Conditional logistic regression vs lmer
On Wed, 3 Mar 2010, Federico Calboli wrote:
I was trying to compare conditional logistic regression with logistic regression with random terms:
I am doing a conditional logistic regression with clogit() of library survival, but I have a number of random factors I'd like to add to my model and I was thinking of lmer... clg.tigeR = clogit(c.c ~ tIgE.Resp + strata(match), data.ready) and all is good. I also have two more variables, both random which I'd like to use, but I am not 100% sure what's the way to go with lmer. I suspect I would need to specify a different intercept for each strata, but seems to baffle me at the moment. The code below might do what I want, but I have no idea if that's correct (i.e. does it match the clogit one + two more random effects?): lmer.tigeR = lmer(c.c ~ tIgE.Resp + (tIgE.Resp|match) + (1|Run) + (1|Box), family = binomial, data.ready) lmer.tigeR is computed without problems btw.
Was the study a matched case-control design, or is "match" the family or some natural clustering variable? How many cases and controls for each level of match? (maybe this was in your earlier email.) If the strata are small (eg 1:1), then I would be nervous about (tIgE.Resp|match) giving a meaningful estimate, cf c.c ~ tIgE.Resp + (1|match)+ (1|Run) + (1|Box).
Most importantly, I utterly fail to see the conceptual difference between *nesting* in a logistic regression with random terms and *strata* in a conditional logistic regression, but that's probably just me.
You might read over the intro to the paper by Liang, Qaqish and Zeger on the GEE for binary data in JRSSB (?1990 or so), where they contrast the different approaches to clustered data. Basically, the (usual) GLMM fits a parametric model for the intercepts for each stratum, while the CLR discards this information, and for a categorical covariate is "just" a permutation test. FWIW, David Duffy.
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