj01 item01 X1 1
## 2 subj01 item02 X2 -1
## 3 subj01 item03 X1 1
## 4 subj01 item04 X2 -1
## 5 subj01 item05 X1 1
## 6 subj01 item06 X2 -1
## 7 subj01 item07 X1 1
## 8 subj01 item08 X2 -1
## 9 subj01 item09 X1 1
## 10 subj01 item10 X2 -1
## 11 subj01 item11 X1 1
## 12 subj01 item12 X2 -1
## 13 subj01 item13 X1 1
## 14 subj01 item14 X2 -1
## 15 subj01 item15 X1 1
## 16 subj01 item16 X2 -1
## 17 subj02 item01 X2 -1
## 18 subj02 item02 X1 1
## 19 subj02 item03 X2 -1
## 20 subj02 item04 X1 1
## subj item so type2 rt
## 59661 39 11 1 object relative 2053
## 59151 39 13 1 object relative 445
## 60061 39 14 -1 subject relative 222
## 59951 39 15 1 object relative 430
## 58901 39 16 -1 subject relative 302
## 63041 40 1 -1 subject relative 422
## 64031 40 2 1 object relative 318
## 63191 40 3 -1 subject relative 421
## 62871 40 4 1 object relative 462
## 64301 40 5 -1 subject relative 1262
## 64551 40 6 1 object relative 438
## 64181 40 7 -1 subject relative 356
## 63761 40 8 1 object relative 1509
## 63471 40 9 -1 subject relative 390
## 63891 40 10 1 object relative 358
## 64801 40 11 -1 subject relative 390
## 64421 40 13 -1 subject relative 318
## 64671 40 14 1 object relative 278
## 63361 40 15 -1 subject relative 461
## 63631 40 16 1 object relative 294
## subj item X so
## 557 subj35 item13 X1 1
## 558 subj35 item14 X2 -1
## 559 subj35 item15 X1 1
## 560 subj35 item16 X2 -1
## 561 subj36 item01 X2 -1
## 562 subj36 item02 X1 1
## 563 subj36 item03 X2 -1
## 564 subj36 item04 X1 1
## 565 subj36 item05 X2 -1
## 566 subj36 item06 X1 1
## 567 subj36 item07 X2 -1
## 568 subj36 item08 X1 1
## 569 subj36 item09 X2 -1
## 570 subj36 item10 X1 1
## 571 subj36 item11 X2 -1
## 572 subj36 item12 X1 1
## 573 subj36 item13 X2 -1
## 574 subj36 item14 X1 1
## 575 subj36 item15 X2 -1
## 576 subj36 item16 X1 1
# transform dependent variable
hist(datE$rt)
![](data:image/png;base64,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)
boxcox(rt ~ so, data=datE)
![](data:image/png;base64,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)
datE$speed <- 1/datE$rt
hist(datE$speed)
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAASAAAAEgCAYAAAAUg66AAAAEGWlDQ1BrQ0dDb2xvclNwYWNlR2VuZXJpY1JHQgAAOI2NVV1oHFUUPrtzZyMkzlNsNIV0qD8NJQ2TVjShtLp/3d02bpZJNtoi6GT27s6Yyc44M7v9oU9FUHwx6psUxL+3gCAo9Q/bPrQvlQol2tQgKD60+INQ6Ium65k7M5lpurHeZe58853vnnvuuWfvBei5qliWkRQBFpquLRcy4nOHj4g9K5CEh6AXBqFXUR0rXalMAjZPC3e1W99Dwntf2dXd/p+tt0YdFSBxH2Kz5qgLiI8B8KdVy3YBevqRHz/qWh72Yui3MUDEL3q44WPXw3M+fo1pZuQs4tOIBVVTaoiXEI/MxfhGDPsxsNZfoE1q66ro5aJim3XdoLFw72H+n23BaIXzbcOnz5mfPoTvYVz7KzUl5+FRxEuqkp9G/Ajia219thzg25abkRE/BpDc3pqvphHvRFys2weqvp+krbWKIX7nhDbzLOItiM8358pTwdirqpPFnMF2xLc1WvLyOwTAibpbmvHHcvttU57y5+XqNZrLe3lE/Pq8eUj2fXKfOe3pfOjzhJYtB/yll5SDFcSDiH+hRkH25+L+sdxKEAMZahrlSX8ukqMOWy/jXW2m6M9LDBc31B9LFuv6gVKg/0Szi3KAr1kGq1GMjU/aLbnq6/lRxc4XfJ98hTargX++DbMJBSiYMIe9Ck1YAxFkKEAG3xbYaKmDDgYyFK0UGYpfoWYXG+fAPPI6tJnNwb7ClP7IyF+D+bjOtCpkhz6CFrIa/I6sFtNl8auFXGMTP34sNwI/JhkgEtmDz14ySfaRcTIBInmKPE32kxyyE2Tv+thKbEVePDfW/byMM1Kmm0XdObS7oGD/MypMXFPXrCwOtoYjyyn7BV29/MZfsVzpLDdRtuIZnbpXzvlf+ev8MvYr/Gqk4H/kV/G3csdazLuyTMPsbFhzd1UabQbjFvDRmcWJxR3zcfHkVw9GfpbJmeev9F08WW8uDkaslwX6avlWGU6NRKz0g/SHtCy9J30o/ca9zX3Kfc19zn3BXQKRO8ud477hLnAfc1/G9mrzGlrfexZ5GLdn6ZZrrEohI2wVHhZywjbhUWEy8icMCGNCUdiBlq3r+xafL549HQ5jH+an+1y+LlYBifuxAvRN/lVVVOlwlCkdVm9NOL5BE4wkQ2SMlDZU97hX86EilU/lUmkQUztTE6mx1EEPh7OmdqBtAvv8HdWpbrJS6tJj3n0CWdM6busNzRV3S9KTYhqvNiqWmuroiKgYhshMjmhTh9ptWhsF7970j/SbMrsPE1suR5z7DMC+P/Hs+y7ijrQAlhyAgccjbhjPygfeBTjzhNqy28EdkUh8C+DU9+z2v/oyeH791OncxHOs5y2AtTc7nb/f73TWPkD/qwBnjX8BoJ98VQNcC+8AAAA4ZVhJZk1NACoAAAAIAAGHaQAEAAAAAQAAABoAAAAAAAKgAgAEAAAAAQAAASCgAwAEAAAAAQAAASAAAAAAq0AljQAANiVJREFUeAHtfQncTcX//9hD9p2KLJUk2VqkrFlCUlmKSL9kKRUtlBSKbyFLShIpJSkhW2Rfv5YQQpItkaXIkqXU/Oc9/+Z8z73Pvc8553nufe4993l/Xq97zzlzPrO9Z877zHxmzkwGqURQiAARIAIxQCBjDOJklESACBABjQAJiBWBCBCBmCFAAooZ9IyYCBABEhDrABEgAjFDgAQUM+gZMREgAiQg1gEiQARihgAJKGbQM2IiQARIQKwDRIAIxAwBElDMoGfERIAIkIBYB4gAEYgZAiSgmEHPiIkAESABsQ4QASIQMwRIQDGDnhETASJAAmIdIAJEIGYIkIBiBj0jJgJEgATEOkAEiEDMECABxQx6RkwEiAAJiHWACBCBmCFAAooZ9IyYCBABEhDrABEgAjFDgAQUM+gZMREgAiQg1gEiQARihgAJKGbQM2IiQARIQKwDRIAIxAwBElDMoGfERIAIkIBYB4gAEYgZAiSgmEHPiIkAESABsQ4QASIQMwRIQDGDnhETASJAAmIdIAJEIGYIkIBiBj0jJgJEgATEOkAEoozALbfcIj744IMox+LP4DP7M9n/S/Xw4cPFrFmztMO4ceNE6dKl/3dTnc2bN08MHjxYuz3zzDPizjvv1Odwwz3IwoULRcaMKePivXv3ivz584s8efLosPjnHYFvvvlGvPzyywLHSy+9VOCB/fjjjz0FdOTIEXH//fdrP+3btxcPPfSQJ/9G+Z9//hHfffeduP7667XTb7/9Jlq2bGluJ3ucNm2ayJs3r9aRUooxY8aISZMmibVr14qff/5ZHD58WHTq1EkUKFAg2XD8eDPF+CugfC1dunSRqsD0b/PmzUny8v7771v333vvPeu+qqCW+8WLFy13tydnzpyRffr0kZdcconctWuXW2/UC0Lg1KlTMl++fFZZoCzr1asXpOV8uW/fPiuMvn37OnsIobFq1SpZtWpV2bZtW+vuwYMHrXBNPQt3VA+h5U8RTUh/6kUlFalZeolyklL8fd8CUpUhRVK5cmVx/Phx7TdDhgyewxg6dKgYOHCgZ3/0EIjADz/8IE6cOKEdO3bsKAYNGiTUQxmolEZXt956q47pmmuuCRljmTJlRKNGjULeg2P27Nn1vW+//Vaol50+f+KJJ3RrrkqVKmLRokXi5MmTYtiwYeLVV1/V99P7X7olIFQM/MIJKgqazOrtLAoWLJjiLtrff/8tfvrpJ3HFFVeITJkyhYtOux87dkxkyZLFasYnq/zvTaQT3cdcuXIFqJ8+fVr88ssvOryiRYtaD0eAUtAFugmFCxcWWbNmte6ADA4cOCBKlCjhmH7Lk+3EKf+qhWFpN27cWCCtbgV4AVN0gZ0kJXgEh4mX1ltvvRXsnOQaXS5Izpw5BV5UkydP1l3/u+66Sxw6dEhUqFAhiR/VChfAAngBgxw5ciTRCeVw9OhRXbbB5W/XRRnu379fl61TuF50veBvT0/AuYrQ15LSLljnzp2lqiD6Z++CqcoilR0poPlcpEgROXLkSAune+65RyqisHTUm0+qSmPdx8lXX30l1dtSqoqh9bJlyybr168vd+7cGaCHi2XLlsmrrrpK6ykykTfddJPcs2ePVLYCnT7V0rL8NG3aVLu1aNFCKjuWVA+gTovR2bFjh1RvcittqrClIhTZoUMHee7cOSscxIH8d+vWTX766adSEYz2gy7lo48+KtWDIN9++22pyFe7586dWz711FOWf6cTN/mvW7euBC5II344R5qUbS7Z4BcvXizLli2r/ajWq7zxxhvl119/bYVj74K5wUPZnnS8Jh2ZM2fW16NGjZL2Lth9992XbLrMTWVwttKydetWWahQIalaPeZ2wFG95OSDDz4oEaeJH3lCXVEvrgBdZYvS6WrQoIFcuXKlvO6667Qf1Jnbb79dohtkl/Pnz+syM3UQepUqVZKrV6+2q+lzL7pe8E8SUZADmru+FjsBDRkyRH722WcBv65du1oF62QDUsZoicJHRUClwYOsjIr6Gu4AHqIM2VaYptLgATUyd+5c/dCbe/YjyGr58uVGVaq3pSYRo4NwcA5CA7ngvF+/fpY+KibckD6TVlzPnj1bkwYeRlzjV7x4cYlKZ66VcdYKRxlZtTviwX3VigggA1O5Tf5NGHgoncRt/pWx2UqbCR/HOXPmhI0CD489TwYvO5EZAgKJusFj3bp1IdMB0rATULVq1STIJdQP5Whk9+7dFqHA5oO0DRgwwNwOOII4kGcQUMWKFfXPlGudOnWkMopb+s2aNdO6KDPVktHn9hehar1K1Z219GFLM7iChAxuiAuEbRe3ul7wt4cf7jyhCMiAHe7oREB488MvHlxT8Hgz1K5dW6rugVTNb40jKmX37t2twl2wYIFEpYPgrYVWBMK5/PLL5YQJEySMk6+//rpUIzzavVy5cvLs2bNa31RA6L/77rvyzz//1G+oq6++2gpfjRBpXfwZAoJ+jRo1dEVCS+ivv/7SLany5cvrFpEhS9VFk6r7Z6XHBGQICOGA4PCwqmZ6AAk9++yzEq1DtBDMG/ree+81QYQ8esk/cEGZIA0m//Bvb6kFR3LbbbdZ+qNHj5YXLlzQeF177bWWuyEgtCzd4IEyxkCCSYfqKulrPMx2AjL3Qx1RH+zyyiuvWOEZfRAYWptGVHfM0kHZG/nkk0+k6u5JDJSgJWzEEBDCQ9mjXBDGI488YoXTq1cvrT5lyhTLDS1XDJqgjppyh7HdiBddL/ib8JM7JhQBgeGDf+ZtgkJzIiA8cKayoID69++vm7r2LpoBEw+t0bWPgtlH3dQUAaOuj2iBGD/oZuDhMW8lEI5d/vOf/1i64Qho/fr1di/WOUgMgvDRVFcGUB0W3oJGTEWEG8jHCB5YpBG44cE0AtKEu73imnv2o5f8w9+MGTOsfH7xxRf2oJKc2/FCl9UueLANtoaAzH03eEDX+A83CgYSRosr1A91J1g+//xzCdIx4ZrjSy+9pFUxAmhauSgH1I8PP/xQKttdcFD62k5AauqJpYOXj+lC33DDDdq9devWOl6Er+xEli5MCSYd27dv96SbUvytyEOcpGzyi8pBPMqmTZu0EU89UNZx/PjxrpOqWkBCdW20/oYNG/TclJo1a2rjnXrDCRjdnGTp0qWWSvPmza1znNivlW1AqD67wLwTiGrZ6KP5U/18cxryqB4GoSpbknvqja1HWWrVqiXUgyKQ/o0bN2o9Vf5J9FVrL8DAbkZyYIxWXQdLHwZViKqElluoEy/5D+U/OTcYUg1eDRs2DFANZdiFglc8AgINurj77rv1KBYM/8E/M9fM7kXZjIR6Seg6dfPNN+s5TrivXi4C82YU6QjUKwiM5BMnThTKVidQJspGJ2bOnKnvBf9hkEDZzyxn1AXVZdbXqpWjj+qlqI/qBSdUV07fh86IESMsfxhcgLjVTQn+VmRhTtLtKFgoPJRhU0+Gw0iHentpgoAehuvhtmLFCn0fBR5OzAOM++rtE6CmWhVhr4PDxAS45AQT9oL9YAIdiAyVG5UU53fccYdQNhmhuokBRGPCVt1Fc6qPJo1uRpYCPP574SX/ofwn52bSBp3g0Zzff/89ideU4JEkkBQ64CWoutnW6GSrVq30iBheCKrFIvACUoMb+mWB4f+xY8cKZRvUBI8XhbJL6RcW6iGILFjsONvvgXAgqhurj6iDqCtGcI6XCwRphLjV9Yq/DtzhL6FaQA55dXUbb3pl2BaY4az633o2q+oeab9qoqNQoypJwrG3LDCL18iXX35pTvXR/kZTBseAoXnVVQrQVUblgOvgC/tQubmnmteafNByUc1roYy5QvX/rYfVVE6jn9zRXtmS0wu+5yX/wX6drkuVKmWRLsjFLvPnz7df6vOU4mEvzySBunDAjGyUAYbtTYsN3vCCM2JalCAB1AXVFRUgUcwVUgMnRk2orqV1bk5Ul1Js2bLFXOo4vv/+e32NuUqQK6+8Uh8xvI+6tGbNGv1TxmexZMkSfY5pD150veKvA3f4IwHZAMJkMcz5wRFzaFCIarheNGnSxNLCvCAI5usYMdPscY03nHnQ0dzFGwzNazWkLTBVH4KKqIzPupIqo652Q5cP56gcypAonLqOwa0rBIJJfRDcM+lEkxxhQv744w99jOafl/x7TQdafKbrgc9o1IinDgL5C/Xphlc8TJliro6yf1kTVU060Z0DUYT7oR5AlN1Hty6APcoShAbslW1K30fXGN0hZfPSc3gw8VHZGwVao8ifMmBbc7HMpx3ao+0Pc9gwgROk9dxzz+l5Prhtuu6muw8CUqPDumUFMoQ7WkEgR2WD0iG61fWKvy254U8VOL4W+zB8aj/F+Oijj6yhbcydgcVfkZBltFM2AAsru9FTtRa0MdkYOxGOIgHLn/0cQ7IYnTGCeUHFihWzdFVJ6fPq1atbbv1CDMPDT7DAuGn8Y0gWQ6sYpkX6jLsZpjVGaMwLsQuMzNDFqJJdYNyEO4bnncRL/r0YoRGvsvNZI3JID4a5ccTQNMoM58YI7QUPhK2IQPtHGMDsxRdfdD0KBj8YvYIospHGaA93/NRLyQrbjKZitA9D70anZMmSus6p7pV2Q37sw/vGCI36hHJVhGANxyMMlLkiJJ0GGIwxkmbCxrQNzGcz1xidNeJF1wv+Jvzkjgk1CpZaAgJQmEdkRoJMYWFYvUePHhKjFkZQyexD6BjFsI9eTJ8+XQ+VmocClUa1DuS2bdtMENYRw6OY5IaHCKM7vXv31hMWTfzq8wRL1wzDhyIgjFo98MADViVDnBjRUV1By019HKnDiiYBIQK3+fdKQAhb2eKk6g5YecJIk+oyW3O2DAF5wQPhouzNww8C6tmzZ4oICGGp1pBULecA4gEpGfyhA1EDG1J9ghIw/QHlDsLHvDS7GALC3CzMJTMjX9DHxFLUI7ugjiqjtjUZFiQIrDBtI1i86LrFPziOUNe+J6BQmYqEG+aogO1RsTHMGU4wdwbD8Kp5G1IFbznMhjXzfoKVVPdBqv68xHwdu2COhyEgzHfxIvjYEWQcLk4vYaVW1yn/qQkfZYOZxE7iBQ9gFqo8nOIId18NYOiPbcNNRDT+gBPqEcrNtFLNPXO0E5Bxgx/7MLtxtx9RN6EHsnMSL7pu8U8uThJQcuikwT37xC7M5MabCJWlXbt2FgGBjCj+RQBdu3feeSfVGQhFQKkONMYBZED86k1LiREC+FBRdZvCxq6++bKM12GVeCNdIICPWbH2FQzTMEAngoSf0JIIufNBHjBki1EJLKym7EN6siOuMeTZpk0boWxPPsgFk5gWCCj7oFDftllzi9IizmjHwRZQtBH2GD7mhSjjsUdfVCcC/kSABOTPcmOqiUBCIMCJiAlRjMwEEfAnAiQgf5YbU00EEgIBElBCFCMzQQT8iQAJyJ/lxlQTgYRAgASUEMXITBABfyJAAvJnuTHVRCAhECABJUQxMhNEwJ8IkID8WW5MNRFICARIQAlRjMwEEfAnAiQgf5YbU00EEgIBElBCFCMzQQT8iQAJyJ/lxlQTgYRAgASUEMXITBABfyJAAvJnuTHVRCAhECABJUQxMhNEwJ8IkID8WW5MNRFICARIQAlRjMwEEfAnAiQgf5YbU00EEgIBElBCFCMzQQT8iQAJyJ/lxlQTgYRAgASUEMXITBABfyJAAvJnuTHVRCAhECABJUQxMhNEwJ8IkID8WW5MNRFICARIQAlRjMwEEfAnAiQgf5YbU00EEgIBElBCFCMzQQT8iQAJyJ/lxlQTgYRAgASUEMXITBABfyKQ2Z/JZqrjGYHTp0+LTp06iYsXL7pO5tmzZ0Xv3r3F7bff7toPFf2PAAnI/2UYdzn46quvxN69e0WzZs1cp+3kyZNiwIABYuHCha79UNH/CJCA/F+GcZmDPHnyiAYNGrhO28qVK8XWrVtd61MxMRCgDSgxypG5IAK+RIAtIF8WW2Im+vjx42L69OmeMlerVi2RP39+T36oHD8IkIDipyzSdUr27Nkj1q9fL0aNGuUah++++06UK1dOrFq1yrUfKsYXAiSg+CqPdJuac+fOiapVq4rXXnvNNQYgrM8++8y1PhXjDwHagOKvTJgiIpBuECABpZuiZkaJQPwh4HsCklKKY8eOCRgwKUSACPgLAV8S0MGDB0WvXr1EqVKlRNasWUXhwoVFgQIFBOaeVKpUSTz99NPizJkz/ioJppYIpEMEfGeE3r9/v6hZs6bIkCGDaNmypShdurQehsU1WkGYgTt16lTxxRdfiEWLFokyZcqkw2JllomAPxDwHQENGTJEt3wwZT9btmwhUR40aJBo3LixmDhxoujfv39IHToSASIQewR81wX79ttvRfv27cOSDyDNkiWLeOihh8S8efNijzBTQASIQFgEfEdANWrUcDXxbPHixaJEiRJhM84bRIAIxB4Bxy7YihUrxLRp03SLAgbeWMsDDzwgQEJHjhwRbdu21TYeGKAzZsyobUD79u0TkyZNEnPnzuWX1bEuLMZPBBwQcCSgvHnzivnz54sRI0boESZ0bfDgFypUyCHo6Ny+4YYbxJYtW0Tnzp1Fhw4dxD///JMkovr164uvv/5a4Dshr/Ljjz+6amFt3rxZp+Hqq6/2GgX1iQAR+BcBRwKqWLGi2L59u/jmm2+0UXfgwIHiueeeE3feeacmgKZNm2qbS1oiWrZsWT3C9eeff4qffvpJoNXz119/ieLFi4vLLrtMD8mnND2HDx8WS5YscfQ+Z84c3RIjATlCRQUiEBYBRwIyPqtVqybwe+ONN3SLCF8tozWEeThoEXXp0kVcc801Rj1NjogbZIQfBK0hDMNjPlDmzK6zFpBWDPHj5yS33HKLJjsnPd4nAkQgPAKejdBocWzatEls3LhRnDp1Ss/DWbt2rbj22mtF3759w8cUwTv4ChqE9/DDD4tly5bpkEGMRYsW1WSUL18+MXbs2AjGyKCIABGIBgKumgm//vqrmDJlivj444/FmjVrRJEiRcSDDz6orytUqKDT9fnnn4tWrVqJFi1aiCpVqkQjrTpMkE/16tV1y6tgwYLi008/FSNHjhT9+vUTbdq0EfXq1RNIS9euXcWVV14p7rjjjqilhQETASKQOgQcCWj58uUCRl0I7D0zZ87Uk/yCuziwCUEwOhVNwXINlStXFgsWLBA5cuTQ9qhHH31UvPzyy5qEEDeIqEmTJmL06NEkoGgWBsMmAqlEwLELhod88ODBAt9fYTgeC40Hkw/SgFnJMOBiBnI05YcffhAYis+ZM6f+HAMtMQg+y7DLfffdJ7DIFYUIEIH4RcCRgGB4fvLJJ3WLw/5Ad+vWTXz//fdWzkBK6JpFWzDShUmGRsz50qVLjZM+oquGETEKESAC8YuAYxcMSW/YsKHAA44fPv7EEhiYB3PdddeJoUOHiqeeeirNcgjjM1pZsAPBBoQPTnv27CkwPQD7UKG7iG1hYBeaMGFCmqWLEREBIuAdAUcC2rVrlx5pQoviqquu0jHgy3Osw/vmm2+K559/XqA1hCHxtJBGjRrpZThBMNhLCqNdmA4A21OPHj00OSJ9ODfds7RIV6LGgRUGMLjgpXx3797N1meiVogI58uRgNDCQDfMkI89/nbt2unuGYbmzVwc+/1oncPeE2zzwQgdvpTH9AC0zEqWLBmt6NNVuLNmzdKTPEH8bgXd8RMnTrhVp146RsCRgDC5cN26deLAgQPi8ssvD4Bq9uzZIlOmTHHz0WexYsX06FdAInmRagRy587tacvkDRs2kIBSjXr6CMDRCH3zzTfrCX7ozsDg+/PPPwt8LzV58mTx4osv6pZI9uzZ0wdazCURIAIRRcCxBXTJJZeI1atX65YFJvnZBUPdmGtDIQJEgAikBAFHAkKg6HrhC3S0frAgGLpd6JphpjGFCBABIpBSBFwRkAkc82o4t8agwSMRIAKpRcAVAaELhvWA0ALCEhjBgqU6KESACBABrwg4EhBGvzAEiyUusAQFRkQoRIAIEIFIIOBIQJgHhOVOYQPCMhcUIkAEiECkEHAchsdnF7D7kHwiBTnDIQJEwCDg2AKqU6eOeOyxx8S2bduEWfvHeOaRCMQSgdOnTwtMegw1Sz9cuvBpSffu3fXyLeF06J52CDgSEOYBYfkLLPDeunVr3RrCMLxdsEY0hQikNQKHDh3Ss/AHDBjgOmosrjd+/HgSkGvEoqvoSED46h0rDELwvVUoSSQCwhf/biZXYl0iGOgxU9wvgu+zsH43XipuBUuuxPN8L2xC6SV9Z86c0fPY3OafetFFwJGAsBQHvjpPL1KqVKkkH7qGyjsmZPptRBDL12L3kNtuuy1UlkK6oZsTaupFSGU6EgGPCDgSkD28P/74Q2CpBawJhDdPuL3Z7X78dg4Cws9Jhg0bpqcmOOnF231Mpwj+pCa5NGLDAZQ7hQhEAwHHUTBEigmI+O7r0ksv1ZsTYp+wXr16iWeeeUacPXs2GulimESACKQDBBwJCM3vu+66S8DmMXz4cL0QPHBBM37cuHFpuhpiOigPZpEIpCsEHLtgCxcu1AvSg4DQfMfuE5B7771X20CwPTLmCmEVQgoRIAJEwAsCji0gLMmK+T8gn2DBusy//PKL3ho5+B6viQARIAJOCDgSEIY4sf7zsWPHkoSFURUsv1miRIkk9+hABIgAEXBCwLELVrduXT35EBsPYvcJ7L+OVhHWCh4zZoyepOhlwXKnBPE+ESAC6QcBRwLCyNf06dPFQ2rnCcyIhmAxesjdd9+tt7/RF/wjAkSACHhEwJGAEN71118vsOYPvrtB6wctHtiFypcv7zE6qhMBIkAE/oeAKwKCOpbkgNEZPwoRIAJEIBIIOBLQmjVrRO/evZONC99PUYgAESACXhFwJCB8boH9tuxy6tQpvS88Zkin5bbM9jTwnAgQAf8j4EhAlStX1nuABWcVkw+xrgp2RY2lIB1YYgFLhOTPnz+WSWHcRIAIeETAcR5QuPAw8xnfgmGpDixxkJZy8OBB/S0aPhqFQbxw4cKiQIECerJkpUqVxNNPP53maUrL/DMuIpAoCDi2gJLL6JEjR8Tff/+tl+vAcH1ayP79+0XNmjX1px/YHx5f5qPlA0LEand79+4VU6dOFV988YXAetZlypRJi2QxDiJABFKAgCMB7du3T8ycOTMgaJAOHvb33ntPb1CYljOhhwwZItDywTdq4ZYDGTRokGjcuLGYOHGi6N+/f0DaeUEEiED8IOBIQFh649lnn02S4pw5c4obbrghzSciYiEwfAAbjnyQUKxVhImTo0aNIgElKTk6EIH4QcCRgPAJxoULF+ImxTVq1NDfpnXq1CnZNC1evNhX36ih6wiDuhdBt9OLHxjrKUQgnhBwJKB4SizSgs9BQEKwP2F9Y9h4YIDGREl0C9FlnDRpkpg7d67upsVb+kOlB9/VYc0lL9teYwoExKuf5s2bh0oC3YhATBBwJCA3ExHtKX///fe1YdjuFslzdPuwSWLnzp11VwwfxwZL/fr1xddff6138gi+F4/XWPgfXcauXbu6Th5GIDE/CyN+buXFF1/01GJyGy71iEBKEXAkIGxImD17djF//ny9lvC1114rsB0KjMC///67wL5hRYoUseLH8hzRlrJly+oRLqzWiHlIaPVgsfXixYvrFgFaRCmVjz76SHTp0sXR+/nz5wXsY37aFcMxU1QgAmmMgCNbYHgdhl8QDpbmMIKRsMcff1xs3bo15ERFoxfNI+YAgYzwg2DxdHTDUkNA6OJhtUcnqV27th4BdNLjfSJABMIj4EhA6MpgNrSdfBAcZh6jSQ8bBFZFDP5cI3yU0bszbdo00aNHDz0zOqWxIF85cuRw9A492J0oRIAIpBwBRwLC3lfr1q3TM4uDJxsePnxYP4TB7ilPjrPPoUOH6i5XKM2dO3fqVhBaZpAqVaqIhx9+OJQq3YgAEYgDBBwJCAZd2Ds6duyoWzwYdcJWPCtXrtSfYrRq1UrkypUrzbKCNYmwFCxsU8ETIGGTgi1o2bJlOj3JzRVKswQzIiJABMIi4EhAWIwea0I3a9ZMTzy0hwTyeffdd+1OUT/HEDsWSMNs5/bt2+tRINMVggEZXTDYpShEgAjEPwKOBIQs4ANP7Ii6bds2bZDGLOiKFSvGxAgLsnn++edFgwYN9Dyg2bNn608uSpYsGf9oM4VEgAgEIOCKgOADnzeUK1dO23zM1swBIaXxRdWqVcXGjRt1NxAtojfffJNG4TQuA0ZHBFKLgCsCMguP4QtzCPYL/+STT/SWPAMGDHA1apTahIbyj9Gq0aNHiyZNmmhjM+YrUYiAEwKYroF5bV4EAxqFChXy4oW6LhBwJCCzNfPFixf11sx9+vTRwWJr5v/7v/8TWB1x7NixLqKKngoICHafJ598MuT+ZdGLmSH7DQGsJbVjxw6BF6dbwRIweLlhQwZKZBFwJCC/bM2MRckmT54cWXQYWsIhgBFdjOQOHz7cdd6wLflrr73mWp+K7hFwnEnHrZndg0lNIkAEvCHgSEDcmtkboNQmAkTAPQKOXTBuzeweTGoSASLgDQFHAsJnFtya2Ruo1CYCRMAdAo4EhM8bMAERs6G/++47bs3sDldqEQEi4AIBRwKaM2eOaNeunThw4AC3ZnYBKFWIABFwj4CjEbpgwYI6tJMnT7oPlZpEgAgQARcIOLaAsAQqFum6/fbbRYsWLfQciuCvzHv27OkiKqoQASJABAIRcCSgTZs2iRkzZmhf4Sb6kYACQeVV4iFw+vRpvc2Tl5w1atRIfz/pxU9603UkIICIb2coRCC9IgD7J9YexxpYbgXfT2JpGHzCRAmPQEgCAmj4XXLJJeF9JugdrPL4/fffO+YONjESsyNMCaGAnVew9LCXHUhAWL169UqI/EczEyEJaOTIkeKNN97Qu1+YyMHoaIaWL1/eOCXkEQvwv/766455w0eNx44dc9SjAhEgAuERCElAodTx8R6WOv3mm29C3U4YN3Q58XOSW265Re9R76TH+0SACIRHwHEYPrxX3iECRIAIpA4BElDq8KNvIkAEUoEACSgV4NErESACqUPAtQ0oddGkH98wYlerVs3ardVNzrHgVYcOHdyoUocIJBQCYQkIIzzXXXedlVkMT2PY2e5mbuIjVcr/R+Czzz7T3841bNjQNSSDBw92rUtFIpBICIQkIOy13rRp04B8YkcMijsEsH4wlv10K5kzhywGt96pRwR8i0DImt+8eXOBH4UIEIGUIYDJi+gxmG3C3YQipdQbgLqZBuImPD/ohCQgPyScaSQC8YwATBaYuBv84XZyacYONG3atBFYgyu9CAkovZQ085nmCGDfutatW7uO98iRI8Lsvefak88VOQzv8wJk8omAnxEgAfm59Jh2IuBzBEhAPi9AJp8I+BkBEpCfS49pJwI+R4AE5PMCZPKJgJ8RIAH5ufSYdiLgcwRIQD4vQCafCPgZAd8TEGaP4ru148eP+7kcmHYikC4R8OVERCyH+uabb4opU6YInJuFv3Pnzq1XKaxfv77o37+/wLbSFCLgFwT++usvcf78eYH661ZQ97Fl1oABA9x6iSs93xHQ/v37Rc2aNUWGDBlEy5YtRenSpUX+/Pn1NVpBe/fuFVOnTtUzShctWuTpo9C4KhkmJt0hgE8wzp07p78Hc5t5EFDfvn1JQG4BS63ekCFDdCtn4cKFYb+zGTRokGjcuLGYOHGibgl5iRNrXqNl5SQgQnzvEyxZsmQRY8aM0d8BBd8Ld33ixAnxwQcfCLwB3Qq6nStWrBCIz60cOnRIbNu2TeTKlcutF7Fv3z6xefNmUaRIEdd+du3aJTZs2KBbqW49/fjjj5794GWD/KA17FawucLu3bs9+UE5w5+XeH777Tfx66+/evKDnVbQAlq/fr3b7OjWP0jLr5JB2VCknxKP1g8W7+rUqVOyyf7444/1RnJr165NVi/4JtY2mjdvXrBzkuuNGzeK5557TmDnWLvgK+hhw4bZnVydo0XntSiwjIfpfrqKRCmBsLwQHcLNmjWrwIeSXgRbOuFh8iJYxsTrw4Tvrc6ePeslGt01P3PmTFz6wcsBH7F6EXTZguuhF/+x1PUdAeGhP3r0qG4xJAfcww8/rL8qnjZtWnJqvEcEiEAMEfCdDQj71NeoUUPgy+G2bdtqG0+BAgVExowZ9UgYugyTJk0Sc+fOFeimUYgAEYhfBHzXAgKUsBd07txZLF26VKDLEyxokr7wwguiTp06wbeifj1+/HiBNZ6vuOKKqMYFm8SFCxeibmQH0cM4evXVV0c1PxhAgI0q1JK/kYz41KlT2gZUuXLlSAabJCx0JdGdr169epJ7kXRAdxrrkH+gbIh+FN+1gAAylozFCBfsEtgCF60eFETx4sX1FrpoEcVK5s+fr9OEhemjKah0sGN4tc14TRO2qQbZhSJ6r2Elp48yxAObKVOm5NRSfQ8GZezxHu1tx0Has2fPjvpUENjZMGjiVwKC4ZMSQQRUy0sOHDgwgiGGDkptnS179uwZ+mYEXVXFlsroH8EQQwc1a9YsqdYhD30zgq6rV6+WalfbCIYYOqidO3fKq666KvTNCLqqkTapXrgRDDFtg/L9TOhUvxIZABEgAjFDgAQUM+gZMREgAiQg1gEiQARihgAJKGbQM2IiQARIQKwDRIAIxAwBElDMoGfERIAIkIBYB4gAEYgZAiSgmEHPiIkAEfDlpxjxXGz4dAFfthcuXDiqycRSD5j9XaxYsajGg6VCsMf5ZZddFtV48AU4lrAoVapUVOPBl/O//PJL1D9hwQx1LBcS7U9Y/v77b6EmPYprr702qrhFK3ASULSQZbhEgAg4IsAumCNEVCACRCBaCJCAooUswyUCRMARARKQI0RUIAJEIFoIkICihSzDJQJEwBEBEpAjRFQgAkQgWgiQgKKFLMMlAkTAEQESkCNEVCACRCBaCJCAooUswyUCRMARARKQI0RUIAJEIFoIkICihSzDJQJEwBEBElAIiNSy3CFck3dy4ydSOsmnJHZ33eQvOHVu/ERKJzjueLl2k79QaXXy53TfhOlWz+hH8kgC+hdNbHHTq1cvUa5cOZE/f35xzz336I8jncD+8MMPRe3atQW2CL7xxhv1XmXBfiKlExxuvFy7yV9wWjdt2qQ3lsyXL58oXbq0eOWVV4JVhJMOPsYdPny4uPnmm/X2N7Vq1RJet+JOEmkaOjjlL1RS3NRTN+Fie6J7771XYAsrfAD87LPPioMHD4aKMrpuiv0oCoHu3bvLMmXKyAULFshly5bJSpUqSbXftlT7YYXFB3pq33Q5atQoqQpddunSRar9puTmzZstP5HSsQKMsxM3+QtOsvq6XirSkffff7/cuHGjnDBhglQELl999VVL1Y3OW2+9JfPkySPffvttuWrVKtm6dWuZM2dOuWPHDiuceD1xk79QaXeqp27CVXuJSbVxplQvTKl2D5affPKJVC9eqXYaDhVlVN24L5iCd8uWLVJt7SxnzJhhgb19+3b0w+S8efMst+CT8uXLJyk0tbOnVPvSW6qR0rECjLMTN/kLTvLLL78sc+fOLdXuodat/v37y4IFC0o8HBAnHbWshixatKh87rnnrDBOnjypCSgt9mWzIk3hiVP+QgXrpp66CXfs2LFStTyl2tTTimbOnDny8ssvl6plZLmlxQkJSKGMTf7QclFbHQdgjo3l8MYJJQcOHNAENXXq1IDbffr00Q8GHCOlExBBHF24yV+o5Kouk26t2O+pnV41nitWrNDObnSOHTsm1VbLVjBqd1WZOXNmOXjwYMstXk/c5C847W7qqZtwa9asqVvrweHH4po2INXMwV7zhQoVEqo7FdDfxVbPWGAslOzatUs7lyhRIuA2rtWDobcyjpROQARxdOEmf6GSC7xD4QZd2CYgbnRUi0nkypVLL8y2fPly0bVrV12OLVu21GHE85+b/AWn3009dRMutjOvWLGi3tK5cePG2nYJG9zFixeDo4z6NQlIQazeotrwHIw2DKThCAgr+EGC96GHH6xSh9X9IqUTnK54uXaTv1BpBd7BuOXNm1erGrzd6JiwYYiGAfqrr74Syo4U9VUVTbypOXrJn4nHTT11Cle1cjTJf/HFF6Jjx476RYABlJdeekm0b9/eRJVmRxKQgjpLlixC2YCSgI6lVbG0ZihRTX3tDJ1QAn+R0gkVfjy4uclfqHQC72DczDVGtiBudEzYypgtlH1Ej+SgFQQSinfxkj+TFzf11ClcZWPTdXrJkiVi69atYty4cXrktl+/fmLy5Mliw4YNJro0OSZ96tIk2viKRBkzBdY+Dha4KWNpsLO+Nmsx//777wH3TTjwFymdgAji6MJN/kIlNxTeBkd0qSBudEzYyniquxTK9iOaNGkiRo8eDdumuR2XRy/5MxkI5Qf37PU0lI4d2+zZs+tu62233RawLnabNm10NOvXrzfRpcmRBKRgxoMEuw26TnaBPQJzVEIJChqCBc7tAj/GNhEpHXv48XTuJn+h0gt/xtZj7hsc1VQI7eSko0a8hBq5ETjapX79+rpMfv75Z7tz3J075S9Ugt3UUzfhwraphuEDooA/9AJMSzTgZhQvSEAK3Hr16umdH5YuXWpBvWfPHqHmk4i6detabvYTVIYKFSroh8DuPnv2bMtPpHTs4cfTuZv8hUovSEJNbwggfJAJWo1Vq1bVXpx0QGBNmzYV77zzTkAUCAc2DTxk8SxO+QuVdjf11E240Fm5cmWAeWHu3Ll64OSmm24KFXX03GIx9BaPcdapU0diDo/a4kSqt6dUxCMxXGmfiNitWzdpn2OiKr8evsdQPOagDBo0SF/v3r3bymKkdKwA4+zETf4++ugj2apVK4m5O5BDhw5JZauQjz32mDx+/LhUxC/V7HM5YsQIK3dudJThWRYpUkR++eWXUs3ilcqOITNlyiT79u1rhROvJ27yF4wb8uJUT92Eq0bK9HSFdu3a6akiinzkNddcI1W3TKqRsDSFjPOA/oUbpFOjRg09FwVzSe644w6JyYh2wezRhg0bWk4orJ49e+qHSb0iJCblqc8SrPs4iZROQKBxdOEmf88884zGVY3QWClXLUU98RC4gXweffTRJJXfSQcPW6NGjXTYCCdbtmwS87DUAIAVTzyfOOUvFG5u6qlTuMAEM9jVJxhWfQexqb3m0hwu7gsW1LjEhn/oC+N7MLeCkYWjR48m6Vfb/UdKxx5mPJ27yV9welVtF/v379ebHpoRtZToqFaUtuHBXodRID+JGwxC5cepnroNF99/wfAfbrAlVNyRdCMBRRJNhkUEiIAnBGiE9gQXlYkAEYgkAiSgSKLJsIgAEfCEAAnIE1xUJgJEIJIIkIAiiSbDIgJEwBMCJCBPcFGZCBCBSCJAAookmgyLCBABTwiQgDzBRWUiQAQiiQAJKJJoMiwiQAQ8IUAC8gQXlYkAEYgkAiSgSKLJsIgAEfCEAAnIE1xUJgJEIJIIkIAiiSbDIgJEwBMCJCBPcFGZCBCBSCJAAookmgyLCBABTwiQgDzBRWUiQAQiiQAJKJJoMiwiQAQ8IUAC8gQXlYkAEYgkAiSgSKLJsIgAEfCEAAnIE1xUJgJEIJIIkIAiiSbDIgJEwBMCJCBPcFGZCBCBSCJAAookmgyLCBABTwiQgDzBRWUiQAQiiQAJKJJoMiwiQAQ8IUAC8gQXlVOLwG+//SbU9tZCbR+c2qDoPwEQIAElQCGmJAvTpk0TGTJkECAEt4LtgD/88ENL/cSJEzoMhBPut27dOq1/9uxZ0bx5c1GsWDGxcuVK0bJlS1GmTBmxdetWK7x4P7n//vtFvXr14j2ZvkpfZl+llomNKQKdO3cW586dEx06dAhIxwMPPCAaN24c4GYuQDKQ/v37i4ULF2ryee2110Tv3r3FU089Jfr06SNmzpxp1HlMZwiQgNJZgacmu//8849u6QSHUbVqVdGuXbtg54DrZcuWiaZNm4obb7xRu+fLl0+88sormnzQOsqRI0eAPi/SBwLsgqWPctY2F9heChQooLtCR44cSZJzdMtq1qwp8ufPL4oWLapbNTt27NB63bt3F0uXLtUtmGrVqolffvklif/kHAoWLCj27NkToILuzMiRIy3yQXetVq1aIleuXOLKK68UDz30kDh+/LjlB/emT58u0OJCeLfddpuYMGGCdd+cjB8/XlSuXFmHA8IL1cJy0gHZotVWsWJFccUVV4iXXnpJwI0SYQQkJeER2LRpk8yWLZvs2LGjnDVrluzatavMmjWrVFVJKruOzv/nn3+ur7t16yYVEcl+/fpJRUKyfPny+r7qPskqVarI66+/Xk6cOFGeOXNGKnLQft544w1HDOEH8d13333y1ltvlT/88EOAH4SnyFHeeeedEml56623pLIXyUaNGll6uXPnlnny5JHKFiOXL18uBwwYIDNlyiS//PJLS2fw4MEyc+bMUpGUnDFjhuzRo4dU9ik5depUTzqKfKRqlckRI0Zov4rINGZ169a1wuFJ6hEQqQ+CIcQ7AqqlIW+//faAZLZo0SKAgPCg3nXXXQE6gwYN0jrK2Kzd7777bk0QRskQUMaMGTURgAzsvxo1ahhVfVStHVm4cGEdZqlSpeQLL7wgVfdL31u7dq1237hxo+UHRPj0009L1fLQbiCgSpUqWddwfOSRR2TJkiX1faQTOiBau7Ru3VqWLVvWtc7Ro0cl8jRq1CgrGIStWmayTp06lhtPUo8AbUARblHGY3DffvutNvba06YeSt2dMW7Dhg0zp+LQoUNi27ZtYvv27doNNpq8efNa94NPYNtB9yhYMOJllyeeeEKo1pcehv/rr7+EIjixZMkS3a2rUKGCuPTSS8U999wjFKkIRYZCkaT+2cPASBRG3IwoUhTjxo3TXbUtW7aIU6dOCUVSYvXq1UZFlCtXTkyZMkUcO3ZM58tJByNz6G4hbCPIf4MGDQK6hOYejylHgASUcux84RM2FAy1FylSJCC9xYsXD7iGzrPPPitUt0VgeB33L7vsMq2j3nMBusEXIJ+ePXsGO4e8zpIliyaz119/XcAw3alTJzF//nxtb1q0aJF47LHHxIsvvqh/II6hQ4dqMjKBlShRwpzqo2pR6eOPP/4o9u/fr88xuhZK9u3b50pn165d2nsozOw2qVBx0M0bAjRCe8PLd9oYbYJRN/jBOX36dEBe2rZtqw3VIAY8gAcPHtRkACUnAgoIKMTFxYsXBcKFEdsuaIWhNbNz507tDIPx+vXrBYhC2YCEslvpFtDevXstbydPnrTOcWLmMZUuXVobz+G2Zs0a3YJBK8b+q169uisdGJ0hTphpJf6lCgESUKrgi3/PeMDRJVm8eHFAYletWmVd//nnn3qOzuOPP65bJMpeou8pe4w+/v333/qIsMy55dnFiTIK624SRrzsgq4hyA0tLaSndu3aApMdlU1Hk58yXGsCQdfKCCYx2gX5QqsIo2LoxiGN6G7haH5jxozREx/Pnz/vSgcjaBB0D40gnf/973/NJY+RQkABS0lwBNRnD9o4jJElZf+QalhaG1RVHbJGwTAypVoIUrU+pGplyLFjx2o/0FG2II1Q+/btpSILOW/evIBRMDWrWevDT/API3CQ559/Xqrulxw4cKBs0qSJHmm7+eab9UgX0vTHH39I1eXRo1dq6F+qVo82MGNEC0ZhCAzMMHIrm49ULTg9OoWRKsRppE2bNnqkbMiQIfLw4cNSDdvr0ay+ffsaFelGB4Zs5FXZkiQM0Kp7in4ojdAWipE54ShYZHCM+1AwoqPsOvohUq0FqbpE+twMwyv7iyYg1WrQw9hqPpBUrQ39wKu5Njp/GIoHCeBBVK0Daxge1+F+IByI6oZpQjHD/9DHyJSa+6Pv4w/D5iBCkA7ugwAWLFhg3UfcGIIvpUbQcB/5UPNzrPs4AXmq+UNWGBjKV3Yma7TNrY5qLclWrVrJ7Nmz67jUnCOpZoBLDsMHwJ3qCxJQqiH0TwAYzkYLB8dwoiYY6oc43H34VXaXcLcd3THfB0PZqusUVhckokbiktwHAWGeD0QZnKXqDibRMQ4XLlyQauJjsnl1o4NpAsCEEh0EOAqmXqXpRWATgX0lOcEM6OQEYWCmdEolZ86colmzZkJNcAwbhCIagV9yYgzF4XRUS0vPpg53H+5udFQLSOBHiQ4CJKDo4MpQk0FATXpM5i5vpScESEDpqbR9nldMLjTzfnyeFSb/XwQyoGdHNIgAESACsUCA84BigTrjJAJEQCNAAmJFIAJEIGYIkIBiBj0jJgJEgATEOkAEiEDMECABxQx6RkwEiAAJiHWACBCBmCFAAooZ9IyYCBABEhDrABEgAjFDgAQUM+gZMREgAiQg1gEiQARihgAJKGbQM2IiQARIQKwDRIAIxAwBElDMoGfERIAIkIBYB4gAEYgZAiSgmEHPiIkAESABsQ4QASIQMwRIQDGDnhETASJAAmIdIAJEIGYIkIBiBj0jJgJE4P8B3yhmad4oKVEAAAAASUVORK5CYII=)
qqnorm(datE$speed); qqline(datE$speed)
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)
# run LMM on speed variable
lmm <- lmer(speed ~ so + (so|subj) + (so|item), data=datE, control=lmerControl(calc.derivs=FALSE))
summary(lmm)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: speed ~ so + (so | subj) + (so | item)
## Data: datE
## Control: lmerControl(calc.derivs = FALSE)
##
## REML criterion at convergence: -5932.5
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.2501 -0.5996 0.1237 0.6430 2.5441
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subj (Intercept) 3.712e-07 6.093e-04
## so 1.331e-08 1.154e-04 -0.51
## item (Intercept) 1.100e-07 3.317e-04
## so 2.305e-09 4.801e-05 1.00
## Residual 8.916e-07 9.442e-04
## Number of obs: 547, groups: subj, 37; item, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.672e-03 1.379e-04 3.806e+01 19.369 <2e-16 ***
## so 3.879e-05 4.644e-05 2.966e+01 0.835 0.41
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## so 0.012
# the random effects correlation for items is estimated as 1, indicating a singular fit
lmm <- lmer(speed ~ so + (so|subj) + (so||item), data=datE, control=lmerControl(calc.derivs=FALSE))
summary(lmm)
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: speed ~ so + (so | subj) + (so || item)
## Data: datE
## Control: lmerControl(calc.derivs = FALSE)
##
## REML criterion at convergence: -5931.3
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -3.1531 -0.5908 0.1328 0.6442 2.5066
##
## Random effects:
## Groups Name Variance Std.Dev. Corr
## subj (Intercept) 3.718e-07 6.098e-04
## so 1.315e-08 1.147e-04 -0.51
## item (Intercept) 1.098e-07 3.314e-04
## item.1 so 1.809e-15 4.253e-08
## Residual 8.941e-07 9.456e-04
## Number of obs: 547, groups: subj, 37; item, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 2.672e-03 1.379e-04 3.807e+01 19.371 <2e-16 ***
## so 3.810e-05 4.477e-05 3.553e+01 0.851 0.4
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr)
## so -0.159
Based on these analyses, we take the last fitted lmm model, and use this to simulate new data. This is possible with the simple function call simLMM(LMM=lmm)
. This uses the data that the model was fit on. However, we can also use the fit lmm object to simulate data for a new data set (i.e., here the experimental design we created we created using designr), by simply adding the new data frame: simLMM(data=dat, LMM=lmm)
. Importantly, the new data frame needs to have the variables that are used in the model.
