RE: st: Mixed model for longitudinal data: Time discrete or continuous?

[Abdelouahid Tajar <a_tajar@hotmail.co.uk>]

Thanks Nick,

 I have a pilot study of 39 patients, 18 in group A (treatment 1) and 21 in group B (treatment 2). 
I have 6 time points baseline then a response after each four weeks 
 the time variable is coded as: 5 ,9,13,17,21 and 25. I have a binary outcome (yes=1 and No=0)

I  used gllamm in stata  because it allows computing predicted probabilities taking into account the random effect using gllapred,


I have considered 3 types of models:

Model1 ( Time discrete) the covariates: are group+ 5 dummy variables for time (1 time value was included as reference) and 5 interactions of group and the 5 time-dummies, in total 11 parameters.

Model2 ( time as continuous) 3 parameters, group time and interaction group*time (time centered at t=13)

Model 3: adds to model 2, a square term for time, time^2 and an interaction between group*time^2 which gives 5 parameters in model 3.

The models criteria are as follows:

Model1: AIC=211.48 and condition number =7.49
Model 2:AIC=204.78 and condition number =79.85
Model3: AIC=206.91 and condition number =673.20

According to gllamm book, the condition number is the square of the largest to the smallest eigenvalues of the Hessian matrix. Lower condition number are preferred for model identification.