[R] identical results with PQL and Laplace options in lmer function (package lme4)

[ronggui]

i am aware of this but i don't know why.

On Thu, 16 Jun 2005 10:31:25 +0200
Emmanuel Tillard <tillard at cirad.fr> wrote:

> Dear R users
> 
> I encounter a problem when i perform a generalized linear mixed model (binary data) with the lmer function (package lme4)
> with R 2.1.0 on windows XP and the latest version of package "lme4" (0.96-1) and "matrix" (0.96-2)
> both options "PQL" and "Laplace" for the method argument in lmer function gave me the same results (random and fixed effects estimates, standard error and p.values). However, Loglikelihood and deviance are different.
> 
> here is an example reproduced with the bacteria data set available in the MASS package:
> 
> library(lme4)
> library(MASS)
> 
> data(bacteria)
> bacteria$week2 <- as.factor(ifelse(bacteria$week <=2, 0, 1))
> model.PQL <- lmer(y ~ trt + week2 + (1 | ID), family = binomial, data  = bacteria, method ="PQL")
> model.Laplace <- lmer(y ~ trt + week2 + (1 | ID), family = binomial, data = bacteria, method ="Laplace")
> 
> model.PQL
> model.Laplace
> 
> > model.PQL
> Generalized linear mixed model fit using PQL 
> Formula: y ~ trt + week2 + (1 | ID) 
>    Data: bacteria 
>  Family: binomial(logit link)
>      AIC      BIC   logLik deviance
>  152.443 138.8685 -80.2215  160.443
> Random effects:
>      Groups        Name    Variance    Std.Dev. 
>          ID (Intercept)      3.2721      1.8089 
> # of obs: 220, groups: ID, 50
> 
> Estimated scale (compare to 1)  0.7800484 
> 
> Fixed effects:
>             Estimate Std. Error z value  Pr(>|z|)    
> (Intercept)  3.41227    0.65884  5.1792 2.228e-07 ***
> trtdrug     -1.24743    0.81841 -1.5242 0.1274555    
> trtdrug+    -0.75440    0.82009 -0.9199 0.3576229    
> week21      -1.60737    0.45527 -3.5306 0.0004146 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> > model.Laplace
> Generalized linear mixed model fit using Laplace 
> Formula: y ~ trt + week2 + (1 | ID) 
>    Data: bacteria 
>  Family: binomial(logit link)
>       AIC      BIC    logLik deviance
>  304.9488 291.3743 -156.4744 312.9488
> Random effects:
>      Groups        Name    Variance    Std.Dev. 
>          ID (Intercept)      3.2721      1.8089 
> # of obs: 220, groups: ID, 50
> 
> Estimated scale (compare to 1)  0.7800484 
> 
> Fixed effects:
>             Estimate Std. Error z value  Pr(>|z|)    
> (Intercept)  3.41227    0.65884  5.1792 2.228e-07 ***
> trtdrug     -1.24743    0.81841 -1.5242 0.1274555    
> trtdrug+    -0.75440    0.82009 -0.9199 0.3576229    
> week21      -1.60737    0.45527 -3.5306 0.0004146 ***
> ---
> Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 
> 
> is anybody else aware of this? or did I forget something important ?
> 
> Many thanks for your help.
> 
> -- 
> Emmanuel Tillard
> Veterinaire
> CIRAD-EMVT
> Unite de recherche 18
> 
> UMR868 Elevage des Ruminants en Regions Chaudes (ERRC)
> Campus ENSA-INRA
> 2 place Viala
> 34060 Montpellier cedex 1
> 
> tel:	0499612265 (fixe)
> 	0633850598 (gsm)
> fax:	0467545694
> e-mail: tillard at cirad.fr
> 
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