datE$simSpeed <- simLMM(LMM=lmm, empirical=TRUE)
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 1 + so + ( 1 + so | subj ) + ( 1 | item ) + ( 0 + so | item )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev. Corr
## subj (Intercept) 0.0006098
## so 0.0001147 -0.51
## item (Intercept) 0.0003314
## item so 0.0000000
## Residual 0.0009456
## Number of obs: 547, groups: subj, 37; item, 15
## Fixed effects:
## (Intercept) so
## 2.672153e-03 3.809511e-05
dat$speed <- simLMM(data=dat, LMM=lmm, empirical=TRUE)
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 1 + so + ( 1 + so | subj ) + ( 1 | item ) + ( 0 + so | item )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev. Corr
## subj (Intercept) 0.0006098
## so 0.0001147 -0.51
## item (Intercept) 0.0003314
## item so 0.0000000
## Residual 0.0009456
## Number of obs: 576, groups: subj, 36; item, 16
## Fixed effects:
## (Intercept) so
## 2.672153e-03 3.809511e-05
dat %>% group_by(so) %>% summarize(M=mean(speed))
## # A tibble: 2 x 2
## so M
## * <dbl> <dbl>
## 1 -1 0.00263
## 2 1 0.00271
lmer(speed ~ so + (so||subj) + (so||item), data=dat, control=lmerControl(calc.derivs=FALSE))
## Linear mixed model fit by REML ['lmerModLmerTest']
## Formula: speed ~ so + (so || subj) + (so || item)
## Data: dat
## REML criterion at convergence: -6250.4
## Random effects:
## Groups Name Std.Dev.
## subj (Intercept) 5.353e-04
## subj.1 so 3.669e-05
## item (Intercept) 3.383e-04
## item.1 so 0.000e+00
## Residual 9.565e-04
## Number of obs: 576, groups: subj, 36; item, 16
## Fixed Effects:
## (Intercept) so
## 0.0026722 0.0000381
The results show that we can exactly recover the parameters from the previous model in the new simulated data set.
Next, we can turn to perform power analyses.
# perform power analysis based on fitted model
nsubj <- seq(10,100,1)
nsim <- length(nsubj)
COF <- data.frame()
for (i in 1:nsim) { # i <- 1
#print(paste0(i,"/",nsim))
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("subj", instances=nsubj[i]) +
random.factor("item", instances= 8) +
random.factor(c("subj", "item"), groups=c("X"))
dat <- dplyr::arrange(design.codes(design), subj, item)
contrasts(dat$X) <- c(+1, -1)
dat$so <- model.matrix(~X,dat)[,2]
nsj <- length(unique(dat$subj))
for (j in 1:10) { # j <- 1
dat$speed <- simLMM(data=dat, LMM=lmm, empirical=FALSE, verbose=FALSE)
LMMcof <- coef(summary(lmer(speed ~ so + (so||subj) + (so||item), data=dat, control=lmerControl(calc.derivs=FALSE))))[2,]
COF <- rbind(COF,c(nsj,LMMcof))
}
}
names(COF) <- c("nsj","Estimate","SE","df","t","p")
COF$sign <- as.numeric(COF$p < .05 & COF$Estimate>0)
COF$nsjF <- gtools::quantcut(COF$nsj, q=seq(0,1,length=10))
COF$nsjFL <- plyr::ddply(COF,"nsjF",transform,nsjFL=mean(nsj))$nsjFL
#save(COF, file="data/Power4.rda")
load(file=system.file("power-analyses", "Power4.rda", package = "designr"))
ggplot(data=COF) +
geom_smooth(aes(x=nsj, y=sign))+
geom_point(stat="summary", aes(x=nsjFL, y=sign))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign))+
geom_line(stat="summary", aes(x=nsjFL, y=sign))
![](data:image/png;base64,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)
## (Intercept) so
## 2.672153e-03 3.809511e-05
## [1] 3.859278e-05
# determine number of subjects needed for a power of 40%
m0 <- loess(sign ~ nsj, data=COF)
COF$pred <- predict(m0)
idx <- COF$pred>0.4
min(COF$nsj[idx]) # 164
## [1] 174
We can see that the power for this study is quite low. Notice that we are using a realistic effect size estimate from a previous study. Yet, even 200 subjects are not sufficient to obtain a power of 80% to detect the true effect.
LMM: Crossed random effects for subjects and items - with continuous covariate
Next, we treat the case of a continuous covariate. Interestingly, we can use simLMM
to simulate not only a dependent variable, but also a covariate.
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=15) +
random.factor("Item", groups="X", instances=10)
dat <- design.codes(design)
(contrasts(dat$X) <- c(-1, +1))
## [1] -1 1
dat$Xn <- model.matrix(~X,dat)[,2]
simLMM
has a further argument: family
. This can be set to “lp”, which stands for “linear predictor”. This means that simLMM
does not add any residual noise, but puts out the best prediction for each data point. Using this functionality, we can generate covariates that only differ by subject (i.e., age in the example below), or covariates that only differ by item (i.e., word frequency in the example below). However, we can also simulate a covariate that varies across subjects, items, and across individual trials. For example, when modeling fixation durations during reading, we might include the previous fixation duration as a predictor (covariate). When modeling ratings, we might have a task where each trial has two ratings, and we want to predict the second rating using the first as predictor (covariate). However, these differences are mainly important for simulating the covariate.
# simulate covariate
dat$age <- round( simLMM(form=~ 1 + (1 | Subj), data=dat,
Fixef=30, VC_sd=list(5),
empirical=TRUE, family="lp") )
## Data simulation from a linear mixed-effects model (LMM): linear predictor
## Formula: lp ~ 1 + ( 1 | Subj )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev.Corr
## Subj (Intercept) 5.0
## Number of obs: 300, groups: Subj, 15
## Fixed effects:
## (Intercept)
## 30
#table(dat$Subj,dat$age)
hist(dat$age)
![](data:image/png;base64,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)
dat$wordFrequency <- round( simLMM(form=~ 1 + (1 | Item), data=dat,
Fixef=4, VC_sd=list(1),
empirical=TRUE, family="lp") )
## Data simulation from a linear mixed-effects model (LMM): linear predictor
## Formula: lp ~ 1 + ( 1 | Item )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev.Corr
## Item (Intercept) 1.0
## Number of obs: 300, groups: Item, 20
## Fixed effects:
## (Intercept)
## 4
#table(dat$Item,dat$wordFrequency)
hist(dat$wordFrequency)
![](data:image/png;base64,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)
fix <- c(5) # set fixed effects
sd_Subj <- c(1) # set random effects standard deviations for subjects
sd_Item <- c(1) # set random effects standard deviations for items
sd_Res <- 1 # set residual standard deviation
dat$rating <- round( simLMM(form=~ 1 + (1 | Subj) + (1 | Item), data=dat,
Fixef=fix, VC_sd=list(sd_Subj, sd_Item, sd_Res),
empirical=TRUE) )
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 1 + ( 1 | Subj ) + ( 1 | Item )
