The simultaneous assessment of normality and homoscedasticity in linear fixed effects models
This article investigates the problem of simultaneously testing the normality and homoscedasticity assumptions in a linear fixed effects model when we have grouped data. This has been facilitated by the assumption of a smooth alternative to the normal distribution. The smooth alternative is specified using Legendre polynomials, and the score statistic is derived under two scenarios: a common smooth alternative across the different groups, or different smooth alternatives across the different groups. A data-driven approach available in the literature is used for determining the order of the polynomials. For the null distribution of the score statistic, the accuracy of the asymptotic chi-squared distribution is numerically investigated under a one-way fixed effects model with balanced and unbalanced data. The results are illustrated with an example.
KeywordsBalanced data Legendre polynomials one-way fixed effects model score test smooth alternative unbalanced data
AMS Subject Classification62F03 62J20
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