st: RE: multilevel logistic and reml

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

Thank you Stephen for your suggestions and presentation.


I was wishing to explore REML because it is used by other software (Genstat) and because it seems to give more reasonable parameter estimates than variations of adaptive quadrature.

Noh M and Lee Y (2007) REML estimation for binary data in GLMMs. Journal of Multivariate Analysis 98: 896-915

Lee W and Lee Y (2012) Modifications of REML algorithm for HGLMs. Stat Comput 22: 959-966

My following example shows how the odds ratio of 0.85 in Stata is very different to other software, with an odds ratio of about 7. Can adding a random effect cause such a change to a fixed parameter?

The following seems to have been clipped from the previous reply.

My 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 Anderson
g.anderson@unimelb.edu.au



-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of S.Jenkins@lse.ac.uk
Sent: Tuesday, 12 November 2013 8:42 PM
To: statalist@hsphsun2.harvard.edu
Subject: st: multilevel logistic and reml

Short answer: it's not possible to use REML to estimate fixed effect parameters of a multilevel logistic regression using Stata, as far as I know. Look at the documentation for -xtmelogit- in Stata 12, and  -meqrlogit- and -melogit- in Stata 13.

The bigger question is why you should want to do this. REML is typically employed for linear mixed models. With -xtmixed- in Stata 12 or -mixed- in Stata 13, REML is an option.

Otherwise adaptive quadrature is the default estimation procedure. And with good reason in the multilevel logistic regression case -- alternative estimators such as PQL perform worse. (MCMC may do better, but it's not built into Stata ... though you can use -runmlwin- on SSC to try this estimator.)

For some discussion of estimators of multilevel logistic regression models, see http://www.stata.com/meeting/uk13/abstracts/materials/uk13_jenkins.pdf
[The emphasis of the talk is slightly different, but there are some relevant citations.]

"Schall (1991)" is unhelpful. As the Statalist FAQ states, provide full references please.


Stephen
------------------
Stephen P. Jenkins <s.jenkins@lse.ac.uk>
------------------------------

Date: Tue, 12 Nov 2013 07:22:43 +0000
From: Garry Anderson <g.anderson@unimelb.edu.au>
Subject: st: multilevel logistic and reml

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.


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