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Avrasya Ekonometri �statistik ve Ampirik Ekonomi DergisiYl:2017 Say: 6 Alan: statistik

Seda BADATLI KALKAN
BOYLAMSAL VERLERN ANALZNDE KULLANILAN SPLAYN MODELLER
 
Boylamsal veriler, ayn birimlere ait zelliklerin zaman ierisinde tekrarl olarak llmesi ile elde edilen verilerdir. Boylamsal verilerin analizi, bamszlk ve sabit varyansllk varsaym salanamadndan klasik regresyon modelleri ile gerekletirilememektedir. Bu nedenden dolay boylamsal veriler iin zel regresyon modelleri gelitirilmitir. Klasik parametrik modeller, baml deiken ile bamsz deiken(ler) arasndaki ilikinin dorusal olmas veya ilikinin bilinen parametrik fonksiyonlarla ifade edilmesi temeline dayanmaktadr. Bu durumda da gerek iliki yaps ortaya karlamamaktadr. Boylamsal veri setlerinde bu durum gvenilir ve mantkl sonulara ulalmasn engelleyecektir. Dolaysyla boylamsal verilerde baml deiken ile bamsz deiken(ler) arasndaki ilikinin daha karmak olduu durumlarda, parametrik olmayan regresyon modelleri kullanlmaktadr. Bu almada boylamsal verilerin analizinde kullanlan parametrik olmayan regresyon modellerinden splayn modelleri teorik olarak incelenmitir.

Anahtar Kelimeler: Boylamsal veriler, Parametrik Olmayan Regresyon, Splayn Modelleri, Dzeltme Splaynlar, Cezal Splaynlar, Regresyon Splaynlar


SPLINE MODELS WHICH USE IN LONGITUDINAL DATA ANALYSIS
 
Longitudinal data is defined as data obtained by a repeated measurement of variables pertaining to the same units over time. The analysis of longitudinal data cannot be achieved through classical regression models because of the independence and multicollinearity assumptions. For this reason, specific regression models have been developed for such data. Classical parametric models are based on the rationale that the relation between the dependent variable and the independent variable(s) is linear or the relation is expressed through known parametric functions. In such a case, it is not possible to reveal the actual structure of the relation, which will prevent the researcher from achieving reliable and rational outcomes particularly in longitudinal datasets. Non-parametric regression model is utilized in cases where the relation between the dependent variable and the independent variable(s) is more complicated in longitudinal data. In this study spline models in nonparametric regression models which use in longitudinal data are investigated theoretically.

Keywords: Longitudinal data, Nonparametric Regression, Spline Models, Smoothing Splines, penalized Splines, Regression Splines


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