MONTE CARLO EVALUATION OF WHITE'S TEST FOR DETECTING HETEROSCEDASTICITY IN GENERALIZED LINEAR MODELS

Abstract

Heteroscedasticity in regression analysis occurs when the variance of the error term changes across different levels of the independent variable(s), leading to inefficient estimates and incorrect inference. In Generalized Linear Models (GLMs), heteroscedasticity significantly impacts prediction and inference accuracy. This study evaluates White's test for detecting heteroscedasticity in GLMs through Monte Carlo simulations. We investigate the test's power, Type II errors, and Type I errors at different sample sizes (100, 250, and 500). Our findings reveal that White test performs well in detecting strong heteroscedasticity, particularly for exponential heteroscedasticity structures (EHS), but poorly for weaker forms like linear heteroscedasticity structures (LHS) and square root heteroscedasticity structures (SQRTHS). While increased sample size enhances performance, the test remains susceptible to over-rejection of homoscedasticity. We recommend cautious use, especially with weaker heteroscedasticity or specific structures. For improved performance, use the test with moderate to high sample sizes (e.g., n = 500), particularly for EHS and quadratic heteroscedasticity structures (QHS). Alternative tests may be considered for researchers with limited sample sizes or dealing with LHS and SQRTHS. Finally, we emphasize the importance of assessing the underlying structure of heteroscedasticity in the dataset to choose the most suitable test and interpretation.