Testing Goodness of Fit of a Multinomial Model Against Overdispersed Alternatives
Byung‐Soo Kim, Barry H. Margolin · Biometrics · 1992
The problem of testing the goodness of fit of the multinomial sampling model against an overdispersed Dirichlet-multinomial alternative is studied and an improved approximate sampling distribution is presented for the corresponding C(ca) test statistic. The elements of this improvement include better control of test size and increased power against overdispersion. The Pearson chi-square test is also considered for the detection of this form of overdispersion and its asymptotic efficiency relative to the C(a) test is obtained and shown to be always less than or equal to 1. Monte Carlo investigations suggest that the gain in power of the C(a) test relative to the Pearson chi-square test is small unless there is substantial inequality among the Dirichlet-multinomial sample sizes.