[R-sig-ME] glmmTMB and ar1

[Jarrod Hadfield]

Hi,

It is *really* great that glmmTMB allows ar1 models. However, I'm having 
some trouble understanding the output and reconciling the estimates with 
asreml.

The data consist of the number of birds censused each year for 34 years. 
In 13 years the birds were censused twice.

The model I would like to fit has year as a continuous fixed effect, and 
then an ar1 process across years. The residual variance should pick up 
the within-year variance.

  m1.glmmTMB<-glmmTMB(log(pop)~year+ar1(year.factor+0|Common.Name), 
data=shag_data)

However, this gives one fewer parameters than I was expecting:

  summary( m1.glmmTMB)
  Family: gaussian  ( identity )
Formula:          log(pop) ~ year + ar1(year.factor + 0 | Common.Name)
Data: shag_data

      AIC      BIC   logLik deviance df.resid
     12.5     21.7     -1.2      2.5       42

Random effects:

Conditional model:
  Groups      Name            Variance Std.Dev. Corr
  Common.Name year.factor1973 0.214434 0.46307   (ar1)
  Residual                    0.004099 0.06403
Number of obs: 47, groups:  Common.Name, 1

Dispersion estimate for gaussian family (sigma^2): 0.0041

Conditional model:
             Estimate Std. Error z value Pr(>|z|)
(Intercept) 55.73041   29.70301   1.876   0.0606 .
year        -0.02464    0.01493  -1.650   0.0989 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Is 0.214434 the process variance for the ar1?  But then where is the 
autocorrelation parameter?

What I hoped was the equivalent model in asreml gives different answers

m1.asreml<-asreml(log(pop)~year, random=~ar1v(year.factor), data=shag_data)

The estimate are 0.74 (autocorrelation), 0.30 (process variance) and 
0.0041 (the residual variance). Asreml uses REML not ML so this might 
explain some of the discrepancy but I'd be surprised if it explained all.

Cheers,

Jarrod





-- 
The University of Edinburgh is a charitable body, registered in
Scotland, with registration number SC005336.