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[Mixed Model 4.2.1] Random Coefficient Models 2018.04.16
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[Mixed Model 4.2.1] Random Coefficient Models

 

 

 

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¢º Random coefficient model Á¤ÀÇ

 


°øºÐ»êºÐ¼®(Analysis of covariance)¿¡¼­, °øº¯·®ÀÇ È¸±Í°è¼ö´Â fixed effect·Î °¡Á¤ÇÕ´Ï´Ù.

Áï, µ¥ÀÌÅͷκÎÅÍ ÃßÁ¤µÈ unknown fixed parameters·Î °¡Á¤ÇÕ´Ï´Ù.


Random coefficient modelÀº Çϳª ÀÌ»óÀÇ °øº¯·®¿¡ ´ëÇÑ È¸±Í°è¼ö¸¦ °¡´ÉÇÑ °è¼ö¿¡¼­ÀÇ random sample·Î °¡Á¤ÇϹǷΠrandom coefficient¶ó´Â ¿ë¾î¸¦ »ç¿ëÇÕ´Ï´Ù.

Random coefficient modelÀº µ¶¸³ÀûÀÎ subjects ¶Ç´Â clusters¿¡¼­ µ¥ÀÌÅͰ¡ »ý°Ü³ª¸é ¹Î°¨ÇÏ°Ô ¹ÝÀÀÇÕ´Ï´Ù.

µû¶ó¼­ Random deviationÀº ¸ðÁý´Ü ȸ±Í¸ðÇü¿¡¼­ ¹þ¾î³­ subjects ¶Ç´Â clusters¿¡ ´ëÇÑ °ªÀ¸·Î °¡Á¤µË´Ï´Ù.







¢¹ °øºÐ»êºÐ¼®(ANCOVA)

 


¾Õ¿¡¼­ ¼³¸íÇßµíÀÌ °øºÐ»êºÐ¼®¿¡¼­ fixed effect´Â ºÐ·ùº¯¼ö(classification variable)°¡ ¸ðµç °ü½É ¼öÁØÀ» ³ªÅ¸³»´Â °ÍÀ¸·Î °¡Á¤ÇÕ´Ï´Ù.

ºÐ·ùº¯¼öÀÇ °¢ ¼öÁØ¿¡ ´ëÇÑ È¸±Í°è¼ö´Â µ¥ÀÌÅÍ¿¡¼­ ÃßÁ¤µÈ unknown fixed parametersÀÔ´Ï´Ù.









¢¹ Random coefficient Model

ÀÌ ±×·¡ÇÁ¿¡¼­´Â °¢ subject(´ë»óÀÚ)¿¡ ´ëÇÑ ÀÓÀÇÀÇ È¸±ÍÁ÷¼±Àº Àüü ¸ðÁý´Ü¿¡ ´ëÇÑ È¸±ÍÁ÷¼±()°ú Â÷À̰¡ ÀÖ½À´Ï´Ù.

Random coefficient modelÀ» ÀûÇÕÇÏ´Â ¸ñÇ¥´Â

(1) ÀýÆí°ú ±â¿ï±âÀÇ ºÐ»ê°ú µÎ º¯¼ö°£ÀÇ °øºÐ»êÀ» ÃßÁ¤ÇÏ´Â °Í°ú

(2) °¢°¢ÀÇ subject¿Í cluster¿¡ ´ëÇØ °¡Àå Àß ÀûÇÕÇÏ´Â best linear unbiased predictors (BLUP)¸¦ ¾ò´Â °ÍÀÔ´Ï´Ù.


´õ ¸¹Àº ¼öÁØÀÇ °èÃþÀ¸·Î È®Àå½ÃŰ°Å³ª °¢ ¼öÁØ¿¡¼­ µÎ °³ ÀÌ»óÀÇ random coefficient·Î È®Àå½Ãų ¼ö ÀÖÁö¸¸, ¿©±â¼­´Â standard random intercept-slope modelÀ» °í·ÁÇϰڽÀ´Ï´Ù.












¢º ¿¹Á¦ µ¥ÀÌÅÍ

 

 

 

 

10 ǰÁ¾(variety)ÀÇ ¹ÐÀ» ¹«ÀÛÀ§·Î ¼±º°ÇÏ¿´°í, °¢ ǰÁ¾Àº 6°³ÀÇ À§Ä¡¿¡ ¹«ÀÛÀ§·Î ¹èÁ¤µÇ¾ú½À´Ï´Ù.

ÃÖÁ¾ ¼öÈ®·®(yield)Àº ½Ä¹°ÀÇ ¼öºÐÇÔ·®(moist)¿¡ ÀÇÇØ ¿µÇâÀ» ¹ÞÀ» ¼ö ÀÖ´Ù°í »ý°¢µÇ¾î, ¼öºÐÇÔ·®°ú ¼öÈ®·®À» ÃøÁ¤ÇÏ¿´½À´Ï´Ù.


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¹ÐÀÇ 10°³ÀÇ Ç°Á¾ÀÌ ¸ðÁý´Ü¿¡¼­ ¹«ÀÛÀ§·Î ¼±ÅõǾú±â ¶§¹®¿¡ random effectÀ̸ç, °¢°¢ÀÇ ¸ðÇüÀº ¸ðÁý´Ü ¸ðÇü¿¡¼­ÀÇ deviations·Î Ç¥ÇöµÉ ¼ö ÀÖ½À´Ï´Ù.








¢¹ ¼öÈ®·®°ú ¼öºÐÇÔ·®

 

¼öÈ®·®(yield)°ú ¼öºÐÇÔ·®(moist)ÀÇ ºÐÆ÷¸¦ »ìÆìº¸¸é, ¸ðÁý´Ü¿¡¼­´Â ¼öºÐÇÔ·®ÀÌ Áõ°¡ÇÒ¼ö·Ï ¼öÈ®·®ÀÌ Áõ°¡ÇÏ¿´½À´Ï´Ù.

¶ÇÇÑ ÀÌ ÀڷḦ ÀÌ¿ëÇØ¼­ ¼±Çü ȸ±ÍºÐ¼®(linear regression) ¸ðÇüÀ» »ç¿ëÇÏ´Â °ÍÀ» ÀûÀýÇÑ °ÍÀ¸·Î ÆÇ´ÜÇÏ¿´½À´Ï´Ù.






´ÙÀ½ ½Ã°£¿¡´Â À§¿¡¼­ ¼Ò°³ÇÑ ¿¹Á¦µ¥ÀÌÅ͸¦ »ç¿ëÇÏ¿© Random coefficient model¿¡ ÀûÇÕÇØº¸µµ·Ï ÇϰڽÀ´Ï´Ù.

 

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 [Mixed Model 4.2.2] Random Coefficient Models
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