ADMB Files
Normal random effects



Model description
It is customary to assume that random effects are normally distributed.
Skrondal and RabeHesketh (2004, Section 14.2) consider a measurement error problem, and
compare the following two models:
 Random effects normally distributed
 Nonparametric model for the random effects
A description of the model and data is given here. The nonparametric model 2)
indicates that the random effects distribution is skewed to the right.
In this example we show: 1) how to implement the model with normal random effects in ADMBRE (diet.tpl) and 2)
how to modify the the program to obtain skewed random effects (diet_sk.tpl).
Only a small number of changes are needed to modify the ADMBRE code to
implement the skewed random effects.
Results
By looking at the result files (diet.par and diet_sk.par) we observe the following:
 The estimated parameters under the normal model match very closely the estimates in
Table 14.1 of Skrondal and RabeHesketh (2004).
 The loglikelihood value for the normal model is 1372.35, while the loglikelihood for the model with
skewed random effects is 1326.49. Hence, given that the skewed model only contains one extra parameter,
it gives a much better fit to data.
References
Skrondal and RabeHesketh (2004), Generalized Latent Variable Modeling: Multilevel,
Longitudinal and Structural Equation Models. Chapman & Hall
