Abstract
This paper addresses the issue of statistical inference for multinomial processing tree models of cognition. An important question in the statistical analysis of multinomial models concerns the accuracy of asymptotic formulas when they are applied to actual cases involving finite samples. To explore this question, we present the results of an extensive analytic and Monte Carlo investigation of loglikelihood ratio inference procedures for our multinomial model for storage and retrieval. We demonstrate how to estimate bias in the parameters, set confidence intervals for estimators, calculate power for various hypothesis tests, and estimate the sample size needed to justify the use of asymptotic theory in real settings. Also, we study the impact of moderate amounts of individual differences in the parameters. The results of the Monte Carlo simulations reveal that the storage-retrieval model is fairly robust for sample sizes around 150, and they also reveal those conditions under which larger sample sizes will be needed. The paper is structured to show potential users of multinomial models how to carry out these types of simulations for other models, and what findings and recommendations they can expect to find along the way.
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© 1991 Springer-Verlag New York, Inc.
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Riefer, D.M., Batchelder, W.H. (1991). Statistical Inference for Multinomial Processing Tree Models. In: Doignon, JP., Falmagne, JC. (eds) Mathematical Psychology. Recent Research in Psychology. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9728-1_18
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DOI: https://doi.org/10.1007/978-1-4613-9728-1_18
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97665-5
Online ISBN: 978-1-4613-9728-1
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