Notes on the Use of Log-Linear Models for Fitting Discrete Probability Distributions

Author(s):

Holland, Paul W.

Publication Year:

1987

Report Number:

RR-87-31

Source:

ETS Research Report

Document Type:

Report

Page Count:

44

Subject/Key Words:

Data Analysis, Mathematical Models, Maximum Likelihood Statistics, Multivariate Analysis, Newton-Raphson Method, Statistical Analysis

Abstract

The theory of log-linear models is developed for multinomially distributed data--i.e., frequency distributions and discrete multivariate distributions. Such models have applications to data smoothing and can be used in test equating. Attention is given to the computations used to find maximum likelihood estimates using Newton's method and to the computation of asymptotic standard errors for the fitted frequencies. Two examples, using real data, are used to illustrate the output of a computer program that implements these ideas.

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• http://dx.doi.org/10.1002/j.2330-8516.1987.tb00235.x