ﺑﺮآوردﻳﺎﺑﯽ ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺪل ﻫﺎي ﺧﻄﯽ دو ﻣﺮﺣﻠﻪ اي ﻣﻨﻈﻢ

Parameters Estimation in the Regular Two-Stage Linear Models

ﭼﮑﯿﺪه: ﻣﺪل ﻫﺎي ﺧﻄﯽ دو ﻣﺮﺣﻠﻪ اي وﻗﺘﯽ ﻛﺎرﺑﺮد دارﻧﺪ ﻛﻪ داده ﻫﺎي ﻣﺘﻐﻴﺮﻫﺎي ﻣﺴﺘﻘﻞ و واﺑﺴﺘﻪ در دو ﻣﻘﻄﻊ ﯾﺎ ﻣﺮﺣﻠﻪ زﻣﺎﻧﯽ ﺑﻪ دﺳﺖ آﻣﺪه و ﻻزم ﺑﺎﺷﺪ از اﻃﻼﻋﺎت ﻫﺮ دو ﻣﺮﺣﻠﻪ در ﺑﺮازش ﻣﺪل اﺳﺘﻔﺎده ﺷﻮد. در اﻳﻦ ﻣﻘﺎﻟﻪ ﭘﺲ از ﻣﻌﺮﻓﯽ ﻣﺪل ﻫﺎي ﺧﻄﯽ ﭼﻨﺪ ﻣﺮﺣﻠﻪ اي و دو ﻣﺮﺣﻠﻪ اي، ﺑﻪ دو ﺷﻴﻮه ﻣﺨﺘﻠﻒ ﺑﺮآورد ﭘﺎراﻣﺘﺮﻫﺎي ﻣﺪل ﻫﺎي ﺧﻄﯽ دو ﻣﺮﺣﻠﻪ اي ﻣﻨﻈﻢ ﺑﻪ دﺳﺖ آورده ﻣﯽ ﺷﻮﻧﺪ. ﭘﺲ ﺑﺎ ﺗﻮﺟﻪ ﺑﻪ ﭘﻴﭽﻴﺪه ﺑﻮدن ﺑﺮآوردﻫﺎ، روش ﻫﺎي ﻣﺤﺎﺳﺒﺎﺗﯽ ﺑﺎ ﻧﺮم اﻓﺰارR ﺑﺮاي ﺑﺮآورد ﭘﺎراﻣﺘﺮﻫﺎ اراﺋﻪ ﻣﯽ ﺷﻮﻧﺪ. در ﭘﺎﯾﺎن ﻧﺤﻮه ﮐﺎرﺑﺴﺖ ﻣﺪل اراﺋﻪ ﺷﺪه در ﻗﺎﻟﺐ ﯾﮏ ﻣﺜﺎل ﻛﺎرﺑﺮدي ﻧﺸﺎن داده ﻣﯽ ﺷﻮد.

Two stage linear models are applicable when the data of some dependent and independent variables was obtained at to time stage, and we want to use from the data of two stage for linear model fitting. In this article we introduce multistage and, as a special case, two-stage linear models. Then we obtain the parameter estimation by two methods and show that the estimation are the same for methods. Since the expression of estimations are very complicated we give some R program for computing the parameter estimation of two-stage linear models, then show its application in an illustrative example. Also we propose a very simple computational methods for parameter estimation which did not need to complicated expression and give and R program for it.