[R-sig-ME] Question on random effects glm interpretation

[Emmanuel Curis]

Dear all,

With a colleague, we are discussing about the appropriateness of a
random effects mixed effects generalized linear model (more
specifically, logistic regression) in a given experimental situation,
and wonder about it's correct interpretation.

Short version: is it correct to interpret random effects glm, with a
single random effect, as hierarchical models as random effects linear
models ?

Detailed version: our data consist of daily status of a set of
patients, the status beeing « Infected » or « Not infected », during a
variable period of time. The aim is to see what changes the infection
probability.

A proposed approach was to use a random effect logistic regression to
evaluate this probability, with patient as a random effect.

However, we have one concern with that approach: interpretating it in
a hierarchical model idea, it seems that for a given patient, the
model should be a binomial one, in other words that the set of
Bernoulli variables observed each day for a given patient should be
independent, identically distributed. But this is obviously not the
case here: the variable is 0 until infection occurs (if it occurs),
and 1 after.  Consequently, we fear that the probability estimated in
the glmm will have no real meaningful interpretation.

Are we right with this hierarchical interpretation of the GLMM
(logistic) model, or is this fear not justified, and the
interpretation of the GLMM more complex, but would lead to correct and
interpretable estimations of infection probability?

As an alternative approach, we thought about a two-states Markov
chain, and working on transition probabilities from the « non-infected »
to the « infected » state. It seems to model what happens more
closely.  Is there any link between such a model and the logistic GLMM
described above, or another kind of GLMM model? 

And, semantic question, is such a model also in the scope of « random
effects » model and could be discussed here, in case help is needed, or
is it out of the scope of this list?

Thanks in advance for your opinions,
Best regards,

-- 
                                Emmanuel CURIS
                                emmanuel.curis at parisdescartes.fr

Page WWW: http://emmanuel.curis.online.fr/index.html