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


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Mixed model for longitudinal data: Time discrete or continuous?
Date   Fri, 1 Jun 2012 11:15:14 +0100

This is really a question about the science behind your data. The
difference is between fitting a term linear in time (and possibly one
squared in time)  and a more general but less parsimonious treatment
of time. Which makes most sense depends on what you think is the
better representation of your generating process. Another answer is
try them both and see which works better. This is likely to sound
flippant, but I don't see how your formulation lets us advise you well
on what is better for your data and your research problem.

Nick

On Fri, Jun 1, 2012 at 10:52 AM, Abdelouahid Tajar
<a_tajar@hotmail.co.uk> wrote:

> For mixed models (using xtmixed, xtlogit ect...) with
> longitudinal data in the standard situation with two covariates: time (0,1,2,3)
> (as an example) and a binary variable (0,1) for group.
>
> People often use time as a CONTINUOUS variable.
>
>
>
> In models which include an interaction term between time and group (which often
> is the case) we have three fixed effect parameters b1=time, b2=group and
> b3=interaction_time_group.
>
>
>
> Now if time is treated as DISRETE
> with time (0,1,2,3) we have 7 parameters: 1 for group,  3 for the 3
> dummies of time and the 3 for interaction terms between time and group.
>
>
>
> Compared to the model with discrete time, the model with time as continuous
> (which could also have a time^2 term) has clearly fewer parameters even when
> time^2 is included.
>
>
>
> My question is how to choose between the two models? The continuous time model and
> discrete time model?

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