Re: [Boost-users] multinomial mixed-effects regression model

Subject: Re: [Boost-users] multinomial mixed-effects regression model
From: Thomas Mang (thomasmang.ng_at_[hidden])
Date: 2011-05-10 16:08:21

Sorry guys, picked the wrong newsgroup :-)

best,
Thomas

On 10.05.2011 15:59, Thomas Mang wrote:
> Hi,
>
> Consider the need for a regression model which can handle an ordered
> multinomial response variable. There are, for example, proportional odds
> / cumulative logit models, but actually the regression should include
> random effects (a mixed model), and I would not be aware of multinomial
> regression model as part of lme4 (am I wrong here ?). Further, the
> constraint of proportional odd models that predictors have the same
> relative impact across all levels does not hold for the study in question.
>
> I was wondering if an ordinary binomial mixed model can be turned in an
> multinomial one through preparing the input data.frame in a different way:
> Consider three response levels, A, B, C, ordered. I can accurately
> describe the occurrence of each of these three realizations using one to
> two Bernoulli random variables:
>
> Let
> P(X == A) = a
> P(X in {B, C}) = 1 - a
> P(X == B | X in {B, C}) = (1 - a) * b
> P(X == C | X in {B, C}) = (1 - a) * (1 - b)
>
> so the first comparison checks if A or either of B/C is the case, and
> the second, conditional on it's either B/C, checks which of these two
> holds. Sort of traversing sequentially the hierarchy of the ordered levels.
> In terms of the likelihood of the desired model, the probabilities on
> the right hand side would be exactly achieved if I use one input row in
> case the random variable takes on the value A and assign the response
> variable the value 0, while in the other cases the probabilities are
> achieved by using two input table rows, with the first one having value
> 1 for the response variable so the random variate is either B/C) and a
> second row with response equal to 0 if B is the case, and 1 otherwise,
> that is C is the case.
>
> Certainly, degrees of freedom must be manually adjusted in inferences,
> as every measured response should provide only a single degree of freedom.
>
> Question: Do I overlook here something, or is above outlined way a valid
> method to yield an ordered multinomial mixed model by tweaking the input
> table in such manners ?
>
> many thanks and best,
> Thomas