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Logistic Regression Using SAS®: Theory and Application by Paul D. Allison

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3.10. Probit and Complementary Log-Log Models

The logit model is not the only model appropriate for binary dependent variables. The LOGISTIC and GENMOD procedures can also estimate two other widely-used models, the probit model and the complementary log-log model. In this section, I’ll briefly discuss each of these models, with an emphasis on how they compare with the logit model.

The latent variable model we examined in the last section should help to motivate these models. The equation for the continuous latent variable z was

z = α0 + α1x1 + α2x2 + ... + αkxk + σε

The observed variable y was equal to 1 or 0 depending on whether z was above or below some threshold value μ. We saw that if ε has a standard logistic distribution, the dependence ...

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