Nonlinear Estimation Evaluating the Fit of the Model - Goodness-of-fit Chi-square

For probit and logit regression models, the Nonlinear Estimation module uses maximum likelihood estimation (i.e., maximize the likelihood function; see Probit/Logit Regression). As it turns out, you can directly compare the likelihood L0 for the null model where all slope parameters are zero, with the likelihood L1 of the fitted model. Specifically, one can compute the Chi-square statistic for this comparison as:

Chi-square = -2 * (log(L₀) - log(L₁))

The degrees of freedom for this Chi-square value are equal to the difference in the number of parameters for the null and the fitted model; thus, the degrees of freedom will be equal to the number of independent variables in the logit or probit regression. If the p-value associated with this Chi-square is significant, then we can say that the estimated model yields a significantly better fit to the data than the null model, that is, that the regression parameters are statistically significant.