# Random effects with a skewed distribution
ADMB Files Normal random effects
Code: diet.tpl Data: diet.dat Initial values: diet.pin Expected Results: diet-expected-results.par
Skewed random effects
Code: diet_sk.tpl Data: diet_sk.dat Initial values: diet_sk.pin Expected Results: diet_sk.par
| ### Model description It is customary to assume that random effects are normally distributed. Skrondal and Rabe-Hesketh (2004, Section 14.2) consider a measurement error problem, and compare the following two models: Random effects normally distributed Non-parametric model for the random effects A description of the model and data is given here. The non-parametric 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 ADMB-RE (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 ADMB-RE 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 Rabe-Hesketh (2004). The log-likelihood value for the normal model is -1372.35, while the log-likelihood 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 Rabe-Hesketh (2004), Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models. Chapman & Hall