Analysis of Two-Way Contingency Tables : Log-Linear Models and Dual Scaling

Summary

The paper focuses upon the measurement of association in two-way contingency tables, using the log-linear models and dual scaling approaches. The former comprises [1] the use of pseudo-Bayes estimators to remove zeros, [2] fitting the resulting smoothed array to all possible configurations of log-linear models, [3] fitting the quasi-independence model to detect anomalous cells that caused deviation from the null-independence model. The latter includes [1] estimation of the optimal weights that maximize the canonical correlation between the two categorical variables by an optimization iterative method, [2] testing the discriminability of the estimated scoring scheme. The two approaches were applied to a set of real data for the study of the association between maternal age at marriage and types of reproductive wastage in a sampling survey conducted in the population of female nurses in Kuwait.

Schwerpunkt der Arbeit ist die Messung der Assoziation in Zwei-Weg-Kontingenztafeln unter Benutzung loglinearer Modelle und von Zweifachskalierungsansätzen. Erstere umfassen [1] die Anwendung von Pseudo-Bayes-Schätzern zur Eliminierung von Nullen, [2] die Anpassung der resultierenden geglätteten Tafel an alle möglichen Konfigurationen loglinearer Modelle, [3] die Anpassung des quasi-unabhängigen Modells, um anomale Zellen zu entdecken, die eine Abweichung von dem Nichtabhängigkeitsmodell verursachten. Letztere umfassen [1] die Schätzung optimaler Gewichte, welche die kanonische Korrelation zwischen den beiden kategorischen Variablen durch einen iterativen Optimierungsprozess maximieren, [2] die Prüfung der Diskriminanzfähigkeit des geschätzten Gewichtungsschemas. Die beiden Ansätze wurden auf einen Satz realer Daten zur Untersuchung der Assoziation zwischen dem Alter der Mutter bei der Verehelichung und Formen von Fehlgeburten in einer Beobachtungsreihe, durchgeführt an den Krankenschwestern in Kuwait, angewandt. .

Key-Words

Log-Linear Models - Correspondence Analysis - Eigenvalues - Analysis of Variance

Schlüssel-Wörter

Loglineare Modelle - Korrespondenzanalyse - Eigenwerte - Varianzanalyse

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