Residual Sum Squares Issues with Linear Mixed Models

2 messages · Howsun.Jow at newcastle.ac.uk, Douglas Bates

Fri, Nov 20, 2009 2:23 AM #

I'm having problems understanding why the residual sum squares for a reduced
linear mixed model is sometimes smaller for a "reduced" model than for a
"full" model. Take the "Pastes" dataset for example:

fm3M <- lmer(strength ~ 1 + (1|batch) + (1|sample), Pastes), REML=F)
fm4M <- lmer(strength ~ 1 + (1|sample), Pastes), REML=F)

[1] 21.04984

[1] 21.03147

The reduced model seems to fit the data better than the full model. Is there
something fundamental I'm missing about linear mixed effects models?

Douglas Bates

Fri, Nov 20, 2009 6:50 AM #

On Fri, Nov 20, 2009 at 4:23 AM, <Howsun.Jow at newcastle.ac.uk> wrote:

The maximum likelihood estimates of the parameters in a linear
mixed-effects model are not the least squares estimates.  The
conditional means of the random effects and the estimates of the
fixed-effects parameters are penalized least squares estimates.  When
you remove one random effects term you may change the estimates of
variance of the random effects for the other term, resulting in a
different penalty and possibly a larger sum of squares of residuals.