## empirical = TRUE
## Random effects:
## Groups Name Std.Dev.Corr
## Subj (Intercept) 1.0
## Item (Intercept) 1.0
## Residual 1.0
## Number of obs: 300, groups: Subj, 15; Item, 20
## Fixed effects:
## (Intercept)
## 5
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zj3LC5IbhbKWIfvVHh4odHeBrYxwsJLzYIFNDcuXP1HsH+F198gZ8QMZZSgfrESwejqNGtj6EHZ511lgwePNhJJ1LdhCQaxw74oHy2uF+A9jE3w0TvOTuNRH4L3nGJxM6zsLjJYKVMnTpVb2jjc1BrwsaAMSDh4n5zocvefgPhzYtRvrasXr3aGTV93HHH6cMOq8gWY47bm7Jx40a9SZ0DETZM70nIUdPc0rc0Dl5zzTVqXWGcivFFOOESucndN6qTgMdGotfvkVyB0zVr1nSO4YG2xTiFxc0Px5PhYdcprBPjhFdrxTRD7ez01y5LuCLEyfC6wTHji9OhEVAQ33//vbz99ts6hsge4hGtbuyyII1USDL3nJ/8qYDipDZ58mTBGxwDC/v16yewDPCZR//+/Z0bym11oJkEMc5rMY5p2bRpk+6bnjT9xfgXvIGheDB83zhn9Tj+mW5T3cZnIvaDbpyaYrryVfmZXooQ5eVEdG2Ev92WL1/unMUnDbY899xz9qaYEbbOdro2Ern+RMvgbnbhswhYPfjDpxx2E8NOM1Eedn0iPsZWGf+iDji0ORvfiSoOnMcgRNPjik2xB6Tqzv/+2XHcx+zy4BzGZkHQHLI/6cCYHVsilcU+l+xvMvecr7yNBi204nZCJ/spBnpl4Ag1kPUPPR+mra9jQnAM4zXMoDSHpXuMj1Ei2nOFk+gNMz4jJx1zwznbSAfdrG4xD1LIeYTBeBi3U9UO73ZCu3vqcN4oQKfLHOXBkAK79wb7SNc0yTQptxN6ypQpdvIWHMwIhz8MabDFWITOcbs3xT4X/pvo9SfihEZeF110kVMW04RQViivfa3YhhM6ER5I11i3TrrgZSwS7UlEj6XNBL82S2wba9cyzTNEV7Gd0HBOh4u7pw7d+aYJpj1i7vTsntRoZVkV5RMiuxseabkFY9bssqPH1JZE7jk7jt9fWkCmBuIRWDymi1KuuuoqbUfDcjHd52IUkzoUZ8yYIWYch5OUGeCmFpN9AM0ACKwk0/ug6cDBa/sO8NbD6NlwZ7bpmdIh/XAqIy78TyiHGduj6UUy5/VE2D+kj7cyRjKbm0X9FMgbI75hyUFwDemWRK8/0fK8/PLLct1116mPBSN50XR5+OGHtTnjTitRHu3atRPbegM/NK3gh0NzFlYkHNEQnIOl3LlzZzE9XQJ/TzwCK+2yyy7ToBs2bJA5c+YIPpBGc98Wu36ilcUOl+xvqu65uMrhV3PlczxYQ+iK/frrr9WiicYCA9IwOhjjOaKJ6RmyjDKLeBrHjUNTz7u77BHYHiyGt2UigjEny5Yts/C2DILEuv5kygf2GAeE640lifJAnaDuMejULdg3TXPtikfefgUj1nFfxZNGtLL4zRvx0nHPxSoPNDYloATcA+uMU1MHv8Gkx8BCe8wJFBElGAQwkBOfquSyZPqe00ZhXKYSA2WcAJzXGGMUbU4hOCxh5puR2BkvGzMsnAQyfc8VM6MqHyicKHP/qjAOo2PHjnoh+HodNwe67uE7gj8C/g7OwJf79RykK8j0PUcLKEi1H0dZ4DiO1I0bR1QGIQFfBNJ5z1EB+aoSRiIBEkgFAXbDp4Ii0yABEvBFgArIFzZGIgESSAUBKqBUUGQaJEACvghQAfnCxkgkQAKpIEAFlAqKTIMESMAXASogX9gYiQRIIBUEqIBSQZFpkAAJ+CJABeQLGyORAAmkggAVUCooMg0SIAFfBKiAfGFjJBIggVQQoAJKBUWmQQIk4IsAFZAvbIxEAiSQCgJUQKmgyDRIgAR8EaAC8oWNkUiABFJBgAooFRSZBgmQgC8CVEC+sDESCZBAKghQAaWCItMgARLwRYAKyBc2RiIBEkgFASqgVFBkGiRAAr4IUAH5wsZIJEACqSBABZQKikyDBEjAFwEqIF/YGIkESCAVBKiAUkGRaZAACfgiQAXkCxsjkQAJpIIAFVAqKDINEiABXwSogHxhYyQSIIFUEKACSgVFpkECJOCLABWQL2yMRAIkkAoCVECpoMg0SIAEfBEo7itWgCJZliUbN26UYsWKSfny5QNUssJRlK1bt8pVV10lRYoUSeqC6tWrJ//973+TSoORCx+BIuYBtnLtstauXStPPfWUvPrqq4LtPXv26CWULVtWqlevLmeffbb069dPSpcunWuXltLyggsUSDIyYcIEmThxorRq1SqZZOS+++7TesKLgkICNoGcU0CrV6+WZs2a6Ru5U6dOUqNGDbV88IbetGmTrFy5UiZNmiTQqx988IEcffTR9rXm3e9FF10kkydPFihmvwIF1rJlS+nfv7/fJDRekyZNZPfu3WqpJpUQIxcqAjnXBBs0aJBaObNmzZL9998/YmUMHDhQ2rRpI+PGjVNLKGKgPDi4bt06GTVqlDRs2ND31YLljh07fMdnRBKIRSDnnNBfffWVXHnllVGVDy52v/32k27dusm7774b69p5jgRIIMsEck4BNW3aVD755BNPbLNnz5YqVap4hmMAEiCB7BHIuSbYZZddJlBCv//+u1x++eXq4znkkEOkaNGi6gNatWqVjB8/XmbMmCFoplFIgASCSyDnFFCDBg3km2++kR49ekjXrl1l3759BeiiF+z999+X5s2bFzjHAyRAAsEhkHMKCOhq1qypPVz//vuv/PLLLwKrBz0slStXlqpVqwosIr8CxfXEE094Rl+6dKk6eM8991zPsAxAAiQQmUBOKiD7UkqUKKHKCAoJsmHDhpjOaTterN/jjz9ebrnlllhB9NyNN94oyJ9CAiTgn0BOKqCFCxfKgw8+KBgkV6ZMGZk+fbr06dNHMEYIA93q168vQ4YMkdNOOy1hMrCi8OclBx98cN4PdPRixPMk4EUg5xTQggUL5JRTTnFG5s6fP18uuOACVTo33HCDWkAYiIjBc2hO+VFCXtB4PnEC6CTo27dvUp90HHDAAfriwTALSuEgkHMKCFZP27ZtZdq0aVoDzzzzjFSqVEmgmIoX/7/LgTUER/SLL75IBRSQ+3Tv3r1Jl2TevHlap9dee23SaTGBYBDIOQW0aNEiQVe8LZs3b5YOHTo4ysc+jjAjRoywd/kbAAKXXHJJUp9ioIlNKVwEcm4gIr6qfv3112Xnzp1aE2eccYZaQ+43LL4De+edd6R27dqFq7Z4NSRQyAh4WkAff/yxvPHGG/ppA5y72ZY77rhDGjVqJI0bN5a77rpLByUee+yxOuYH00bAKY2BiO+9915cI6azfT3MnwTymYCnAkJvDx5m9CpBAeEbK4xAPuyww7LCrVq1ajJ37lx56KGH5IorrhC35WN/onHCCSeoVQRFRSEBEgguAc8mWN26deX777+Xzz//XE4//XQZMGCAfmN1/vnny5QpU3QAYKYvr06dOvLKK6/o5xgo19SpU2Xs2LEyc+ZMwQDBxYsXay9YpsvF/EiABBIj4GkB2cmdeOKJgj+MEoZFBOUDawiD8WAR9ezZU9AUyqRgxDP+UC4KCZBA7hHwtIDCLwmfPnz55ZdqZWCyKkwIhi5wWCWY9Y5CAiRAAvESiMsCwpzLmP705ZdfFgz8q1ixonTp0kX3jzvuOM0LPVMXX3yxDgpMZgKseAvOcCRAArlPwFMBweGLQX0QewAgZhu0B/3ZCOyPMjFNBoUESIAE4iHgqYAOPPBAeeyxxzx7vjA96vr169U6iidjhiEBEiABTx8QHLz48hs9TD///LND7Prrr9ceJ/sALCI0zSgkQAIkEC8BTwsICWFJljlz5ugfnM4Yafz1118Lpq54/PHH5aabboo3v8CHwyoSGOzoJb/++qssX75csNoDhQRIwB8BTwW0YsUK+eijj+Tbb7+VWrVqaS5YAgeD/rA2F0YjwxoqLHPj4Ct6zLroJVjyprpZg4xCAiTgn4CnAsLaWmiG2crHnRVGIqN5hq55e1Iw9/lc3ManHPjzkpIlSxYapet1rTxPAuki4OkDwuBCTAC2Zs2aAmV466239Otmrj5RAA0PkAAJxEHAUwHBx4H5djDuB0vdwPfx448/6myE9957r2B1UkwURSEBEiCBRAl4NsHQ1Pj000/lvPPOk7POOiskffhBRo4cGXKMOyRAAiQQLwFPBYSEjjjiCF0KB9YPVibFvMtomh111FHx5sNwJEACJFCAQFwKyI6FJW/wRyEBEiCBVBCISwGhCYb5gGABYS2ucME0qdkSjEnCt2qwysqXL5+tYjBfEiABHwQ8FRB6v1q3bi0HHXSQrkZRtmxZH9mkNsratWt1DBI+kMX2nj17NAOUDWNz8O1av379uGxOarEzNRJIOQFPBYRxQFhSBcshlytXLuUFSDRBTEzerFkzXd4FPXAYmQ3LB4MjN23aJCtXrhQsy4MRzSj70UcfnWgWDE8CJJAhAp4KCE0c+H2CoHzAZNCgQWrlzJo1K+oqqAMHDhR8sT9u3Di1hDLEktmQAAkkSMBzHFCLFi30I9TvvvsuwaTTExy9cFdeeWVU5YNcsXAdZmt8991301MIpkoCJJASAp4WEMYBYY2t5s2bS+fOndUagsPXLbfffrt7N63bTZs21e/QvBanw6BJjtBOa1UwcRJImoCnAsJX75jtEIIZESNJJhUQlCGUECY+w1zU8PFgXmj4qeADWrVqlS7LM2PGDEEzjUICJBBcAp4KCFNxbNmyJTBXgC/V4RDv0aOHdO3aVfbt21egbOgFw7rwsNooJEACwSXgqYDcRd+xY4f89NNP2vMEPwtmQcyG4Mt79HBhTBK+xIfVs3v3bqlcubI2EWER+ZUxY8ZI9+7d44qOKUo4H1BcqBiIBCIS8HRCIxYGIOK7r9KlS+vihFgnDJN23XrrrfL3339HTDgTBzEHEZQRLB70emE72fJgdVX0/Hn9QfFgQjYKCZCAfwKeCghWRvv27XX2v8GDBwvmiIacdtpp8txzzwVqNkQsIY1VUSkkQAK5QcCzCQZHLkYbY/pRjIa+//779co6duwoGHkMPwysBQwEzIRgClg0uSLJsmXLBM3EG264QU9jeaB4m1OR0uMxEiCB9BLwVECYkhVrf0H5hMtJJ50k69atU4WQqS/jv/jiC5k4caIOjAzvZt+8ebP6gjCFLCRbPqpwTtwnARKITMBTAUGxYP7nP/74Qw477LCQVKAIsBpGuCIICZTinfHjx0u9evUEo50xIPGWW27RLnhk89JLL8nNN98sS5YsSXGuTI4ESCAdBDwV0Jlnnqk9S1h4sG/fvtrtDato+vTp8vTTT+sgxUxOSI/xPpgIH5PHYxwQpoXFJxfVqlVLBx+mGSAC27dvl+HDh+sQC7/F2rVrl2AQa7t27fwmwXgpJOCpgNDzNWXKFP20AYMAIZiMHnL++efL0KFDdTvT/xo1aqTr06MnDhYRVuiAcqIUXgL40Picc87R4RZ+rxI+wvvuu48KyC/AFMfzVEDIDw845vyB/wXWDywe+IVq166d4uIklhx65DAlLKaLhbOZc1Mnxi/XQqOjAx9FY3CsX0HzHGPIKMEgEJcCQlFhXcDpjL+gCRQQbiwsEQRfVWGQadOmJe3LglOeQgJBJuCpgObPny933nlnzGvAqqnZlgoVKuhKHdkuRyryxxLYHTp00GZvMulhlDiFBIJMwFMBoSv78MMPD7mGrVu36rrwGCFdmJZlDrnILO5gXBUWAujVq1dSpXj77beTis/IJJBuAp4KCCOLJ0yYUKAceEj69Omj32IVOMkDJEACJBAHAd/dRnAIogcKU3Wge5RCAiRAAokS8K2AkBHm5Nm7d2+gputIFADDkwAJZI+AZxMM312hR8YtUDqY/OvZZ5/VBQozORLaXY50bMOa27Bhg2fSO3fujLhEkWdEBiABEnAIeCogTL1x2223ORHsjVKlSgkmB8vWQES7HKn+xTzSmGrES/CBLpTz6aef7hWU50mABKIQ8FRA+AQDw9fzRTDvEf685JRTTpFatWp5BeN5EiCBGASS8gHFSJenSIAESMCTgKcFFM9ARHcuL7zwgk7Z6j7GbRIgARKIRMDTAsK3N/jGau7cubreVv369XVaDqyWgXl38IkGBiraf5ieg0ICJEAC8RDw1Bb4Gh6LAWJmREzNYQt6wjDzIL7BijRQ0Q7HXxIgARKIRsBTAWF5G4yGdisfJIbFCe+9916dKwizIoZ/rhEtQx4nARIgAZuAZxMM8z4vXLgw4mjn9evXaxMMVhKFBEiABBIl4KmAsOQNBt1huRr4feyBeliBolOnTnLxxRdLmTJlEs03ZeHxTRqm4MDASAoJkEBuEfBUQJiMHnNCL1iwQAceQtlUrFhRsCoG5gYaPXp0xq8YgwAxWLB69eo6ORqm4sBihCgrnOSYJ5rfp2W8WpghCSRMwNMHhBTxUGNF1O+++04d0hgFXbduXf0MI+Eck4ywevVqadasmS4DBAusRo0aUr58ed2HFYRpOydNmiSTJ0/Wme+wdjyFBEggmATiUkAoOpZiPuaYY9Tng4ce+9mQQYMGqeWDXrloy+5gxQyslIrJ6vv165eNYjJPEiCBOAh4NsGQRpCWZsaQACzHE035oLxQjt26dRN810UhARIILgFPBRS0pZmbNm2qPikvpLNnz87oemVe5eF5EiCBggQ8m2BBW5oZSwNBCWEuIqwLBh8PHNAYkQ0fEL5Qx+KFM2bM0MGTBS+ZR/KZwLZt29SXmexKvpiQD9Y4hqlQ/BPwVEBBW5oZU4B888030qNHD12Xft++fQWuHkMHMICyefPmBc55Hfjtt9/0BvUKhxUnIvW0YVjAzJkzvaLHPI8yIB1K6glgries8Pv4448nlThW4EVvLBVQUhjFUwEFbWlmXG7NmjW1hwvNQ6z8AKtn9+7dumBd1apV1SLyi+Xbb7+N6+bE6O+NGzcWyGbUqFHSu3dvwXQdfgU3NhbQo6SHAHyEmPQ/GclWJ0wyZQ5iXE8FFLSlmd0QcRNAGeEvXP755x89lOhihVjyGX9eAgWDcUjhAod9z549deBm+Ll497EIJFbvpJBAYSfg6YS2l2bGx6fwv6DZgaWZH3roIR2Pk40ZEdG9DsusZMmSamlgoGS4oKxdu3YNP8x9EiCBABHwtIDg68AARDzkaJ5ke2lm+FegWODfgRN64sSJOi0qFCG+zqeQAAnkDgFPBYTF7WDxrFmzJhBLM+PTD6wNbo/x6d+/v9x///26Rhk+E6HVkzs3H0tKAp4K6NBDD1VKW7Zs0ak3so0Mn2K4lQy6Qx988EFdHujaa6/VsT/oBaOQAAkEn4CnAkK3N/wpWP3hggsu0HE34aOQ+/btm7ErrVy5smCQYXhza8CAAWqlYUJ5zN5IIQESCD4BTwX05ZdfytSpU/VKos18mEkFBGWIJiGsneuvv14nS7MxYz5qKCD4hzA4sWHDhvYp/pIACQSQgKcCat26daDGpHTu3FmWL18usHjg88FsjbZgPupXX31Vu8FffPFFKiAbDH9JIKAEIiqgPXv2CP7QzR1EwRgZLJaIHrpwQfNwzJgxqoTwuQaFBEgguAQijgNClzam3HALBtj98MMP7kNZ3YZyrFSpUtQyNG7cWNq3bx/1PE+QAAlkn0BEBRSpWIMHD5YuXbpEOsVjJEACJOCLQNwKyFfqjEQCJEACMQhQAcWAw1MkQALpJUAFlF6+TJ0ESCAGgYi9YDHCF/pTy5Ytkw8//NDzOtHDxqWAPDExAAnEJBBVAWGtreOPP96JjEUIMUeN+5h9Eh+pFhaBUsH6Z14CFlgvjUICJOCfQEQFhPl12rZtG5IqVsTIB8E8P/FMJobpOPFZCIUESMA/gYgKqEOHDoI/CgmQAAmkkwCd0Omky7RJgARiEqACiomHJ0mABNJJgAoonXSZNgmQQEwCVEAx8fAkCZBAOglQAaWTLtMmARKISYAKKCYeniQBEkgnASqgdNJl2iRAAjEJUAHFxMOTJEAC6SRABZROukybBEggJoGcV0CWZQm+W+OHoTHrmSdJIJAEIn6KEciSugq1du1aeeqpp3QCemxj/mpI2bJldb12rAvWr18/wbLSFBJIB4F9+/bpMlDhS1QlmhfWtcNLNBnB2n2493NRck4BYWHCZs2aCSquU6dOOnd1+fLldR9W0MqVK2XSpEkyefJk+eCDD3Qds1ysGJY52AQ2btwo7dq1kwoVKvguKOZZh1StWtV3Gn///bf8+++/sm3bNt9pZDNizimgQYMGqZUza9Ysifb2GThwoLRp00bGjRunllAigBctWqSWlVccKEJMURIu++23nzz99NNJ3RB//fWXNilh5SUjWM12+PDhgsUl/cqqVat0epKKFSv6TcKJN2zYMCla1H+rH8uDjxgxQn755RcnzUQ38ND/9NNPakEnGtcdHtOxNG3aVO9F9/FEtj///HNdYgrr2PkVWP9YiipXpYgx/5Kz/zJ85bB+sDQzFiaMJS+//LLghl+wYEGsYAXOYW4je935AiddBxYvXiy33357gYcbpvmTTz7pCulvE2ueJftWO/DAAwVvyGSlRIkS+pZNJh00EbZu3ZpMEgLlvnv37qTSQGQ0zbdv355UOqlIAwWAQsY9k4zA5ZDMSyaZvJONm3MKCA/9hg0bBAsPxpLu3bvrumFvvPFGrGA8RwIkkEUCOdcEw9LMMH0xJerll1+uPh4sw4w3CXxAaDKMHz9eZsyYIWimUUiABIJLIOcsIKD88ccfpUePHjJnzpyI5itM0rvvvltatGgRXPIxSgY/xT333CMnn3xyjFCZOQVFjxVo//Of/2Qmwxi5YEluNOViLUgZI3pKT8F/c9xxxwmaudkUNEkxO6dXiyCbZYyVd85ZQLgYTBmLHi54/+GQhNWDisAUqehRgEWUy7Ju3TqZOnWqwA+UbVm6dKlAISbrp0jFdcyePVuVT506dVKRXFJpvPnmm3rPlStXLql0ko2MecnhhM5VBZSTFlCylRb0+OiladWqlVp62S7r2LFjdZWQINzg6HjAktvXXHNNtrFI7dq1ZcqUKXLsscdmtSx//vmnWqcYFpCL4r9PNBevlmUmARIIFAEqoEBVBwtDAvlFgAoov+qbV0sCgSJABRSo6mBhSCC/CFAB5Vd982pJIFAEqIACVR0sDAnkFwEqoPyqb14tCQSKABVQoKqDhSGB/CLAgYgBrG+M8Ma8RkH4/AFTg2DqiWTmrEkVYkw+d8ABBwjmf8q24LOQatWqRZ0SJlPl27t3ryxbtkyCMDrczzVTAfmhxjgkQAIpIcAmWEowMhESIAE/BKiA/FBjHBIggZQQoAJKCUYmQgIk4IcAFZAfaoxDAiSQEgJUQCnByERIgAT8EKAC8kONcUiABFJCgAooJRiZCAmQgB8CVEB+qDEOCZBASghQAaUEIxMhARLwQ4AKyA81xiEBEkgJASqglGBMfSJBWIUi9VeVfIpBWcg3m/WDbwXxDVg0CQqjaOVzH6cCctPI8vb3338v5557rq59hfWmTjzxRJk5c2aWSyXy0Ucf6cKPc+fOzUpZ1q9fLx07dtTllqpXry633Xab4MPUTAuUzoMPPqjLP2GZaHws/Morr2S0GPhIGctPRVo+/Msvv9TFOrFUUI0aNaR///4ZLZuvzLA2PCX7BMzyKlaVKlWshg0bWmZlV+u9996zzjvvPMvc6NYXX3yRtQKa9emto446yjI3l2UUUcbLYda9so488kjLLNJomZVuLfPAW8ccc4xlVsXNeFkeffRRq0iRItaAAQOs+fPnW2aZIOVilEFGyvLzzz9bxx9/vOb51ltvheRpZiywjNKxLr30Umvx4sXWmDFjLPMSsx566KGQcEHbkaAVKF/L8/zzz+uNtXDhQgfBli1brNKlS1s33HCDcyzTGz179rTMCqBZU0DPPPOMZd7ollmA0rn0t99+2zriiCMsYxk5xzKxccIJJ1itW7d2stqzZ4++NLp06eIcS9fGyJEjrVKlSlnG6oqogO6//37LrBpr/fPPP04R+vXrZx166KEWlHhQhU0wX3Zj6iMZy0dGjRolJ510kpM4liE2N5AYReQcy+SGsTh01c2hQ4dmMtuQvMaNGyedO3cWo3Cc42imYkXcihUrOscysYEVd911YR5qMUpIm8zpzt9YXdKnTx+ZMWNGxKyMxSxt2rSRkiVLOuc7dOggWLAQy0gHVaiAAlIzDRo0EGNthJRm3rx5uux0kyZNQo5nYmfr1q3SvXt3eeKJJ9TnkIk8I+UBRVO3bl1VhHjATFNMfRt48DMtvXr1EtO8kTvvvFNXi7366qtl165d0q1bt7QXBf6dhx9+WEqUKBExrx9//FFMEz7knL0PH1pgJaimWb6XyygAq169epZZ+tcyN3nGcRjlY7Vs2VLzNc7xrDTBjNPXMg+cdeaZZ1pmJkTLPPBW8+bNtSzwdWRDbr/9ds3fPND6+8ILL2S0GGvWrNF8w31A4ATflFt2796tYYcPH+4+HKjt4oHVjHlcMFgfbdu21WbGnDlzor710oUIZv7rr78uS5YsSVcWcaVrfBeCLucPP/xQVqxYIUcffbTGM74NeeCBB+SWW26RRo0axZVWKgLBIpw+fbo8/vjjcs4554jpLBDjn5Pt27dr8ygVefhNA71yxkEeEt3eN4oo5HiQdtgEC1JtmLKY3jBp0aKFoEseXfD169fPaAkx/7Pp3ZELL7xQ56WGAjSOcS0DmgGmRy5j5cH8z2XKlJHTTjvNUT7I/JJLLtEyZNK3gXoZO3as9O3bVxWfsU7F9IrJ+eefL4888kjGmETLqFKlSoL5u92yefNm3QXDoAotoADVzKZNm+Tss89WxyHG3GRjovENGzbIb7/9pg8bHji33HTTTeoktxWS+1y6tjHmxXTDhySPh61o0aIF3vghgVK8Y7rdBeOA2rdvH5IyHL0YC2S6yHXsTcjJDO6ASbivZ926dVoC23LMYHHizooWUNyo0hsQNzecrHiLwfmcDeWDK0Rv0+rVq0P+0BsGee2112TatGm6nal/UMjggaaYLWgiglfjxo3tQ2n/tZXgd999F5IXLMRixYrJ4YcfHnI80zvghMGJ7hHSZriC9tBlspma8HUHyiOVx4UZPXq0Ogwx7gZjX9x/5oHLKplsOaFx0aZ3xypevLh1xRVXWHDAggUc86ZZZmEcTqYEDvEzzjjDqlChgjV79mwLA0eHDRumY28wIDFTEs0JbaxWHbTau3dvy1jSllGMllm+yBoyZEimiuYrHw5E9IUt9ZFOPfVUVUDmDVLgt1WrVqnPMIEUs6mAUEyMwDafYCgXKCPjI7PM+JYEriA1QfGQmyaYjoZGPRnLx7ruuussjBbPlERTQMgfPWMYeIiyQfmgbJlU0n4YcF2whG1GRsgWAXz/BYcqBmhmU9DrhbLgu7T9998/m0UpkLdRAtp8xkKSRlkXOB+0A1RAQasRlocE8ogAndB5VNm8VBIIGgEqoKDVCMtDAnlEgAoojyqbl0oCQSNABRS0GmF5SCCPCFAB5VFl81JJIGgEqICCViMsDwnkEQEqoDyqbF4qCQSNABVQ0GqE5SGBPCJABZRHlc1LJYGgEaACClqNsDwkkEcEqIDyqLJ5qSQQNAJUQEGrEZaHBPKIABVQHlU2L5UEgkaACihoNcLykEAeEaACyqPK5qWSQNAIUAEFrUZYHhLIIwJUQHlU2bxUEggaASqgoNUIy0MCeUSACiiPKpuXSgJBI0AFFLQaYXlIII8IUAHlUWXzUkkgaASogIJWIywPCeQRASqgPKpsXioJBI0AFVDQaoTlIYE8IkAFlEeVnY1LNUsDyyOPPCJ9+vSRf/75JxtFYJ4BJkAFFODKyVbR3njjDSlSpIj8+eefcRdh3759MmrUKNm5c6cTZ9CgQVKpUiXp37+/PPfcc1KxYkUZNmyYcz6ZjQULFsi8efOcJMw66NKoUSNnnxu5QSD4i0fnBse8L+Vrr70m119/vVx55ZXK4vPPP5c77rhD+vXrp2uor169WmAN3X333XLJJZfIYYcd5psZ0jnllFPkhRdekGbNmmk62D/88MN9p8mI2SFABZQd7oUuV1hAbpk7d66ULFlSbrvtNpkyZYoULVpUbr31Vvn1119l5cqVSSkgy7IEf2656qqr3LvczhECbILlSEWls5hvvfWWtGrVSg455BDp0KGD/P777wWyQ7MM1kb58uW1WdWmTRv54YcfNNy0adPk3nvv1W2Eeemll+TQQw9Vn8+6deuctEqXLq1NsZNPPlmPoQnVtGlTef/996Vq1arSvHlz2bRpk+zatUvuuusuqVevnpQqVUpq1aolN954o/z999/616RJE43/wAMPOBbXgAED5IorrtDjn332mSCPFStW6HUdfPDBUr9+fcE1uGXVqlVyzTXXSOXKleX444+XiRMnahrPPvusOxi300iACiiNcHMh6a+++kouuugiqVKliowdO1Z/b7rpppCiT5o0STp27KgP8fPPPy+9evUSxMMxSJ06dfRBx3bv3r3VF3POOeeosoKigjUUSbZs2SILFy4U+G9OP/10DQ8Fh2Yc8unSpYsqszPOOEOeeuopefTRR6VEiRLq0EZ6LVu21OYcttHEsxXi1q1bZdGiRdK6dWtVLoMHD5YDDzxQr/Pnn39GcFVyKD/yHzp0qKYJRzmUlFtpamD+Sx8BY8pS8pjAWWedZZmHP4TABRdcgPaNtXHjRj1+8803W+3btw8JM3DgQA3z119/6fHx48fr/vbt251w5uG2jGNYjxvrx7r44outpUuXOueN5aXnjPXiHNuxY4d1wgknWE8//bRzDBs4dvbZZ+uxf//9V+ONGTNG9/Hv2muvtRo2bKj77777rp5/7LHHnPNr1qzRY6NHj9Zjw4cP1/3vv//eCYP0cN3Gb+Uc40Z6CdACSp9uz4mUYcmcf/75IWXt3LlzyP6TTz4pb775ph777bffZObMmWIeXN1HsyianHTSSWqJDBkyRJtRaOoZJSFGCYVEQdPLFlgqixcvlh49eqjTGmHRNDJKR5tfdrh4fmE52YImHnxSsI4gX3zxhTb7ateubQdxrDjnADfSToAKKO2Ig5sB/C3oakf3uFvgE3ELwnTv3l2bSGiqdevWTZYvX65BzPvRHTTidoUKFbS5tmzZMilWrJgYyyQkHJSDWz755BP1B8H/g+YdxhEZy6qA49kdJ9I2/FBuQfPNdpZDsTVu3Nh9WnvRatSoEXKMO+klQAWUXr6BTr1cuXJSpkwZdfy6C7pt2zb3rlx++eUC6wU+GDh2165dq74eBIqmgOCYht/GLVA0cFJDEbkFSskWpA2/EXrNXn/9dVWQsNLq1q1rB4n7F2OZogmUomk+Fji9efPmAsd4IH0EqIDSxzbwKeMBRe/Q7NmzQ8oKC8QWNH1mzZolN9xwgxg/i9SsWVNPoZkE2bt3r/7aD7ttYcyfP1/HAbmVGc5BmYRbPJrA//59/PHHgjgjR44U43cSKEmM+1myZImTF5QTxM77f1ET+kHvG8po/FxOvE8//bSAMnZOciMtBKiA0oI1dxK98847BdbKiBEj9MGfPn16yGhlNFvQ7Q0LCD1N8KGgm9o4cfUibR8QLCnIyy+/LOhpuvDCC2X37t1qPWHsD3q8brnlFu1hijVm59RTT9VmGnrkjENa0FXetWtXzRv7EFhM8Oeg+x4jov1Iz5491fpDd/0zzzyjo7XbtWunI8D9pMc4Pgmk18fN1HOBgPk8wjJ+H+0BMn4TyzS1dNvuBfvggw8s41C2jJVjFS9e3DLNKMuM4bGMIrDsnij0hjVo0EDjmRHRetkTJkywzIhnPWZuT+uAAw6wjEPaQWL3gqGHyi3m0w3L+Jo0L6MALdM9rvGwbfxWGhQ9cygL0odE6gUzAx71nP2vbNmyem32vlGUlmnuWcbKsowz2kJ5jSK1zCckdhD+pplAEaTvU3cxWiEigNvgl19+kSOPPDKqFbB+/XodT2Me5KhXDh8KBhwa5aBhkC7G4cB6wrdhsKjiEcSD9YPm2n777RcxCj5uRbMOzupE5aefftK4xxxzjBMV1hwsOXziAauLkn4CbIKln3FO5AAfTrVq1aIqH1wEPiyNpXwQBqOObeWDfaSL77TOPPPMuJWPHe+oo46KqnwQxlhUvpQP4s6ZM0fQBY+BiBCMvsa3a/vvv7+0aNFCj/Ff+gnQAko/Y+YQQAJQOPgodsaMGapYN2zYoIoTI6ExipuSGQJUQJnhzFwCSgCObfS8oVse3565rbeAFrlQFYsKqFBVJy+GBHKLAH1AuVVfLC0JFCoCVECFqjp5MSSQWwSogHKrvlhaEihUBKiAClV18mJIILcIUAHlVn2xtCRQqAhQARWq6uTFkEBuEaACyq36YmlJoFARoAIqVNXJiyGB3CJABZRb9cXSkkChIkAFVKiqkxdDArlFgAoot+qLpSWBQkWACqhQVScvhgRyiwAVUG7VF0tLAoWKABVQoapOXgwJ5BYBKqDcqi+WlgQKFQEqoEJVnbwYEsgtAlRAuVVfLC0JFCoCVECFqjp5MSSQWwSogHKrvlhaEihUBP4fghUXV+fDYZIAAAAASUVORK5CYII=)
dat$rating.c <- dat$rating - mean(dat$rating)
Note that we mean-center the covariate.
