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Diet and heart disease

Example where the observations are of mixed type: continuous and discrete. Also and example of skewed random effects.
A description of the model and data is given here: skewed_re.pdf
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:
  1. Random effects normally distributed
  2. Non-parametric model for the random effects
A description of the model and data is given here: skewed_re.pdf. 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.


By looking at the result files (diet.par and diet_sk.par) we observe the following:
  1. The estimated parameters under the normal model match very closely the estimates in Table 14.1 of Skrondal and Rabe-Hesketh (2004).
  2. 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.


Skrondal and Rabe-Hesketh (2004), Generalized Latent Variable Modeling: Multilevel, Longitudinal and Structural Equation Models. Chapman & Hall