Re: [R] About lmer output

From: Douglas Bates <dmbates_at_gmail.com>
Date: Thu 26 Jan 2006 - 06:04:49 EST

On 1/25/06, Juan Pablo Sánchez <juansan@dca.upv.es> wrote:
> Dear R users:
> I am using lmer fo fit binomial data with a probit link function:
>
> > fer_lmer_PQL<-lmer(fer ~ gae + ctipo + (1|perm) -1,
> + family = binomial(link="probit"),
> + method = 'PQL',
> + data = FERTILIDAD,
> + msVerbose= True)
>
> The output look like this:
> > fer_lmer_PQL
> Generalized linear mixed model fit using PQL
> Formula: fer ~ gae + ctipo + (1 | perm) - 1

> Data: FERTILIDAD
> Family: binomial(probit link)
> AIC BIC logLik deviance
> 2728.086 2918.104 -1332.043 2664.086
> Random effects:
> Groups Name Variance Std.Dev.
> perm (Intercept) 0.28256 0.53156
> # of obs: 2802, groups: perm, 529
>
> Estimated scale (compare to 1) 0.8958656
>
> My question is about the meaning of "Estimated scale (compare to 1) 0.8958656 "
>
> I think that the scale would be 0.28256+1.0, Isn´t it?

The estimated scale is what would be the estimate of the scale parameter in the GLM family if there was a scale parameter. For the binomial and Poisson families there is no scale parameter but the Iteratively Reweighted Least Squares (IRLS) algorithm still produces an estimate of one. If the data are neither overdispersed nor underdispersed then that estimate should be close to 1.

It can provide a diagnostic for the model. A value that is substantially different from 1 indicates model failure or over-modeling the data. I would say that the value of 0.896 is close to an indication of underdispersion. Frequently this is caused be including random effects associated with groups that have few observations in each group.



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