[R-sig-ME] Distribution of deviance residuals

[Roelof Coster]

Hello,

What is the theoretical distribution of the residual deviances of a
well-fitting logistic regression mixed model?

The background of my question is as follows: I am looking for a way to
combine the ideas from regression tree modelling (aka model trees) and
mixed models. I have a data set to which I want to fit a logistic
regression model. My data come in groups, so I need a random effect to
account for those groups.

The mob function in the party package does what I need, but only for
fixed-effects models. As I understand it, that function arranges the data
according to the levels of a certain categorical predictor. Next, it looks
at the sequence obtained by cumulating the deviance residuals. Then a
hypothesis test is done to assess whether this sequence can plausibly be a
Brownian motion. If it isn't a Brownian motion, that is an indication that
the data set should be splitted in two and that two separate models should
be fitted. This process is repeated so that a binary tree is produced, with
a logistic regression model for a part of the data in each leaf of the tree.

I would be grateful for any advice on how this technique can be made to
work for my problem.

Best regards,

Roelof Coster

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