 # ⓘ Multivariate probit model. In statistics and econometrics, the multivariate probit model is a generalization of the probit model used to estimate several correl .. ## ⓘ Multivariate probit model

In statistics and econometrics, the multivariate probit model is a generalization of the probit model used to estimate several correlated binary outcomes jointly. For example, if it is believed that the decisions of sending at least one child to public school and that of voting in favor of a school budget are correlated, then the multivariate probit model would be appropriate for jointly predicting these two choices on an individual-specific basis. This approach was initially developed by Siddhartha Chib and Edward Greenberg.

## 1. Example: bivariate probit

In the ordinary probit model, there is only one binary dependent variable Y {\displaystyle Y} and so only one latent variable Y ∗ {\displaystyle Y^{*}} is used. In contrast, in the bivariate probit model there are two binary dependent variables Y 1 {\displaystyle Y_{1}} and Y 2 {\displaystyle Y_{2}}, so there are two latent variables: Y 1 ∗ {\displaystyle Y_{1}^{*}} and Y 2 ∗ {\displaystyle Y_{2}^{*}}. It is assumed that each observed variable takes on the value 1 if and only if its underlying continuous latent variable takes on a positive value:

Y 1 = { 1 if Y 1 ∗ > 0, 0 otherwise, {\displaystyle Y_{1}={\begin{cases}1&{\text{if }}Y_{1}^{*}> 0,\\0&{\text{otherwise}},\end{cases}}} Y 2 = { 1 if Y 2 ∗ > 0, 0 otherwise, {\displaystyle Y_{2}={\begin{cases}1&{\text{if }}Y_{2}^{*}> 0,\\0&{\text{otherwise}},\end{cases}}}

with

{ Y 1 ∗ = X 1 β 1 + ε 1 Y 2 ∗ = X 2 β 2 + ε 2 {\displaystyle {\begin{cases}Y_{1}^{*}=X_{1}\beta _{1}+\varepsilon _{1}\\Y_{2}^{*}=X_{2}\beta _{2}+\varepsilon _{2}\end{cases}}}

and

&{}\quad {}+Y_{1}1-Y_{2}\ln P(\varepsilon _{1}> -X_{1}\beta _{1},\varepsilon _{2}

• multinomial logit model as one method of multiclass classification. It is not to be confused with the multivariate probit model which is used to model correlated
• In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word
• Logit, logit model ordered logit Multivariate probit models Probit probit model ordered probit Tobit model Censored regression model Selection bias
• In statistics, ordered probit is a generalization of the widely used probit analysis to the case of more than two outcomes of an ordinal dependent variable
• The most common binary regression models are the logit model logistic regression and the probit model probit regression Binary regression is principally
• importance sampling method for simulating choice probabilities in the multivariate probit model These simulated probabilities can be used to recover parameter
• variable, such as the preferred brand of cereal, then probit or logit regression or multinomial probit or multinomial logit can be used. If both variables
• regression and probit regression can be used for empirical analysis of discrete choice. Discrete choice models theoretically or empirically model choices made
• the model is called the linear probability model Nonlinear models for binary dependent variables include the probit and logit model The multivariate probit
• Multivariate probit redirects to Multivariate probit model Multivariate random variable Multivariate stable distribution Multivariate statistics Multivariate Student
• are ordered logit and ordered probit Ordinal regression turns up often in the social sciences, for example in the modeling of human levels of preference

...
 ...
...