why Binomial Probit model is called like that?

he „Binomial Probit Model” is a type of regression used in statistics to model binary outcome variables. In this context:

  • Binomial: This indicates that the dependent variable is binary, meaning it has two possible outcomes (e.g., success/failure, yes/no, 1/0).
  • Probit: This comes from the term „probability unit” and refers to a model that uses the probit function. The probit function is the quantile function associated with the standard normal distribution. In simpler terms, it maps the probability of an event occurring to the z-scores (or standard deviations) of the normal distribution. The probit model assumes that the underlying latent (unobserved) variable follows a normal distribution.

The model is specified as:

In essence, the probit model calculates the z-score that corresponds to the probability of the binary outcome, and then uses this z-score in the linear regression equation. Just as with the logit model, the coefficients in the probit model are usually estimated using maximum likelihood estimation. The choice between using a probit or logit model often depends on the specific application and the assumptions about the distribution of the error terms.

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