LINEAR MODEL ANALYSIS OF NEGATIVE BINOMIAL COUNTS USING ORIGINAL AND TRANSFORMED DATA FOR NORMALITY AND HOMOCEDASTICITY.
Antonio Carlos Simões PIÃO[1]
Dilermando PERECIN[2]
§ ABSTRACT: The negative binomial
distributions is quite frequently used to interpret counting variables, through
16 different techniques. In order to compare these techniques, several four
populations of size n =50 were computer generated for different values of the
parameters m and k. Comparisons of the ,minimum level of significance were made
when ten transformations of variables, and analysis of variance, were used. In
conclusion, for some values of the parameters m and k, on data transformations
is needed, particularly if depending on k. Statistics like C(a ), proposed by BARNWAL, PAUL
(1988),showed robust for nonhomogeneous values of k, leading to results
equivalent to those obtained using untransformed data. The analysis of minimum
chi-squared was shown to be biased, overestimating values when the
variance-covariance matrix is unknown. If the variance-covariance matrix is
known, the results are equivalent to those obtained from original data. Similar
results obtained for smaller populations, n = 10.
§ KEYWORDS: Analysis of variance; negative binomial distributions; transformations; minimum chi-squared.