Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
Semiparametric Mixed Models for Longitudinal Data: Wavelets Analysis as Smoothing Approach
Longitudinal Veriler İçin Semiparametrik Karışık Modeller: Smoothing Yaklaşımı Olarak Dalgacık Analizi
Marwa BEN GHOULa, Berna YAZICIa, Ahmet SEZERa
aDepartment of Statistics, Eskişehir Technical University, Faculty of Science, Eskişehir, TURKEY
Turkiye Klinikleri J Biostat. 2019;11(1):24-35
doi: 10.5336/biostatic.2019-64979
Article Language: EN
Full Text
ABSTRACT
 Objective: This paper consists on examining a longitudinal data, output of generated data, via constructing a semiparametric model, the wavelets analysis will be applied as smoothing approach for the nonparametric part of the model. Material and Methods: Mixed effects models have been largely examined due to their flexibility in handling data without constraints. Mixed models could be characterized with their parametric and nonparametric features. Indeed, semiparametric mixed models which combine parametric and nonparametric features, started to receive more attention notably for examining longitudinal data. Regarding the nonparametric features, smoothing approaches should be applied. Recently, the wavelets analysis has been considered as a powerful mathematic tool to decompose a series due to its multiresolution features (frequential and temporal) and some researchers mentioned it as a smoothing approach for large data, but the wavelets features for smoothing still not commonly applied on longitudinal data. Results: A data is generated referring to a previous published hypertension study by National Institute Health. The results show that the wavelets analysis has a strong capacity as smoothing approach compared to well-known other smoothing methods; Root Mean Square Errors are calculated, and via the constructed semiparametric model, it has been confirmed that the incident hypertension is related to the high Systolic blood pressure, high diastolic blood pressure and low BMI.

Keywords: Longitudinal data; smoothing approaches; wavelets decomposition; semiparametric model; mixed models
ÖZET
 Amaç: Bu makale, türetilmiş bir longitudinal veri seti için, bir yarı parametrik model kurularak incelenmesi üzerine olup, modelin parametrik olmayan kısmı için pürüzsüzleştirme yaklaşımı dikkate alınarak dalga analizi uygulanacaktır. Gereç ve Yöntemler: Karışık etki modelleri, verilerin kısıtlama olmadan kullanılmasındaki esneklikleri nedeniyle yaygın biçimde çalışılmaktadır. Karışık modeller parametrik ve parametrik olmayan özellikleri dikkate alınarak incelenebilir. Nitekim, parametrik ve parametrik olmayan özellikleri birleştiren yarı parametrik karışık modeller, özellikle longitudinal verilerin analizi için daha fazla çalışılmaya başlanmıştır. Parametrik olmayan özellikler ile ilgili olarak, pürüzsüzleştirme yaklaşımları uygulanmalıdır. Son zamanlarda, dalga analizi, çoklu çözünürlük özellikleri (sıklık ve zamansal) nedeniyle bir dizi ayrıştırmak için güçlü bir matematiksel araç olarak kabul edilmektedir, ancak dalga analizi hala longitudinal veri seti için yaygın bir biçimde kullanılmamaktadır. Bulgular: National Institute Health tarafından daha önce yayınlanmış bir hipertansiyon çalışmasına atıfta bulunan bir veri üretilmiştir. Sonuçlar, bilinen diğer pürüzsüzleştirme yöntemlerine kıyasla dalga analizinin, pürüzsüzleştirme yaklaşımı olarak güçlü bir yaklaşım olduğunu göstermektedir; Ortalama Kare Kök Hatalar hesaplanmış ve oluşturulan semiparametrik model aracılığıyla, hipertansiyonunun yüksek Sistolik kan basıncı, yüksek diyastolik kan basıncı ve düşük BMI ile ilişkili olduğu doğrulanmıştır.

Anahtar Kelimeler: Longitudinal boylamsal veri; pürüzsüzleştirme yaklaşımları;dalga ayrışması; yarı parametrik model; karma modeller
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