model specification for repeated measure

Hi Dot,

This specification would yield a single coefficient for the
between-individual and within-individual effects. That is, you?re assuming
the association is the same over time as it is across individuals at a
single point in time. I wouldn?t expect this to be a safe assumption, and
there?s a pretty straightforward fix: centre your time-varying predictors
by their mean for each person. That will yield within effects equivalent to
what you?d get from a fixed effects model.

For more information about this, see:
https://www.cambridge.org/core/services/aop-cambridge-core/content/view/
S2049847014000077
and/or
https://www.researchgate.net/publication/299604336_Fixed_
and_Random_effects_models_making_an_informed_choice

Hope that?s useful,
Malcolm


Malcolm Fairbrother
Professor of Sociology
Ume? University <http://www.umu.se/english>
Sweden



Date: Thu, 1 Feb 2018 21:07:10 +1030
From: Dot Dumuid <haveaballphysio at gmail.com>
To: r-sig-mixed-models at r-project.org
Subject: [R-sig-ME] model specification for repeated measure

Dear mixed model experts,
We have a dataset of older adults. We measured their mental health (MH) 6
months before retirement and again 12 months post retirement.
At both of these time points we also measured their physical activity (PA)
(min/day), income (INC) and general health (GH).
We would like to create a model that tells us if change in physical
activity over the retirement threshold predicts change in mental health,
and we'd like to use the model to predict how much mental health is
predicted to change when physical activity is increased from perhaps 15
minutes to 60 minutes. We'd like to use a mixed model rather than just
using change (difference) scores. And we'd like to control for things like
change in general physical health and change in income.

This is what the data look like

*ID  time  MH    PA    GH    INC*
01  pre     4      15     56     560
02  pre     5      30     30    1200
..    .....     ..       ..       ..        ...
01  post   7      40     50      50
02  post   8      45     30      0

I'm not sure how best to build the model. Something like this?

model <- lmer (MH ~ PA * time + GH + INC + (1|participant.ID) )

Thank you in advance.
Dot