Why se.fit differ in predict.glm and predict.glmmadmb?

Xandre <alex at ...> writes:

I am aware of that, sorry. Hopefully, with the following link, 
https://www.dropbox.com/s/pptl595chabjtly/datos.csv?dl=0 , the example 
will be completely reproducible.

Regards,

Alex

It looks like glmmADMB is getting the estimate of the correlation
between the fixed effects wrong (I don't yet know whether this is 
a problem with
the optimization in AD Model Builder or an actual bug in the translation
of results from ADMB output to R):

datos <- read.csv("datos.csv")
M1<-glm(response~explanatory,
        data=datos,
        family="binomial")
library(glmmADMB)
M2 <- glmmadmb(response~explanatory,
             data=datos,
             family="binomial")
## Estimated covariance matrix may not be positive definite
##  4.0211 4.1655
coef(summary(M1))
coef(summary(M2))

newdatos <- with(datos,
          data.frame(explanatory=seq(min(explanatory),
                                     max(explanatory),length.out=10)))
predict(M1,type="link",newdata=newdatos,se.fit=TRUE)
predict(M2,type="link",newdata=newdatos,se.fit=TRUE)
X <- model.matrix(~explanatory, data = newdatos)

## compare var-cov matrices
vcov(M1)
vcov(M2)

## compare SEs
sqrt(diag(vcov(M1)))
sqrt(diag(vcov(M2)))

## compare correlations
cov2cor(vcov(M1))
cov2cor(vcov(M2))

## compare predicted SEs
sqrt(diag(X %*% vcov(M1) %*% t(X)))
sqrt(diag(X %*% vcov(M2) %*% t(X)))

## try with glmmTMB
library(glmmTMB)
M3 <- glmmTMB(response~explanatory,
             data=datos,
             family=binomial)
cov2cor(vcov(M3)$cond)

Just to check problems of code I tried again with a much more simple
example. I made a subset of my original data base (see attached .csv)
and run a much more simple model as follows:

*> M1<-glm(response~explanatory, **
**+           data=datos,**
**+           family="binomial")**
**? M2<-glmmadmb(response~explanatory, **
**+                 data=datos,**
**+                 family="binomial")**
**? **
**? summary(M1)*

[snip snip snip snip]