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Maximum likelihood estimation and likelihood ratio test for square tables with missing data.

W J Shih

    Statistics in Medicine
    |January 1, 1987
    PubMed
    Summary
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    This study introduces methods for analyzing incomplete categorical data using the Expectation-Maximization (EM) algorithm. These techniques address missing data challenges in paired data analysis, improving statistical accuracy.

    Area of Science:

    • Statistics
    • Biostatistics
    • Data Analysis

    Background:

    • Analysis of paired categorical data is often complicated by the presence of missing values.
    • Incomplete datasets pose significant challenges for traditional statistical methods.
    • Accurate analysis requires robust methods to handle missing data points.

    Purpose of the Study:

    • To present statistical methods for analyzing incomplete square contingency tables with missing data.
    • To apply the Expectation-Maximization (EM) algorithm for maximum likelihood estimation in such scenarios.
    • To develop and illustrate a likelihood ratio test for incomplete tables.

    Main Methods:

    • Utilized the Expectation-Maximization (EM) algorithm for maximum likelihood estimation.
    • Developed a likelihood ratio test specifically for incomplete square tables.

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  • Employed statistical modeling techniques to handle missing categorical data.

    • Main Results:

    • The EM algorithm provides a viable approach for maximum likelihood estimation with missing data.
    • The likelihood ratio test is effective for hypothesis testing in incomplete square tables.
    • Demonstrated the practical application of these methods through a relevant example.

    Conclusions:

    • The proposed methods effectively address the complexities of missing data in paired categorical analyses.
    • The EM algorithm and likelihood ratio test offer reliable tools for incomplete data scenarios.
    • The findings are applicable to various fields, including microbiology and drug resistance studies.