Logit, Probit, and Other Response Functions

Authored by: James H. Albert

Handbook of Item Response Theory Volume Two Statistical Tools

Print publication date:  February  2016
Online publication date:  March  2017

Print ISBN: 9781466514324
eBook ISBN: 9781315373645
Adobe ISBN:

10.1201/b19166-3

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Abstract

A general statistical problem is to model a binomial probability in terms of a vector of explanatory variables. We observe independent responses y 1, ..., yN , where yi is assumed binomial with sample size ni and probability of success pi . (In the special case where the sample sizes ni = ··· = nN = 1, we have Bernoulli observations.) Corresponding to the ith observation, we also observe k covariates x i1, ..., xik ; we let xi = (x i1, ..., x ik ) denote the vector of covariates. We relate the binomial probabilities with the covariates by means of the equation

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