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Trend in Correlated Proportions

Published online by Cambridge University Press:  01 January 2025

Robert D. Gibbons  and
R. Darrell Bock
Robert D. Gibbons*
Affiliation:
University of Illinois
R. Darrell Bock
Affiliation:
University of Chicago
*
Requests for reprints should be sent to Robert D. Gibbons, ISPI 529W, 1601 W. Taylor, Chicago, IL 60612.
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Abstract

A random effects probit model is developed for the case in which the same units are sampled repeatedly at each level of an independent variable. Because the observed proportions may be correlated under these conditions, estimating their trend with respect to the independent variable is no longer a standard problem for probit, logit or loglinear analysis. Using a qualitative analogue of a random regressions model, we employ instead marginal maximum likelihood to estimate the average latent trend line. Likelihood ratio tests of the hypothesis of no trend in the average line, and the hypothesis of no differences in average trend lines between experimental treatments, are proposed. We illustrate the model both with simulated data and with observed data from a clinical experiment in which psychiatric patients on two drug therapies are rated on five occasions for the presence or absence of symptoms.

Keywords

random regressionprobit modelconditional dependencerepeated classification
Type
Original Paper
Information
Psychometrika , Volume 52 , Issue 1 , March 1987 , pp. 113 - 124
Copyright
Copyright © 1987 The Psychometric Society

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Footnotes

Supported by a grant from the MacArthur Foundation and National Science Foundation Grant BNS85-11774.

The authors are indebted to James Heckman for calling our attention to the Clark algorithm.

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