if (!requireNamespace("pacman")){
install.packages("pacman")
}## Loading required namespace: pacmanpacman::p_load(sjstats)
pacman::p_load(sjPlot)
pacman::p_load(lme4)
pacman::p_load(MASS)Simulate Data
100 participants will be ranking 20 items based on importance simulated from a multivariate normal distribution.
n.participants <- 100
n.items <- 20
Sigma <- 0.9 ^ toeplitz(1:n.items)
diag(Sigma) <- 1
# Subject needs to be a factor for lmer
DT <- data.frame(Subject_ID = factor(rep(1:n.participants, each = n.items)),
Item = rep(1:n.items, n.participants),
Importance = as.vector(replicate(n.participants, mvrnorm(1, mu = rep(0,n.items), Sigma = Sigma))))
head(DT)## Subject_ID Item Importance
## 1 1 1 1.6680635
## 2 1 2 1.4818320
## 3 1 3 0.8447595
## 4 1 4 1.1937203
## 5 1 5 1.3669878
## 6 1 6 1.3405396str(DT)## 'data.frame': 2000 obs. of 3 variables:
## $ Subject_ID: Factor w/ 100 levels "1","2","3","4",..: 1 1 1 1 1 1 1 1 1 1 ...
## $ Item : int 1 2 3 4 5 6 7 8 9 10 ...
## $ Importance: num 1.668 1.482 0.845 1.194 1.367 ...Calculate ICC
fit0 <- lme4::lmer(Importance ~ 1 + (1 | Subject_ID), data = DT)
sjPlot::tab_model(fit0)| Importance | |||
|---|---|---|---|
| Predictors | Estimates | CI | p |
| (Intercept) | -0.06 | -0.19 – 0.06 | 0.309 |
| Random Effects | |||
| σ2 | 0.55 | ||
| τ00 Subject_ID | 0.37 | ||
| ICC | 0.40 | ||
| N Subject_ID | 100 | ||
| Observations | 2000 | ||
| Marginal R2 / Conditional R2 | 0.000 / 0.400 | ||
performance::icc(fit0)## # Intraclass Correlation Coefficient
##
## Adjusted ICC: 0.400
## Conditional ICC: 0.400