# Do I really need to add time as random effect in mixed model for repeated measures?

I'm fitting a mixed model to explore effects of weather conditions (A,B, C; all factors) and their interactions on response Y (continuous). Study included several subjects and measures have been taken (for every subject) on many days. I'm not interested in the effect of time (or day). I'm selecting fixed explanatory variables based on AIC. I started the selection process with just subject as random effect

fm1 <- lmer (Y ~ A*B*C + (1|subject), df)


everything ran smoothly and I obtained an interesting "final" model with all main effects and one interaction being significant. I tried the same process adding day as random effect

fm2 <- lmer(Y ~ A*B*C + (1|subject) + (1|day), df)
> anova(fm1,fm2)
refitting model(s) with ML (instead of REML)
...
Df    AIC    BIC  logLik deviance  Chisq Chi Df Pr(>Chisq)
fm1 22 8011.0 8111.5 -3983.5   7967.0
fm2 23 7944.9 8049.9 -3949.5   7898.9 68.097      1  < 2.2e-16 ***


and I obtained significantly lower AIC's but ended up with just one significant factor and, in my view, with much less interesting results.

Now my questions are:

-are the random structures in fm1 and fm2 specified correctly for this design?

-do I need to include (1|day) in the model (even if I lose much of the effects I'm studying)?

Any help or comment is very appreciated. Thanks.

• It could make sense if you had repeated measures within subject and day. – Michael M Dec 11 '16 at 18:47

I'm selecting fixed explanatory variables based on AIC

Do you mean to say that in addition to A, B, and C, there are some potential fixed effects that you threw out on the basis of an AIC-based model selection? If you want to consider all the potential fixed effects and also the question of whether to include a random effect of day, then you should be looking at the AIC of all the combinations, rather than using AIC to choose the fixed effects and then doing a separate AIC-based comparison for choosing the random effects.

I obtained significantly lower AIC's

The way you're supposed to use AIC for model selection is just to choose the model with the lowest AIC. If you're using a significance test here, you're doing something wrong.

are the random structures in fm1 and fm2 specified correctly for this design?

They both seem consistent with the very limited information you've given us about the design of the study.

do I need to include (1|day) in the model (even if I lose much of the effects I'm studying)?

There are lots of ways to select models, some of which are reasonable and some of which are unreasonable. AIC has at least some arguments in its favor. On the other hand, choosing a model because it gets more interesting results, or because it has a larger number of significant coefficients, makes no sense.