5.3 Multivariate models

After our GUI is deployed (see Figure 5.1), the user should select Multivariate Models from the top panel. Figure 5.6 will then be displayed, showing a radio button on the left-hand side that lists the specific models within this category.

Figure 5.6 illustrates the multivariate regression setup. The input file should first contain the dependent variables, followed by the regressors. If each equation includes an intercept, a column of 1s should be added after the dependent variables in the input file. Users can preview the data after uploading the file.

The user must specify the number of dependent variables and regressors, indicate whether an intercept should be included, and define the hyperparameter values (see Figure 5.6).

Figure 5.6: Multivariate models: Simple multivariate.

In seemingly unrelated regressions, the input file should first contain the dependent variables, followed by the regressors for each equation, including the intercept (a column of 1s) if necessary. Users must define the number of dependent variables (equations), the total number of regressors (the sum of all regressors associated with the equations), and the number of regressors per equation (including the intercept if necessary). Users can also specify the values of the hyperparameters if prior information is available.

The results of the simple multivariate and seemingly unrelated regressions first display the posterior location parameters by equation, followed by the posterior covariance matrix.

In the instrumental variable setting, users should specify the main equation and the instrumental equation. This setting includes intercepts by default. The first variable on the right-hand side of the main equation must be the variable with endogeneity issues. In the instrumental equation, the dependent variable is the one with endogeneity issues, modeled as a function of the instruments. Users can also specify the values of the hyperparameters if they have prior information. The input file should include the dependent variable, the endogenous regressor, the instruments, and the exogenous regressors. The results first list the posterior estimates of the endogenous regressor, followed by the location parameters of the auxiliary regression (instrumental equation), the location parameters of the exogenous regressors, and finally, the posterior covariance matrix.

Figure 5.7: Multivariate models: Multivariate probit.

The multivariate probit model requires the input dataset to be ordered by unit. For example, three choices imply repeating each unit three times. The first column must contain the identification for each unit, using ordered integers. Next, the dependent variable should be a single vector of 0s and 1s, followed by the regressors, which must include a column of 1s for the intercepts. Users should specify the number of units, the number of regressors, and the number of choices (see Figure 5.7). The results first display the posterior location parameters by equation, followed by the posterior covariance matrix.