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Parameter estimation and goodness‐of‐fit testing in multinomial models
Author(s) -
GarcíaPérez Miguel A.
Publication year - 1994
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1994.tb01037.x
Subject(s) - goodness of fit , statistics , multinomial distribution , sample size determination , mathematics , statistic , sample (material) , econometrics , multinomial logistic regression , divergence (linguistics) , linguistics , chemistry , philosophy , chromatography
The application of multinomial models to describe psychological data usually involves small sample sizes. In these circumstances, the asymptotic properties of the parameter estimation method and goodness‐of‐fit statistics designed for use with multinomial models may not hold up. This paper illustrates the design of a simulation study that will allow researchers and practitioners to determine which of the available estimation methods and goodness‐of‐fit statistics for multinomial models has better finite‐sample properties for the model and sample size of concern. All of the estimation methods and goodness‐of‐fit statistics considered are members of the family of power divergence measures defined by Cressie & Read (1984), which include maximum likelihood and minimum chi‐square among other estimation methods. Criteria for comparing the methods and statistics include the accuracy of the estimates and the closeness of the asymptotic significance levels of the statistics to their exact finite‐sample levels. A number of simulations are carried out in order to investigate these properties for different models and sample sizes. In addition to illustrating the procedure for carrying out the comparison, the results found along the way indicate that the optimal choices are not always the maximum likelihood estimation method and the log‐likelihood ratio statistic.