Testing for random individual and time effects using a Gauss-Newton regressio

This paper derives a simple method for testing for zero random individual and time period effects in a non-linear model using a Gauss-Newton regression. In case, the regression model is linear, this test amounts to running the original regression with two additional regressors. The first is the average of the least squares residuals over time, while the second is the average of the least squares residuals over individuals. The test statistic becomes the F-statistic for the significance of the two additional regressors.