رگرسيون ضرايب متغير طولي حاشيه اي

Marginal Longitudinal Varying Coefficient Regression Via Penalized Spline

ﻣﺪل ﻫﺎي رﮔﺮﺳﯿﻮﻧﯽ ﻧﺎﭘﺎراﻣﺘﺮي و ﻧﯿﻤﻪ ﭘﺎراﻣﺘﺮي در زﻣﯿﻨﻪ داده ﻫﺎي ﻣﺴﺘﻘﻞ ﺗﻮﺳﻌﻪ ﭼﺸﻤﮕﯿﺮي ﭘﯿﺪاﮐﺮده اﻧﺪ، اﻣﺎ رﺷﺪ آن ﻫﺎ در زﻣﯿﻨﻪ داده ﻫﺎي ﻃﻮﻟﯽ، ﻣﺤﺪود ﺑﻪ ﭼﻨﺪ ﺳﺎل اﺧﯿﺮ اﺳﺖ. از آﻧﺠﺎ ﮐﻪ روش ﻫﺎي رﮔﺮﺳﯿﻮﻧﯽ ﻣﻌﻤﻮل ﺑﺮاي داد ه ﻫﺎي ﻫﻤﺒﺴﺘﻪ ﻧﺴﺒﺖ ﺑﻪ داده ﻫﺎي ﻣﺴﺘﻘﻞ ﺗﻮاﻧﺎﯾﯽ ﮐﻤﺘﺮي دارﻧﺪ، ﺑﺎﯾﺪ از ﻣﺪل ﻫﺎﯾﯽ اﺳﺘﻔﺎده ﺷﻮد، ﮐﻪ ﻫﻤﺒﺴﺘﮕﯽ ﺑﯿﻦ داده ﻫﺎ را ﻧﯿﺰ در ﻧﻈﺮ ﺑﮕﯿﺮﻧﺪ. در اﯾﻦ ﻣﯿﺎن ﻣﺪل ﻫﺎي آﻣﯿﺨﺘﻪ و ﺣﺎﺷﯿﻪ اي ﮐﻪ ﻋﺎﻣﻞ ﻫﻤﺒﺴﺘﮕﯽ ﺑﯿﻦ داده ﻫﺎ را ﻧﯿﺰ در ﻧﻈﺮ ﻣﯽ ﮔﯿﺮﻧﺪ، ﻣﺪل ﻫﺎﯾﯽ ﻫﺴﺘﻨﺪ ﮐﻪ ﺑﺮاي ﺑﺮازش داده ﻫﺎي ﻃﻮﻟﯽ ﻣﻮرد اﺳﺘﻔﺎده ﻗﺮار ﻣﯽ ﮔﯿﺮﻧﺪ. ﻫﻤﭽﻨﯿﻦ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ اﻧﻌﻄﺎف ﭘﺬﯾﺮي ﻣﺪل ﻫﺎي ﻧﯿﻤﻪ ﭘﺎراﻣﺘﺮي ﻧﺴﺒﺖ ﺑﻪ ﻣﺪل ﻫﺎي ﭘﺎراﻣﺘﺮي و ﻧﺎﭘﺎراﻣﺘﺮي، ﻣﺪل رﮔﺮﺳﯿﻮن ﻧﯿﻤﻪ ﭘﺎراﻣﺘﺮي ﻃﻮﻟﯽ ﺣﺎﺷﯿﻪ اي ﺑﺎ ﺑﺮآوردﻫﺎي اﺳﭙﻼﯾﻦ ﺗﺎواﻧﯿﺪه ﻣﺪل ﻣﻨﺎﺳﺒﯽ ﺑﺮاي ﺗﺤﻠﯿﻞ داده ﻫﺎي ﻃﻮﻟﯽ اﺳﺖ. در اﯾﻦ ﻣﻘﺎﻟﻪ رﮔﺮﺳﯿﻮن ﻧﯿﻤﻪ ﭘﺎراﻣﺘﺮي ﺑﺎ ﺿﺮاﯾﺐ ﻣﺘﻐﯿﺮ ﮐﻪ در آن ارﺗﺒﺎط ﺑﯿﻦ ﻣﺘﻐﯿﺮ ﭘﺎﺳﺦ و ﯾﮏ ﻣﺘﻐﯿﺮ ﭘﯿﺶ ﺑﯿﻦ ﺑﺮ ﻣﺒﻨﺎي ﻣﺘﻐﯿﺮ ﭘﯿﺶ ﺑﯿﻦ دﯾﮕﺮ ﻣﺸﺨﺺ ﻣﯽ ﺷﻮد، ﺑﺮرﺳﯽ ﺷﺪه اﺳﺖ. ﻫﻤﭽﻨﯿﻦ اﺳﺘﻨﺒﺎط ﺑﯿﺰي ﺑﺮاي ﻣﺪل ﻧﺎﭘﺎراﻣﺘﺮي روي داده ﻫﺎي ﺷﺒﯿﻪ ﺳﺎزي ﺷﺪه و ﺑﺮاي ﻣﺪل ﻧﯿﻤﻪ ﭘﺎراﻣﺘﺮي ﻃﻮﻟﯽ ﺣﺎﺷﯿﻪ اي روي داده ﻫﺎي واﻗﻌﯽ، ﺑﺎ ﻧﺮم اﻓﺰارﻫﺎي اﺳﺘﺎﻧﺪارد اﻧﺠﺎم ﺷﺪه اﺳﺖ ﮐﻪ ﻧﺸﺎن دﻫﻨﺪه ﻋﻤﻠﮑﺮد ﻗﺎﺑﻞ ﻗﺒﻮل اﯾﻦ اﺳﺘﻨﺒﺎط اﺳﺖ.

The nonparametric and semiparametric regression models have been improved extensively in the field of cross-sectional study and independent data, but their improvement in the field of longitudinal data is restricted to the recent years or decade. Since the common methods for correlated data have a much lower ability rather than for the independent data, we should use the models which consider the correlation among the data. The mixed and marginal models consider the correlation factor among the data, and so obtain a better fit for that. Furthermore, the semiparametric regression has more flexibility compared to the parametric and nonparametric regression. Consequently, based on the properties of the longitudinal data, the marginal longitudinal semiparametric regression with the penalized spline estimations, is a suitable choice for the analysis of the longitudinal data. In this article, the semiparametric regression with different coefficients which specifies the relationship between a response variable and an explanatory variable based on another explanatory variable is assessed. In addition, Bayesian inference on the nonparametric model for a simulated data and the marginal longitudinal semiparametric model for a real data have been done by standard software; and the results have good performance.