Aykırı değer varlığında hızlı minimum kovaryans determinantı kestiricilerinin faktör analizinde kullanımı

Çok değişkenli analizlerden biri olan faktör analizi veri indirgeme, değişkenler arasındaki ilişkileri belirleme ve aynı zamanda sınıflandırma yöntemi olarak karşımıza çıkmaktadır. Çok sayıda değişken içeren veri setlerini analiz ederken araştırmacılar problemin sonuçları üzerinde olası zararlı etkileri olabilen ve aykırı değer olarak isimlendirilen olağandışı gözlemlerle karşılaşabilmektedir. Sıklıkla hatalı gözlemler olarak değerlendirilen aykırı değerler, veri seti hakkında önemli bilgileri içinde barındırabileceği gibi kurulan modelin yanlış belirlenmesi, yanlı parametre kestirimi ve yanlış analiz sonuçlarına da neden olabilmektedir. Bu çalışmanın amacı aykırı değerlerin parametre kestirimlerini yanlı yapmayacak özellikte faktör analizi metodunu kullanmaktır. Bu amaçla aykırı değerlerin etkisini azaltan sağlam konum ve ölçek kestiricileri içinden hızlı minimum kovaryans determinantı kestiricileri tercih edilip, bir faktör analizi uygulaması gerçekleştirilmiştir. Sonuç olarak aykırı değerlerin etkisini azaltarak verilerin çoğunluğuna uyan, açıklanan varyansı daha yüksek ve değişkenlerin daha anlamlı olarak faktörlerde toplandığı sağlam faktör analizi kestirim sonuçları elde edilmiştir.

Using fast minimum covariance determinant estimators for factor analysis in the presence of outliers

Factor analysis, one of those multivariate methods, is used for data reduction, determining the relationships between variables, and also as a classification method. The researchers frequently face with the observations that might have bad affects on the results while analysing data sets with many variables. Those kind of observations are called outliers. Outliers, usually evaluated as erroneous observations, may reflect important information about the data set, but on the other hand may cause misspecification of the model, biased parameter estimates, and may lead incorrect analysis results. The aim of this study is to use factor analysis method which will not make biased parameter estimations of the outliers. For this aim, among the robust local and scale parameter estimators which reduce the affects of outliers, fast minimum covariance determinant estimators are choosen and an application is performed. As a result, robust factor analysis estimation results are obtained which are mostly fitted to the data by reducing the affect of the outliers, with higher explained variability and with explained variables which are gathered on more significant factors.

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