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Asymptotic log-linear analysis: some cautions concerning sparse frequency tables.

Paul W Mielke¹, Kenneth J Berry, Janis E Johnston

¹Department of Statistics, Colorado State University, Fort Collins, CO 80523-1877, USA. mielke@lamar.colostate.edu

Psychological Reports

|April 14, 2004

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Traditional probability values from log-linear analyses of sparse tables are often too large. Exact permutation methods offer a more accurate alternative for analyzing sparse frequency tables, especially for multinomial and hypergeometric distributions.

Area of Science:

Statistics
Data Analysis

Background:

Log-linear models are frequently used for analyzing frequency tables.
Sparse frequency tables can lead to inaccurate asymptotic probability values.

Purpose of the Study:

To compare asymptotic probability values with exact and nonasymptotic values for log-linear models with sparse data.
To introduce an exact permutation method for analyzing sparse frequency tables.

Main Methods:

Comparison of asymptotic, nonasymptotic, and exact probability values for chi-squared and likelihood-ratio statistics.
Development of an exact nondirectional permutation method for combined independent multinomial distributions.
Application of exact permutation methods to hypergeometric distributions for r=2.

Related Experiment Videos

Main Results:

Asymptotic probability values are often substantially larger than exact values in sparse frequency tables.
The proposed exact permutation method provides a more accurate analysis for sparse data.

Conclusions:

Traditional asymptotic methods are unreliable for sparse frequency tables.
Exact permutation methods are recommended for accurate analysis of sparse frequency data, particularly for multinomial and hypergeometric distributions.