st: multilevel logistic and reml

[Garry Anderson <g.anderson@unimelb.edu.au>]

Dear Statalist,

Is it possible to use the reml method to estimate fixed effect parameters for a multilevel logistic regression?

Genstat 15th Ed. and SPSS 20th Ed. statistical software seem to use reml and I was wishing to replicate their estimates in Stata.
For the generalized linear mixed model with a binary outcome, Genstat cites Schall (1991) and SPSS gives the same parameter estimate as Genstat for my dataset.

The dataset of 4020 observations provides the following odds ratios (OR) for a parameter

Stata (unilevel)   -logit-     OR = 7.96
Stata -melogit  ,intp(25)-  OR = 0.85
Genstat  -glmm-                 OR = 6.48
SPSS     -genlinmixed-       OR = 6.48

-melogit y01 i.var3levels ||id: , intp(25)-


where 
var3level = 0 if the previous observation within id did not have the outcome
var3level = 1 if the previous observation within id did not exist
var3level = 2 if the previous observation within id had the outcome
This is like a transitional model.
The odds ratio estimate of 0.85 when using -melogit- is very low and is my main cause for concern.

The intmethod option of mcaghermite, in combination with intp(25), also gives an odds ratio of 0.85.
Using intp(7) reports 'adaptive quadrature failed to converge' after each iteration from the 7th to the 44th, but then provides an OR = 0.00023.
Using intp(9) message 'adaptive quadrature failed to converge' continues until at least 195 iterations without an estimate of parameters.

The proportions of the outcome, y01, for the 3 levels of the categorical variable are
Category 0   129 / 899 (14%)
Category 1   657 / 2813 (23%)
Category 2   176 / 308 (57%)

Category 0 is the proportion y01 at the current observation, given the previous observation within id was 0 for y01.
Category 1 is the proportion y01 at the current observation, given there was not a previous observation within id.
Category 2 is the proportion y01 at the current observation, given the previous observation within id was 1 for y01.

The above four odds ratios are for category level 2 compared with level 0.

There are 2813 groups (clusters) and there are 1959 groups (70%) with a single observation. The number of observations per group varies from 1 to 8, with a mean of 1.4.

-xtlogit y01 i.var3level ,i(id) intp(25)- reports an OR of 0.85 and rho = 0.65.

Schall R (1991) Estimation in generalized linear models with random effects. Biometrika 78: 719 - 727

Kind regards, Garry


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