logistic回歸模型總結

1、轉載logistic回歸模型總結logistic回歸模型是最成熟也是應用最廣泛的分類模型，通過學習和實踐擬通過從入門、進階到高級的過程對其進行 總結，以便加深自己的理解也為對此有興趣者提供學習的便 利。一、有關logistic的基本概念logistic回歸主要用來預測離散因變量與一組解釋變量之間的關系最常用的是二值型logistic o即因變量的取值只包含兩個類別例如：好、壞；發(fā)生、不發(fā)生；常用 Y=1或Y=0表示X表 示解釋變量則P (Y二1|X )表示在 X的條件下 Y=1的概率，logistic回歸 的數學表達式為：log (p/1-p ) =A+BX =L其中 p/1-p 稱為優(yōu)勢比(

2、ODDS)即發(fā)生與不發(fā)生的概率之比可以根據上式反求由 P (Y=1|X ) = 1 / ( 1 + e A -L) 根據樣本資料可以通過最大似然估計計算由模型的參數 然后根據求生的模型進行預測下面介紹logistic回歸在S A S中的實現以及輸生結果的解 釋二、logistic 回歸模型初步SAS中l(wèi)ogistic回歸輸由結果主要包括預測模型的評價以及模型的參數預測模型的評價與多元線性回歸模型的評價類似主要從以下幾個層次進行(1)模型的整體擬合優(yōu)度主要評價預測值與觀測值之間的總體一致性?？梢酝ㄟ^以下 兩個指標來進行檢驗1、 H osmer-Lemeshowz 指標HL統計量的原假設Ho是預測

3、值和觀測值之間無顯著差異， 因此HL指標的P-Value的值越大，越不能拒絕原假設，即 說明模型很好的擬合了數據。在S A S中這個指標可以用LACKFIT選項進行調用2、AIC和SC指標 即池雷準則和施瓦茨準則與線性回歸類似 AIC和SC越小說明模型擬合的越好(2)從整體上看解釋變量對因變量有無解釋作用相當于多元回歸中的 F檢驗 在logistic回歸中可以通過似然比 (likelihood ratiotest)進行檢驗(3)解釋變量解釋在多大程度上解釋了因變量與線性回歸中的 RA2作用類似在logistic回歸中可以通過 Rsquare和C統計量進行度量在SAS中通過 RSQ來調用Rsqu

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13、i-font-family:Calibri;mso-hansi- theme-font:minor-latin"> 越好<td width="197" valign="top"style="width:117.9pt;border-top:none;border-left:none;border-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .5pt;mso-border

14、-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt;padding:0cm5.4pt 0cm 5.4pt"><span style="font-family: 宋 體;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-fa mily:宋體；mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;

15、mso-hansi- theme-font:minor-latin”>類似與多元回歸中的殘差平方和<td width="177" valign="top"style="width:106.3pt;border-top:none;border-left:none;border-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .5pt;mso-border-left-alt:solidw

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17、e-font:minor-latin”> 模型自動輸生<td width="123" valign="top"style="width:73.75pt;border-top:none;border-left:none;border-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-bor

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19、方<td valign="top"style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext1.0pt;mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt; padding:0cm 5.4pt 0cm 5.4pt"

20、><span style="font-family: 宋體;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋體；mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;mso-hansi- theme-font:minor-latin"> 越大<td valign="top"style="border-top:none

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23、rder-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt;padding:0cm5.4pt 0cm 5.4pt"><span style="font-family: 宋 體;mso-ascii-font-family:Calibri;mso-asc

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34、元回歸中的RA2<td width="177" valign="top"style="width:106.3pt;border-top:none;border-left:none;border-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowte

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40、tin;mso-fareast-font-family:宋體；mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;mso-hansi- theme-font:minor-latin"> 越大<td valign="top"style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext1.0pt;mso-border

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43、text .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt;padding:0cm5.4pt 0cm 5.4pt"><span style="font-family: 宋 體;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋體；mso-fareast-theme-font:minor-fareast;mso-hansi-f

44、ont-family:Calibri;mso-hansi- theme-font:minor-latin”>度量觀測值和條件預測的相對一致性<td width="177" valign="top"style="width:106.3pt;border-top:none;border-left: none;border-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .5pt;mso-

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46、libri;mso-hansi- theme-font:minor-latin"> 自動輸生<td width="123" valign="top"style="width:73.75pt;border-top:none;border-left:none;border-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .5pt;mso-border-left-alt:soli

47、dwindowtext .5pt;mso-border-alt:solid windowtext .5pt;padding:0cm5.4pt 0cm 5.4pt">HL<span style="font-family: 宋體；mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-f ont-family:宋體;mso-fareast-theme-font:minor-fareast;mso-hansi-font- family:Calibri;mso-hansi-th

48、eme-font:minor-latin”> 統計量<td valign="top"style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext1.0pt;mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt;paddin

49、g:0cm 5.4pt 0cm 5.4pt"><span style="font-family: 宋 體;mso-ascii-font-family:Calibri;mso-ascii-theme-fontminor-latin;mso-fareast-font-fa mily:宋體；mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Calibri;mso-hansi- theme-font:minor-latin"> 越小<td valign="top"

50、;style="border-top:none;border-left:none;border-botto m:solid windowtext 1.0pt;border-right:solid windowtext1.0pt;mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt; padding:0cm 5.4pt 0cm 5.4pt"><span style="fon

51、t-family: 宋 體;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-font-family:宋體；mso-fareast-theme-font: minor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin"> 越好<td width="197" valign="top"style="width:117.9pt;border-top:none;border-left: none;border-bottom:solid windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .5pt;mso-borde