Kategorik Veride Faktör Analizi İçin Kullanılabilecek Alternatif Bir Korelasyon Matrisi: Goodman-Kruskal Gamma

Abstract

Açımlayıcı faktör analizi (AFA) sosyal bilimler alanında ölçeklerden elde edilen verilerin yapı geçerliğine yönelik kanıt toplama sürecinde sıklıkla kullanılmaktadır. Veriler kategorik olduğunda polikorik/tetrakorik korelasyon matrisiyle analizler gerçekleştirilirken veriler sürekli olduğunda Pearson korelasyon matrisiyle analizler gerçekleştirilmektedir. Ancak bazı durumlarda polikorik korelasyon matrisi kullanıldığında modelde yakınsama sağlanamamakta Pearson korelasyon matrisi kullanıldığında ise faktör yükleri olması gerekenden daha düşük kestirilmektedir. Bu nedenle polikorik ve Pearson korelasyon matrisine alternatif olarak Goodman-Kruskal Gamma ve Lambda katsayılarıyla gerçekleştirilen AFA sonuçlarının karşılaştırılması çalışmanın amacını oluşturmaktadır. Bu amaçla gerçekleştirilen Monte Carlo simülasyon çalışmasında; kategori sayısı, ortalama faktör yükü, örneklem büyüklüğü ve verilerin dağılımı değişkenleri simülasyon koşulu olarak belirlenmiştir. Araştırma sonucunda bazı koşullarda polikorik korelasyon matrisiyle gerçekleştirilemeyen AFA kestirimlerinin Goodman-Kruskal Gamma katsayısıyla oluşturulan matrisle yapılabildiği gözlenmiştir. Lambda katsayısı kullanıldığında ise bazı koşullarda kestirim yapılamamıştır. Kestirim yapılan koşullarda ise genellikle faktör yükleri olduğundan düşük kestirilmiştir. Kategori sayısının artmasıyla Goodman-Kruskal Gamma katsayısından elde edilen sonuçların daha az yanlı olduğu gözlenmiştir. Araştırmacılara kategorik veriyle AFA gerçekleştirilirken Goodman-Kruskal Gamma katsayısından elde edilecek sonuçların da incelemesi önerilebilir.

Keywords

• Açımlayıcı Faktör Analizi
• Korelasyon Matrisi
• Polikorik Korelasyon
• Goodman-Kruskal Gamma
• Goodman-Kruskal Lambda

An Alternative Correlation Matrix Based Factor Analysis for Categorical Data: Goodman and Kruskal’s Gamma

Abstract

Exploratory factor analysis (EFA) is a frequently used method in social sciences while gathering evidence for the construct validity of data obtained from scales. When the data are categorical, EFA is performed using the polychoric/tetrachoric correlation matrix, while analyses are performed using the Pearson correlation matrix when the data are continuous. However, in some cases when the polychoric correlation matrix is used, non-convergence issues can emerge, and factor loadings can be underestimated when the Pearson correlation matrix is used. Therefore, this study aims to compare the EFA results obtained from Goodman and Kruskal’s lambda and gamma coefficients as an alternative correlation matrix with the results obtained from the polychoric and Pearson correlation matrix. In the Monte Carlo simulation study carried out for this purpose, variables such as number of categories, average factor loading, sample size, and distribution of variables were determined as the simulated conditions. As a result of the study, in some conditions unachievable using the polychoric correlation matrix, estimations are observed able to be made with the matrix formed by Goodman and Kruskal’s gamma coefficient. In certain conditions using the lambda coefficient, the model did not converge. Lambda had underestimated factor loadings in the converged data sets. The results obtained from Goodman and Kruskal’s gamma are also observed to be less biased as the number of categories increases. Researchers can be recommended to examine the results obtained from Goodman and Kruskal’s gamma while performing EFA with categorical data.

Keywords

• Exploratory Factor Analysis
• Correlation Matrix
• Polychoric Correlation
• Goodman-Kruskal Gamma
• Goodman-Kruskal Lambda

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