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.