Continuous covariates in logistic regression?

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Anonymous
2011-04-18
2012-09-01
  • Anonymous - 2011-04-18

    Greetings,

    Short question: How should I change the alligators example if the size/length
    were continuous?

    Let me expand on that for the patient and curious.

    Both winbugs and jags versions of the alligator example for each combination
    of covariates. See the snippet below:

    X ~ dmulti( p , n );

    for each combination of i,j, a multinomial distrubution is defined, and n is
    the sum of occurances of the values of the response variable, for that
    particular combination of i and j.

    here i is the lake index, and j is the size index. Since size has only 2
    values, (bigger than some_size or smaller than that) everything is nice. But
    what if size was simply the continuous measurement value? In that case, would
    not this imply an infinite combinations of i and j?

    multinomial logistic regression is pointed out as a solid option when the
    response variable is multinomial, and covariates (independent vars) are either
    discrete, continuous or a mixture of these. However, I could not find an
    example of the continuous covariate case for bugs/winbugs.

    Your response would be appreciated a lot (actually, probably much more than
    you could imagine)

    Kind regards

    Seref

     
  • Martyn Plummer

    Martyn Plummer - 2011-04-26

    The multinomial distribution is an efficient way to analyze the data when you
    have discrete covariates and can aggregate the data into groups (lake and size
    category in this case). When you have continuous covariates you can no longer
    aggregate the data and need to drop down to the individual level. So the
    equivalent model would be, for individual k.

    X[k] ~ dcat(p[k])
    

    where p is some function of the covariates for individual k, e.g.

    logit(p[k]) <- alpha + beta * x[k]
    
     
  • Martyn Plummer

    Martyn Plummer - 2011-04-26

    Just one more precision, in this case X is the category that individual k
    belongs to.

     

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