Longitudinal veri analizinde eksik gözlem, aykırı değer ve modelleme üzerine çalışma

Longitudinal data consists in gathering several observations of the same subjects intermittently over time. Attrition, outliers and complexity of modeling are common issues in longitudinal data. Therefore, this dissertation outlines those issues and proposes different approaches to overcome them by following three main pillars. First pillar emphasises the prominence of missingness mechanisms and suggests a novel algorithm to treat missing data via Multilayer Perceptron (MLP) with comparison to the ad hoc methods and Expectation Maximum (EM) algorithm. Second pillar consists in presenting outliers as a friendly subject in statistical data not a misleading dilemma, via proposing two novel algorithms using wavelet decomposition within subjects and across subjects along with applying the winsorisation approach within subjects. Last pillar concentrates on modeling via constructing a semiparametric model that combines parametric and nonparametric features. For the nonparametric part of the model, smoothing approaches are required. This research proposes wavelet analysis to smooth data. To examine the efficiency of the proposed algorithms, a real longitudinal dataset and a generated one, are utilized. The results revealed that wavelet decomposition has an impressive capacity as a smoothing approach and as a microscope figuring out the outliers and handling them without losing the originality of the data features. Also, the novel algorithm related to missing data imputation via the output predictions of MLP showed valuable results better than the ad hoc imputation methods and with very slight difference from the EM algorithm. Keywords: Longitudinal data, Semiparametric model, Missing data, Missingness mechanisms, Outliers, Wavelet analysis, Neural network