[R-sig-ME] Mixed-model-binary logistic model with dependence between individual repeated measures

Ben Bolker bbolker at gmail.com
Fri Jan 7 17:49:31 CET 2011

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On 11-01-07 11:35 AM, Anna Ekman wrote:
> Ben Bolker, thank you for your suggestions.
> Yes, it is suprising that I in SAS and STATA have to assume
> independence between the measurements within an individual.

  It's fundamentally a bit hard to specify correlation among individuals
in a non-normal model. One option is to go completely to the marginal
specification (which you said you don't want to do); probably the most
sensible statistical formulation is

  (fixed effects)  eta0 = X*beta
  (random effects) eta1 ~ MVN(mu=X*beta,Sigma=(something sensible such
as AR(1) within individuals))
   y ~ Bernoulli(eta1)

 i.e., a hierarchical model with a multivariate normal correlated
distribution at the 'lower level', with a level of Bernoulli variation
on top of that.

  The correlation parameters of eta1 will not correspond to the actual
correlations among the measurements (which will be smaller due to the
extra variation coming from the Bernoulli sampling)

 I do not
> want to assume that. In addition I would like to be able to chose
> other distributions than the normal for my random effect, which is
> not possible in SAS (proc NLMIXED). 

  It's not possible in R either as far as I know.

The generalized estimating
> equation packages are probably not an option as I do not whant
> marginal models. I will look at the references you suggested. Thank
> you. /Anna

  If you want a non-marginal model with non-normal random effects and
within-individual correlation structures other than compound symmetry
(i.e. simple block structures), you are probably going to have to
construct your own solution with WinBUGS or AD Model Builder or ... ? If
you're lucky, MCMCglmm may be able to do what you want -- I would check
it out. (Molenbergh and Verbeke's book on longitudinal models describes
approaches for non-normal random effects, but in the context of LMMs
(i.e. normally distributed errors) -- they may have done something to
extend this stuff to GLMMs more recently.  It's possible that someone
out there has done what you want and encapsulated it into a canned
package, but I doubt it.

    Ben Bolker
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