Latent Variable Interpretation / Derivation
A latent variable model involving a binomial observed variable Y can be constructed such that Y is related to the latent variable Y* via
The latent variable Y* is then related to a set of regression variables X by the model
This results in a binomial regression model.
The variance of ϵ can not be identified and when it is not of interest is often assumed to be equal to one. If ϵ is normally distributed, then a probit is the appropriate model and if ϵ is log-Weibull distributed, then a logit is appropriate. If ϵ is uniformly distributed, then a linear probability model is appropriate.
Read more about this topic: Binomial Regression
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