Random effects with multilevel binomial data

[rdmcdowell]

I noted when reading the runmlwin guide (p18) that when fitting a multilevel Bernoulli model no individual level error appears in the linear predictor. I was wondering if someone could clarify why this was the case. When I try to fit a simple multilevel logistic model using runmlwin looking at level 1 residuals e.g.

runmlwin smoke cons age, level2(pracid: cons) level1(patient_id:, residuals(stand)) discrete(distribution(binomial) link(logit) denominator(cons) pql2)

I get an error message:

option rpxvars() required.

However if I fit the model directly in Mlwin, I seem to be able to specify and get output for level 1 (as well as level 2) residuals. I can also get e.g. anscombe residuals if fitting the same model using xtmelogit in stata, and these appear to be calculated at an individual level. I am hence unclear as to how to reconcile these facts. Thank you for any insight you can offer.

[ChrisCharlton]

Level-one residuals being available for discrete models in -runmlwin- is a bug, which will be fixed in the next release. In the mean time I have attached our current development version where this is fixed.

[GeorgeLeckie]

Dear rdmcdowell,

In terms of

"I noted when reading the runmlwin guide (p18) that when fitting a multilevel Bernoulli model no individual level error appears in the linear predictor. I was wondering if someone could clarify why this was the case."

Adding a level-1 random effect to the level-1 predictor equates to attempting to allow for over-dispersion. However, over-dispersion cannot be modelled for binary responses and the Bernoulli distribution. See Sections 2.1 and 2.2 of Skrondal and Rabe-Hesketh (2007) for formal proof

Skrondal, A., & Rabe-Hesketh, S. (2007). Redundant overdispersion parameters in multilevel models for categorical responses. Journal of Educational and Behavioral Statistics, 32(4), 419-430.

Best wishes

George

[rdmcdowell]

Thanks for those helpful posts. When I run a 2 level logit model in mlwin directly, I can get level 1 and level 2 residuals. I'm still unclear how it's possible to obtain level 1 residuals in a discrete model if there's no level 1 residual error term in the model. Stata does the same, and my lack of understanding is leading to my confusion.