An LM test based on generalized residuals for random effects in a nonlinear model

- We derive the LM test statistic for random effects in a panel probit model.
- We obtain a reparameterization of the statistic that produces a feasible calculation.
- We show that the statistic can be computed using generalized residuals.
- We demonstrate that the results generalize to other models.
- The test is employed in a substantive application.

We obtain an LM test for the random effects probit model. In the natural parameterization of the model the necessary derivatives are identically zero under the null hypothesis. After a reparameterization, the feasible LM test is based on generalized residuals.