An empirical investigation of some effects of sparseness in contingency tables
type: Item
instance of: scholarly article
title: An empirical investigation of some effects of sparseness in contingency tables
zbMATH Open document ID: 0605.62061
DOI: 10.1016/0167-9473(87)90003-X
author: Alan Agresti
author: Ming-Chung Yang
published in: Computational Statistics and Data Analysis
publication date: 1987-01-01T00:00:00Z
review text: A simulation study investigates some effects of having 'sparse' categorical data, for which the ratio of the sample size to the number of cells is relatively small. In this study, the true cell proportions satisfy the uniform association model for ordinal variables. Conclusions include the following: (1) For direct testing of the model, the distribution of the Pearson goodness-of-fit statistic is closer to the asymptotic chi-squared distribution than is the distribution of the likelihood-ratio statistic. (2) For comparing two unsaturated loglinear models (such as in testing independence under the assumption that a particular model holds), it is usually preferable to compare likelihood- ratio statistics rather than Pearson statistics. (3) A beneficial aspect of sparseness is that the power of certain single-degree-of-freedom test statistics tends to increase as the table becomes more sparse, for a fixed sample size. (4) The common practice of adding constants to empty cells can cause havoc with the distribution of the Pearson statistic.
Mathematics Subject Classification ID: 62H17
Mathematics Subject Classification ID: 65C99
zbMATH DE Number: 3978170
zbMATH Keywords: contingency tables
zbMATH Keywords: ordinal variables
zbMATH Keywords: simulation study
zbMATH Keywords: Pearson goodness-of-fit statistic
zbMATH Keywords: asymptotic chi-squared distribution
zbMATH Keywords: likelihood-ratio statistic
zbMATH Keywords: unsaturated loglinear models
zbMATH Keywords: independence
zbMATH Keywords: sparseness
zbMATH Keywords: single-degree-of-freedom test statistics
MaRDI profile type: Publication
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full work available at URL: 0167-9473(87)90003-x
OpenAlex ID: W1974870522
description: scientific article; zbMATH DE number 3978170