Performance of multiple imputation methods for incomplete normally distributed longitudinal data

Öz

Missing data can often occur in longitudinal data. Multiple imputation has been very popular for longitudinal analysis in recent years. In this study, we aim to determine which multiple imputation method is superior for longitudinal normally distributed data when we use linear mixed models. In the literature, multiple imputation by chained equations (MICE) is one of the most popular methods for longitudinal data when using linear mixed models. In MICE, there are three parametric multiple imputation methods, and we compare the three methods with maximum likelihood multiple imputation. Maximum likelihood multiple imputation estimates the parameters using maximum likelihood. After the literature review, we determined that this study will be the first to compare these two approaches for longitudinal normally distributed data when we use linear mixed models. After the simulation study, maximum likelihood multiple imputation has less biased results than the three methods in MICE in terms of mean square error (MSE). The three imputation methods in MICE give closer results to each other. Therefore, we find that maximum likelihood multiple imputation is superior to MICE for longitudinal normally distributed data when we use linear mixed models. Moreover, we show that maximum likelihood multiple imputation can be used for longitudinal normally distributed data with linear mixed models.

Anahtar Kelimeler

• Longitudinal data
• missing completely at random
• missing at random
• multiple imputation
• linear mixed models

Eksik normal dağılımlı boylamsal veriler için çoklu atama yöntemlerinin performansı

Öz

Boylamsal verilerde sıklıkla eksik veri oluşabilir. Çoklu atama, son yıllarda boylamsal veri analizi için oldukça popüler hale gelmiştir. Bu çalışmada, doğrusal karma modeller kullanıldığında boylamsal normal dağılımlı veriler için hangi çoklu atama yönteminin daha üstün olduğu belirlenmeye çalışılmaktadır. Literatürde, doğrusal karma modeller kullanıldığında boylamsal veriler için en popüler yöntemlerden biri zincirleme denklemlerle çoklu atama (MICE) yöntemidir. MICE'de üç parametrik çoklu atama yöntemi vardır ve bu üç yöntem en çok olabilirlik çoklu atama yöntemiyle karşılaştırılmaktadır. En çok olabilirlik çoklu atama, parametreleri en çok olabilirlik kullanarak tahmin eder. Literatür taramasının ardından, bu çalışmanın doğrusal karma modeller kullanıldığında boylamsal normal dağılımlı veriler için bu iki yaklaşımın karşılaştırıldığı ilk çalışma olduğu belirlenmiştir. Simülasyon çalışmasının ardından en çok olabilirlik çoklu atama yönteminin MICE'deki üç yöntemden ortalama kare hata bakımından daha az yanlı sonuçlar verdiği görülmüştür. MICE’deki üç yöntem birbirine yakın sonuçlar vermiştir. Bu nedenle, doğrusal karma modeller kullanıldığında boylamsal normal dağılımlı veriler için en çok olabilirlik çoklu atama yöntemi MICE'den daha üstün olduğu bulunmuştur. Ayrıca, en çok olabilirlik çoklu atama yönteminin, doğrusal karma modellerle birlikte boylamsal normal dağılımlı veriler için kullanılabileceği gösterilmiştir.

Anahtar Kelimeler

• Boylamsal veri
• tamamen rastgele eksik
• rastgele eksik
• çoklu atama
• doğrusal karma modeller

Kaynakça

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