logistic回歸模型總結(jié)

1、轉(zhuǎn)載logistic回歸模型總結(jié)logistic回歸模型是最成熟也是應(yīng)用最廣泛的分類模型，通過學(xué)習(xí)和實(shí)踐擬通過從入門、進(jìn)階到高級(jí)的過程對(duì)其進(jìn)行 總結(jié)，以便加深自己的理解也為對(duì)此有興趣者提供學(xué)習(xí)的便 利。一、有關(guān)logistic的基本概念logistic回歸主要用來預(yù)測(cè)離散因變量與一組解釋變量之間的關(guān)系最常用的是二值型logistic o即因變量的取值只包含兩個(gè)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(shù)學(xué)表達(dá)式為：log (p/1-p ) =A+BX =L其中 p/1-p 稱為優(yōu)勢(shì)比(

2、ODDS)即發(fā)生與不發(fā)生的概率之比可以根據(jù)上式反求由 P (Y=1|X ) = 1 / ( 1 + e A -L) 根據(jù)樣本資料可以通過最大似然估計(jì)計(jì)算由模型的參數(shù) 然后根據(jù)求生的模型進(jìn)行預(yù)測(cè)下面介紹logistic回歸在S A S中的實(shí)現(xiàn)以及輸生結(jié)果的解 釋二、logistic 回歸模型初步SAS中l(wèi)ogistic回歸輸由結(jié)果主要包括預(yù)測(cè)模型的評(píng)價(jià)以及模型的參數(shù)預(yù)測(cè)模型的評(píng)價(jià)與多元線性回歸模型的評(píng)價(jià)類似主要從以下幾個(gè)層次進(jìn)行(1)模型的整體擬合優(yōu)度主要評(píng)價(jià)預(yù)測(cè)值與觀測(cè)值之間的總體一致性?？梢酝ㄟ^以下 兩個(gè)指標(biāo)來進(jìn)行檢驗(yàn)1、 H osmer-Lemeshowz 指標(biāo)HL統(tǒng)計(jì)量的原假設(shè)Ho是預(yù)測(cè)

3、值和觀測(cè)值之間無顯著差異， 因此HL指標(biāo)的P-Value的值越大，越不能拒絕原假設(shè)，即 說明模型很好的擬合了數(shù)據(jù)。在S A S中這個(gè)指標(biāo)可以用LACKFIT選項(xiàng)進(jìn)行調(diào)用2、AIC和SC指標(biāo) 即池雷準(zhǔn)則和施瓦茨準(zhǔn)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(duì)因變量有無解釋作用相當(dāng)于多元回歸中的 F檢驗(yàn) 在logistic回歸中可以通過似然比 (likelihood ratiotest)進(jìn)行檢驗(yàn)(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(tǒng)計(jì)量進(jìn)行度量在SAS中通過 RSQ來調(diào)用Rsqu

4、are , C統(tǒng)計(jì)量自動(dòng)輸生模型評(píng)價(jià)指標(biāo)匯總<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-fontminor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-fontmi nor-latin"> 統(tǒng)計(jì)量<span style="font-family: 宋 體;m

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7、font-family:Calibri;mso-hansi-theme-fontmi頁腳nor-latin”> 作用SAS<span style="font-family: 宋體；mso-ascii-font-family:Calibri;mso-ascii-theme-fontminor-latin;mso-fareast-f ont-family:宋體;mso-fareast-theme-fontminor-fareast;mso-hansi-font- family:Calibri;mso-hansi-theme-font:minor-latin">

8、調(diào)用命令<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-fontminor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-fontmi nor-latin"> 備注 AIC<span style="font-family:宋體;mso-ascii-font-fam

9、ily:頁腳Calibri;mso-ascii-theme-fontminor-latin;mso-fareast-f ont-family:宋體;mso-fareast-theme-fontminor-fareast;mso-hansi-font- family:Calibri;mso-hansi-theme-font:minor-latin”> 、SC<td valign="top"style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-

10、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="font-family: 宋體;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-fareast-fon

11、t-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"style="border-top:none;border-left:none;border-botto m:solid windowtext 1.0pt;border-right:solid windowtext1.0pt;mso-border-top-alt:solid wind

12、owtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt; padding:0cm 5.4pt 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-hans

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

16、indowtext .5pt;mso-border-alt:solid windowtext .5pt;padding:0cm 5.4pt 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;mso-hansi- them

17、e-font:minor-latin”> 模型自動(dòng)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

18、der-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-fontminor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-fontmi nor-latin”>似然比卡

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

21、;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="font-family: 宋體;mso-ascii-font-

22、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;bo

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

24、ii-theme-font:minor-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”>類似與多元回歸中的回歸平方和<td width="177" valign="top"style="width:106.3pt;border-top:none;border-left:none;border-bottom:sol

25、id windowtext1.0pt;border-right:solid windowtext 1.0pt;mso-border-top-alt:solidwindowtext .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-fontmin

26、or-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"> 自動(dòng)輸生<td width="123" valign="top"style="width:73.75pt;border-top:none;border-left: none;border-bottom:solid windowtext1.0pt;b

27、order-right:solid windowtext 1.0pt; mso-border-top-alt:solidwindowtext .5pt;mso-border-left-alt:solidwindowtext .5pt;mso-border-alt:solid windowtext .5pt;padding:0cm5.4pt 0cm 5.4pt">P<span style="font-family: 宋體;mso-ascii-font-family:Calibri;mso-ascii-theme-font:minor-latin;mso-farea

28、st-font-family:宋體;mso-fareast-theme-fontminor-fareast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">值越/卜越好RSQUARE<td valign="top"style="border-top:none;border-left:none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext1.0pt;mso-border-top-

29、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="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-f

30、areast;mso-hansi-font-family:Calibri;mso-hansi-theme-font:minor-latin">越大<td valign="top"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:solidwindow

31、text .5pt;mso-border-alt:solid windowtext .5pt; padding:0cm 5.4pt 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-font-family:Calibri;mso-hansi- theme-font

32、: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-left-alt:solidwindowtext .5pt;mso-border-a

33、lt: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;mso-hansi- theme-font:minor-latin”> 類似與多

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

35、xt .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;mso-hansi- theme-font:minor-latin"> 用 RSQ<span st

36、yle="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;mso-hansi- theme-font:minor-latin”>選項(xiàng)調(diào)用<td width="123" valign="top"style="width:73.75

37、pt;border-top:none;border-left: none;border-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">C<span style="font-family:宋體

38、;mso-ascii-font-family:Calibri;mso-ascii-theme-fontminor-latin;mso-fareast-f ont-family:宋體;mso-fareast-theme-font:minor-fareast;mso-hansi-font- family:Calibri;mso-hansi-theme-font:minor-latin”> 統(tǒng)計(jì)量<td valign="top"style="border-top:none;border-left:none;border-botto m:solid windo

39、wtext 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="font-family: 宋 體;mso-ascii-font-family:Calibri;mso-ascii-theme-fontminor-la

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

41、-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="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:min

42、or-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:solidwindow

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(cè)值和條件預(yù)測(cè)的相對(duì)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-

45、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-fa mily:宋體；mso-fareast-theme-font:minor-fareast;mso-hansi-font-family:Ca

46、libri;mso-hansi- theme-font:minor-latin"> 自動(dòng)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(tǒng)計(jì)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