Question

What is logit model? How it can be responses for multicategory responses?

Answer 1

The logit model uses something called the cumulative distribution function of the logistic distribution.the logistic model (or logit model) is used to model the probability of a certain class or event existing such as pass/fail, win/lose, alive/dead or healthy/sick. This can be extended to model several classes of events such as determining whether an image contains a cat, dog, lion, etc... Each object being detected in the image would be assigned a probability between 0 and 1 and the sum adding to one.

Logit models for multinomial responses

When the dependent variable is not binary but has multiple outcome cate-

gories we use the multinomial instead of binomial for modeling.

Two types of multicategory outcome can be considered: nominal and ordinal.

Nominal response variable

In logistic regression the log odds of ’success’ is predicted.

When there are J outcome categories, the multinomial logit model predicts

simultaneously all pairs of log odds. Not all are necessary: a good choice of

J − 1 provides all information.

Ordinal response variable

Cumulative logit models define cumulative probabilities

P(Y ≤ j|x) = π1(x) + π2(x) + . . . + πj(x), j = 1, . . . , J − 1.

and from these the cumulative logits

logit[P(Y ≤ j|x)] = log (P(Y ≤ j|x) /1 − P(Y ≤ j|x))

A model for a single logit[P(Y ≤ j|x)] alone is a standard logit model. It is

better to simultaneously model all cumulative logits (i.e. for different j.)