I'm examining how boldness of individuals change with time. My data consists of individuals repeatedly measured across trials for boldness scores. First, I plotted each individual to see its mean and variance from the following plot:
The x axis depicts individuals and y axis depicts boldness scores. As we can see, individuals differ from each other in their mean scores as well as variance.
Next, I constructed a random slope random intercept plot, to see how boldness vary with time (trials). As lmer resulted in singular fitted model, I used the stan_lmer function from the rstanarm package in R (using the code stan_lmer(Boldness~Trial+(Trial|individualID,data=mydata)). From the model diagnostics, it appeared the model fit was reasonably well. Below is the random intercept random slope plot:
Here, each line represents an individual. From the plot, there appears to be very less variation between individuals in the intercept. Similarly, individual slopes are similar indicating similar variation in boldness across time (trials).
However, the boxplot of the raw data showed significant differences between individuals in their means and variances. These differences are very little in the random intercept random slope plot. I'm trying to figure why this is so? Individuals with greater mean values for boldness should have greater intercepts in the random slope plots. Similarly, individual showing greater variance in boldness should show greater variation in slopes. Is my model correct?
Any help is much appreciated. Thanks.