## Continuous covariates in logistic regression? document.SUBSCRIPTION_OPTIONS = { "thing": "thread", "subscribed": false, "url": "subscribe", "icon": { "css": "fa fa-envelope-o" } };

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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 - 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 - 2011-04-26

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