Power-Divergence Goodness-of-Fit Statistics: Small Sample Behavior in One Way Multinomials and Applications to Multinomial Processing Tree (MPT) Models

摘要

The small-sample behavior of power-divergence goodness-of-fit statistics with composite hypotheses is evaluated in multinomial models of up to five cells and up to three parameters. These models were based on a class of cognitive models called multinomial processing tree (MPT) models, that are characterized for being simple and substantively motivated statistical models than can be applied to categorical data. They are used as data-analysis tools for measuring underlying or latent cognitive capacities and as simple models for representing and testing competing psychological theories. The performance of these tests was assessed by comparing asymptotic sizes with exact sizes obtained by enumeration. This paper addresses all combinations of power-divergence estimates of indices v = {—1/2,0,1/3,1/2,2/3,1,3/2} and statistics of indices λ = {—1/2,0,1/3,1/2,2/3,1,3/2}. Exact conditions are given under which the asymptotic approximation is sufficiently accurate, by the criterion that the average exact size is no larger than ±10% of the asymptotic test size.