Importantly, when we use a covariate (i.e., continuous variable), then it is not possible to use empirical=TRUE
. We have to switch to empirical=FALSE
.
# simulate data
fix <- c(200,20, 7, 5) # set fixed effects
sd_Subj <- c(30, 10, 5, 5) # set random effects standard deviations for subjects
sd_Item <- c(10) # set random effects standard deviations for items
sd_Res <- 50 # set residual standard deviation
dat$ysim <- simLMM(form=~ X*rating.c + (X*rating.c | Subj) + (1 | Item), data=dat,
Fixef=fix, VC_sd=list(sd_Subj, sd_Item, sd_Res), CP=0.3,
empirical=FALSE)
## Data simulation from a linear mixed-effects model (LMM)
## Formula: gaussian ~ 1 + X1 + rating.c + X1:rating.c + ( 1 + X1 + rating.c + X1:rating.c | Subj ) + ( 1 | Item )
## empirical = FALSE
## Random effects:
## Groups Name Std.Dev. Corr
## Subj (Intercept) 30.0
## X1 10.0 0.30
## rating.c 5.0 0.30 0.30
## X1:rating.c 5.0 0.30 0.30 0.30
## Item (Intercept) 10.0
## Residual 50.0
## Number of obs: 300, groups: Subj, 15; Item, 20
## Fixed effects:
## (Intercept) X1 rating.c X1:rating.c
## 200 20 7 5
# check group means
dat %>% group_by(X) %>% summarize(M=mean(ysim))
## # A tibble: 2 x 2
## X M
## * <fct> <dbl>
## 1 X1 174.
## 2 X2 228.
# check fixed effects + random effects
summary(lmer(ysim ~ Xn*rating.c + (Xn*rating.c || Subj) + (1 | Item), data=dat, control=lmerControl(calc.derivs=FALSE)))
## Linear mixed model fit by REML. t-tests use Satterthwaite's method [
## lmerModLmerTest]
## Formula: ysim ~ Xn * rating.c + (Xn * rating.c || Subj) + (1 | Item)
## Data: dat
## Control: lmerControl(calc.derivs = FALSE)
##
## REML criterion at convergence: 3224.8
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -2.95068 -0.61584 -0.03999 0.65256 2.74467
##
## Random effects:
## Groups Name Variance Std.Dev.
## Item (Intercept) 173.637 13.177
## Subj Xn:rating.c 4.919 2.218
## Subj.1 rating.c 0.000 0.000
## Subj.2 Xn 0.000 0.000
## Subj.3 (Intercept) 655.056 25.594
## Residual 2545.620 50.454
## Number of obs: 300, groups: Item, 20; Subj, 15
##
## Fixed effects:
## Estimate Std. Error df t value Pr(>|t|)
## (Intercept) 201.946 7.808 16.951 25.863 4.63e-15 ***
## Xn 29.072 4.195 16.404 6.930 2.96e-06 ***
## rating.c 9.183 2.346 132.621 3.915 0.000144 ***
## Xn:rating.c 6.205 2.039 12.925 3.043 0.009480 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) Xn rtng.c
## Xn 0.000
## rating.c 0.001 0.095
## Xn:rating.c 0.041 0.007 0.014
nsubj <- seq(10,100,1)
nsim <- length(nsubj)
COF <- data.frame()
for (i in 1:nsim) { # i <- 1
#print(paste0(i,"/",nsim))
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=nsubj[i]) +
random.factor("Item", groups="X", instances=2)
dat <- design.codes(design)
nsj <- length(unique(dat$Subj))
contrasts(dat$X) <- c(-1, +1)
dat$Xn <- model.matrix(~X,dat)[,2]
for (j in 1:10) { # j <- 1
dat$rating <- round( simLMM(form=~ 1 + (1 | Subj) + (1 | Item), data=dat,
Fixef=5, VC_sd=list(1, 1, 1), empirical=FALSE, verbose=FALSE) )
dat$rating.c <- dat$rating - mean(dat$rating)
fix <- c(200,20, 7, 5) # set fixed effects
sd_Subj <- c(30, 10, 5, 5) # set random effects standard deviations for subjects
sd_Item <- c(10) # set random effects standard deviations for items
sd_Res <- 50 # set residual standard deviation
dat$ysim <- simLMM(form=~ X*rating.c + (X*rating.c | Subj) + (1 | Item), data=dat,
Fixef=fix, VC_sd=list(sd_Subj, sd_Item, sd_Res), CP=0.3,
empirical=FALSE, verbose=FALSE)
LMM <- lmer(ysim ~ Xn*rating.c + (Xn*rating.c || Subj) + (1 | Item), data=dat,
control=lmerControl(calc.derivs=FALSE))
LMMcof <- coef(summary(LMM))[4,] # extract the stats for the interaction
COF <- rbind(COF,c(nsj,LMMcof))
}
}
names(COF) <- c("nsj","Estimate","SE","df","t","p")
COF$sign <- as.numeric(COF$p < .05 & COF$Estimate>0)
COF$nsjF <- gtools::quantcut(COF$nsj, q=seq(0,1,length=10))
COF$nsjFL <- plyr::ddply(COF,"nsjF",transform,nsjFL=mean(nsj))$nsjFL
#save(COF, file="data/Power5.rda")
We are here only interested in the interaction between the covariate and the factor, i.e., whether the slopes differ between conditions. Of course, one could also study the main effects.
load(file=system.file("power-analyses", "Power5.rda", package = "designr"))
ggplot(data=COF) +
geom_smooth(aes(x=nsj, y=sign))+
geom_point( stat="summary", aes(x=nsjFL, y=sign))+
geom_errorbar(stat="summary", aes(x=nsjFL, y=sign))+
geom_line( stat="summary", aes(x=nsjFL, y=sign))
![](data:image/png;base64,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)
# determine number of subjects needed for a power of 50%
m0 <- loess(sign ~ nsj, data=COF)
COF$pred <- predict(m0)
idx <- COF$pred>0.5
min(COF$nsj[idx]) # 84
## [1] 56
Logistic GLMM
We can also simulate data from a logistic GLMM. This can be implemented by setting the argument family="binomial"
. Note, however, that the argument empirical=TRUE
does not work for family="binomial"
. To be precise, the random effects for subjects or items can still be sampled using empirical=TRUE
; however, the residual Bernoulli noise is not simulated exactly.
design <-
fixed.factor("X", levels=c("X1", "X2")) +
random.factor("Subj", instances=50) +
random.factor("Item", groups="X", instances=10)
dat <- dplyr::arrange(design.codes(design), Subj, Item)[c(3, 1, 2)]
(contrasts(dat$X) <- c(-1, +1))
## [1] -1 1
dat$Xn <- model.matrix(~X,dat)[,2]
fix <- c(0.5,2) # specify fixed-effects
sd_Subj <- c(3 ,1) # specify subject random effects (standard deviation)
sd_Item <- c(1) # specify item random effects (standard deviation)
dat$ysim <- simLMM(form=~ X + (X | Subj) + (1 | Item), data=dat,
Fixef=fix, VC_sd=list(sd_Subj, sd_Item), CP=0.3,
empirical=FALSE, family="binomial")
## Data simulation from a logistic generalized linear mixed-effects model (GLMM)
## Formula: binomial ~ 1 + X1 + ( 1 + X1 | Subj ) + ( 1 | Item )
## empirical = FALSE
## Random effects:
## Groups Name Std.Dev.Corr
## Subj (Intercept) 3.0
## X1 1.0 0.30
## Item (Intercept) 1.0
## Number of obs: 1000, groups: Subj, 50; Item, 20
## Fixed effects:
## (Intercept) X1
## 0.5 2.0
dat %>% group_by(X) %>% summarize(M=mean(ysim))
## # A tibble: 2 x 2
## X M
## * <fct> <dbl>
## 1 X1 0.322
## 2 X2 0.788
glmer(ysim ~ X + (X | Subj) + (1 | Item), data=dat, family="binomial", control=lmerControl(calc.derivs=FALSE))
## Warning in glmer(ysim ~ X + (X | Subj) + (1 | Item), data = dat, family =
## "binomial", : please use glmerControl() instead of lmerControl()
## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: ysim ~ X + (X | Subj) + (1 | Item)
## Data: dat
## AIC BIC logLik deviance df.resid
## 696.9263 726.3729 -342.4632 684.9263 994
## Random effects:
## Groups Name Std.Dev. Corr
## Subj (Intercept) 3.631
## X1 1.251 0.23
## Item (Intercept) 1.450
## Number of obs: 1000, groups: Subj, 50; Item, 20
## Fixed Effects:
## (Intercept) X1
## 0.8765 2.8495
We don’t execute the power simulation here, since this would take a long time. But it should be a straightforward extension from the other analyses shown in detail.
Custom probability distributions and link functions
Maybe you want to simulate data from a GLMM with a different probability density function (PDF) or with a different link function. Currently, such further family options are not implemented in simLMM
(except for family="lognormal"
). However, using the argument family="lp"
, it is possible to extract the linear predictor from the GLMM, and to compute the link function and desired probability distribution manually.
# provide the linear predictor
# i.e., predictions of the LMM before passing through the link function / probability density function (PDF)
# this allows using custom links / PDFs
dat$lp <- simLMM(form=~ X + (X | Subj) + (1 | Item), data=dat,
Fixef=fix, VC_sd=list(sd_Subj, sd_Item), CP=0.3,
empirical=FALSE, family="lp")
## Data simulation from a linear mixed-effects model (LMM): linear predictor
## Formula: lp ~ 1 + X1 + ( 1 + X1 | Subj ) + ( 1 | Item )
## empirical = FALSE
## Random effects:
## Groups Name Std.Dev.Corr
## Subj (Intercept) 3.0
## X1 1.0 0.30
## Item (Intercept) 1.0
## Number of obs: 1000, groups: Subj, 50; Item, 20
## Fixed effects:
## (Intercept) X1
## 0.5 2.0