Loading packages
library(simr)
library(effectsize)
Defining covariates
part <- factor(1:40)
place.residence <- factor(c("A_cat", "B_abroad"))
time <- factor(c("A_prepand", "B_postpand"))
place.residence_full <- rep(rep(place.residence, each=20),2)
time_full <- rep(time, each=40)
part_full <- rep(part, each=2)
covars <- data.frame( participant =part_full, place.residence=place.residence_full, time=time_full)## participant place.residence time
## 1 1 A_cat A_prepand
## 2 1 A_cat A_prepand
## 3 2 A_cat A_prepand
## 4 2 A_cat A_prepand
## 5 3 A_cat A_prepand
## 6 3 A_cat A_prepandCreating the Generalized Mixed Effects Model
Determining the estimates
We have to define intercept and slops for the fixed effects.
The model has 1 intercept.
Every fixed effect has 2 levels = 1 slope per fixed effect
What is the likelihood of Catalans celebrating caga tió when they are abroad compared to when they are in Cat?
What is the likelihood of Catalans celebrating caga tió after the pandemic when compared to before the pandemic?
The interaction (2x2) has 1 slope = 1 slope per interaction
- Does time (before pandemic-after pandemic) moderate the likelihood of Catalans celebrating caga tió with respect to their place of residence (abroad or in Cat)?
Calculating the log odds ratio
We have to calculate the log odds ratio to include them in our model.
We will first determine the effect size (based on previous studies!)
We will work with a medium effect size
The statistic for effect sizes is Cohen’s d (small = 0.2, medium = 0.5, large = 0.8)
## [1] 2.476632Adding random effects
Random intercept for participants
MakeGlmer function from simr package
gmodel <- makeGlmer(x ~ place.residence * time + (1|participant) , family="binomial",fixef=fixed, VarCorr=rand, data=covars)
summary(gmodel)## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: x ~ place.residence * time + (1 | participant)
## Data: covars
##
## AIC BIC logLik deviance df.resid
## 117.7 129.6 -53.9 107.7 75
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.0000 0.8463 0.8463 0.8463 1.0000
##
## Random effects:
## Groups Name Variance Std.Dev.
## participant (Intercept) 0.4 0.6325
## Number of obs: 80, groups: participant, 40
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9083 0.4939 1.839 0.0659 .
## place.residenceB_abroad 0.9083 0.6988 1.300 0.1937
## timeB_postpand 0.9083 0.6980 1.301 0.1932
## place.residenceB_abroad:timeB_postpand 0.9083 0.9886 0.919 0.3582
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) plc.B_ tmB_ps
## plc.rsdncB_ -0.707
## timB_pstpnd -0.708 0.500
## plc.rsB_:B_ 0.500 -0.707 -0.706Running Power
Power for place of residence
## Power for model comparison, (95% confidence interval):
## 26.00% (17.74, 35.73)
##
## Test: Likelihood ratio
## Comparison to ~time + (1 | participant)
##
## Based on 100 simulations, (38 warnings, 1 error)
## alpha = 0.05, nrow = 80
##
## Time elapsed: 0 h 0 m 37 sPower for the interaction
## Power for model comparison, (95% confidence interval):
## 6.00% ( 2.23, 12.60)
##
## Test: Likelihood ratio
## Comparison to ~time + place.residence + (1 | participant)
##
## Based on 100 simulations, (32 warnings, 0 errors)
## alpha = 0.05, nrow = 80
##
## Time elapsed: 0 h 0 m 40 sExtending the model
## [1] 300## Generalized linear mixed model fit by maximum likelihood (Laplace
## Approximation) [glmerMod]
## Family: binomial ( logit )
## Formula: x ~ place.residence * time + (1 | participant)
## Data: covars
##
## AIC BIC logLik deviance df.resid
## 117.7 129.6 -53.9 107.7 75
##
## Scaled residuals:
## Min 1Q Median 3Q Max
## -1.0000 0.8463 0.8463 0.8463 1.0000
##
## Random effects:
## Groups Name Variance Std.Dev.
## participant (Intercept) 0.4 0.6325
## Number of obs: 80, groups: participant, 40
##
## Fixed effects:
## Estimate Std. Error z value Pr(>|z|)
## (Intercept) 0.9083 0.4939 1.839 0.0659 .
## place.residenceB_abroad 0.9083 0.6988 1.300 0.1937
## timeB_postpand 0.9083 0.6980 1.301 0.1932
## place.residenceB_abroad:timeB_postpand 0.9083 0.9886 0.919 0.3582
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Correlation of Fixed Effects:
## (Intr) plc.B_ tmB_ps
## plc.rsdncB_ -0.707
## timB_pstpnd -0.708 0.500
## plc.rsB_:B_ 0.500 -0.707 -0.706Power for place of residence in extended model
## Power for model comparison, (95% confidence interval):
## 90.00% (55.50, 99.75)
##
## Test: Likelihood ratio
## Comparison to ~time + (1 | participant)
##
## Based on 10 simulations, (1 warning, 0 errors)
## alpha = 0.05, nrow = 300
##
## Time elapsed: 0 h 0 m 5 sPower for the interaction in extended model
## Power for model comparison, (95% confidence interval):
## 20.00% ( 2.52, 55.61)
##
## Test: Likelihood ratio
## Comparison to ~time + place.residence + (1 | participant)
##
## Based on 10 simulations, (1 warning, 0 errors)
## alpha = 0.05, nrow = 300
##
## Time elapsed: 0 h 0 m 5 sYou need 16 times the sample size when power is 80% for main effect to estimate an interaction with power 80%!