ﯾﮏ ﻣﻌﯿﺎر ﺟﺪﯾﺪ اﻧﺘﺨﺎب ﻣﺪل ﻣﺒﺘﻨﯽ ﺑﺮ داده ﺗﺎﮔﯽ

A New Model Selection Criterion Based on Data Cloning

ﯾﮏ ﭼﺎﻟﺶ اﺳﺎﺳﯽ در اﺳﺘﻨﺒﺎط ﻣﺪل ﻫﺎي آﻣﯿﺨﺘﻪ، ﻣﻌﺮﻓﯽ ﻣﻌﯿﺎرﻫﺎي ﮐﺎرا ﺑﺮاي اﻧﺘﺨﺎب ﻣﺪل اﺳﺖ. ﻣﻨﺒﻊ اﺻﻠﯽ اﯾﻦ ﭼﺎﻟﺶ ﻧﯿﺰ ﺑﺮازش و ﻣﺤﺎﺳﺒﻪ ﻣﺎﮐﺴﯿﻤﻢ ﺗﺎﺑﻊ درﺳﺘﻨﻤﺎﯾﯽ ﻣﺪل ﻣﯽ ﺑﺎﺷﺪ. داده ﺗﺎﮔﯽ روش ﺟﺪﯾﺪي اﺳﺖ ﮐﻪ ﺑﺮاي ﺑﺮازش ﮐﺎراي ﻣﺪل ﻫﺎي آﻣﯿﺨﺘﻪ ﺑﺎ روش ﻣﺎﮐﺴﯿﻤﻢ درﺳﺘﻨﻤﺎﯾﯽ ﭘﯿﺸﻨﻬﺎد ﺷﺪه اﺳﺖ. اﯾﻦ روش،اﺧﯿﺮا، ﻃﺮﻓﺪاران زﯾﺎدي ﭘﯿﺪا ﮐﺮده اﺳﺖ و ﻣﺸﮑﻼت ﻋﻤﺪه ﺳﺎﯾﺮ روش ﻫﺎي اﺳﺘﻨﺒﺎط ﻣﺒﺘﻨﯽ ﺑﺮ درﺳﺘﻨﻤﺎﯾﯽ در ﻣﺪل ﻫﺎي آﻣﯿﺨﺘﻪ را ﻧﺪارد. ﯾﮑﯽ از ﻣﻌﺎﯾﺐ اﯾﻦ روش، ﻋﺪم ﺗﻮاﻧﺎﯾﯽ ﻣﺤﺎﺳﺒﻪ ﻣﻘﺪار ﻣﺎﮐﺴﯿﻤﻢ ﺗﺎﺑﻊ درﺳﺘﻨﻤﺎﯾﯽ اﺳﺖ. اﯾﻦ ﻣﻘﺪار ﯾﮏ ﮐﻤﯿﺖ ﮐﻠﯿﺪي در ﻣﻌﺮﻓﯽ و ﻣﺤﺎﺳﺒﻪ ﻣﻌﯿﺎرﻫﺎي اﻧﺘﺨﺎب ﻣﺪل ﻣﺤﺴﻮب ﻣﯽ ﺷﻮد. ﺑﻨﺎﺑﺮاﯾﻦ ﺑﻪ ﻧﻈﺮ ﻣﯽ رﺳﺪ ﺑﺎ روش داده ﺗﺎﮔﯽ ﻧﻤﯽ ﺗﻮان ﯾﮏ ﻣﻌﯿﺎر اﻃﻼع ﻣﻨﺎﺳﺐ، ﺑﻪ ﻃﻮر ﻣﺴﺘﻘﯿﻢ، ﺑﺮاي ﯾﺎﻓﺘﻦ ﺑﻬﺘﺮﯾﻦ ﻣﺪل در رده ﻣﺪل ﻫﺎي آﻣﯿﺨﺘﻪ، ﺗﻌﺮﯾﻒ ﮐﺮد. اﯾﻦ ﭘﮋوﻫﺶ ﺗﻼﺷﯽ اﺳﺖ در ﺟﻬﺖ ﻧﻘﺾ اﯾﻦ ﺑﺎور. در اﯾﻦ ﻣﻘﺎﻟﻪ،ﯾﮏ ﻣﻌﯿﺎر ﻣﺒﺘﻨﯽ ﺑﺮ روش داده ﺗﺎﮔﯽ ﻣﻌﺮﻓﯽ ﻣﯽ ﺷﻮد و ﻋﻤﻠﮑﺮد آن در ﯾﮏ ﻣﻄﺎﻟﻌﻪ ﺷﺒﯿﻪ ﺳﺎزي ﻣﻮرد ارزﯾﺎﺑﯽ ﻗﺮار ﻣﯽ ﮔﯿﺮد.

Introducing some efficient model selection criteria for mixed models is a substantial challenge; Its source is indeed fitting the model and computing the maximum likelihood estimates of the parameters. Data cloning is a new method to fit mixed models efficiently in a likelihood-based approach. This method has been popular recently and avoids the main problems of other likelihood-based methods in mixed models. A disadvantage of data cloning is its inability of computing the maximum of likelihood function of the model. This value is a key quantity in proposing and calculating information criteria. Therefore, it seems that we can not, directly, define an appropriate information criterion by data cloning approach. In this paper, this believe is broken and a criterion based on data cloning is introduced. The performance of the proposed model selection criterion is also evaluated by a simulation study.