外文翻譯----sas統(tǒng)計(jì)分析軟件和logistic回歸

1、<p>　　SAS統(tǒng)計(jì)分析軟件和Logistic回歸</p><p><b>　　1．概況： </b></p><p>　　SAS系統(tǒng)全稱為Statistics Analysis System，最早由北卡羅來納大學(xué)的兩位生物統(tǒng)計(jì)學(xué)研究生編制，并于1976年成立了SAS軟件研究所，正式推出了SAS軟件。SAS是用于決策支持的大型集成信息系統(tǒng)，但該軟件系統(tǒng)最早的

2、功能限于統(tǒng)計(jì)分析，至今，統(tǒng)計(jì)分析功能也仍是它的重要組成部分和核心功能。SAS現(xiàn)在的版本為9.0版，大小約為1G。經(jīng)過多年的發(fā)展，SAS已被全世界120多個(gè)國(guó)家和地區(qū)的近三萬家機(jī)構(gòu)所采用，直接用戶則超過三百萬人，遍及金融、醫(yī)藥衛(wèi)生、生產(chǎn)、運(yùn)輸、通訊、政府和教育科研等領(lǐng)域。在英美等國(guó)，能熟練使用SAS進(jìn)行統(tǒng)計(jì)分析是許多公司和科研機(jī)構(gòu)選材的條件之一。在數(shù)據(jù)處理和統(tǒng)計(jì)分析領(lǐng)域，SAS系統(tǒng)被譽(yù)為國(guó)際上的標(biāo)準(zhǔn)軟件系統(tǒng)，并在96～97年度被評(píng)選為建立

3、數(shù)據(jù)庫(kù)的首選產(chǎn)品?？胺Q統(tǒng)計(jì)軟件界的巨無霸。在此僅舉一例如下：在以苛刻嚴(yán)格著稱于世的美國(guó)FDA新藥審批程序中，新藥試驗(yàn)結(jié)果的統(tǒng)計(jì)分析規(guī)定只能用SAS進(jìn)行，其他軟件的計(jì)算結(jié)果一律無效！哪怕只是簡(jiǎn)單的均數(shù)和標(biāo)準(zhǔn)差也不行！由此可見SAS的權(quán)威地位。</p><p>　　SAS系統(tǒng)是一個(gè)組合軟件系統(tǒng)，它由多個(gè)功能模塊組合而成，其基本部分是BASE SAS模塊。BASE SAS模塊是SAS系統(tǒng)的核心，承擔(dān)著主要的數(shù)據(jù)管理任務(wù)

4、，并管理用戶使用環(huán)境，進(jìn)行用戶語言的處理，調(diào)用其他SAS模塊和產(chǎn)品。也就是說，SAS系統(tǒng)的運(yùn)行，首先必須啟動(dòng)BASE SAS模塊，它除了本身所具有數(shù)據(jù)管理、程序設(shè)計(jì)及描述統(tǒng)計(jì)計(jì)算功能以外，還是SAS系統(tǒng)的中央調(diào)度室。它除可單獨(dú)存在外，也可與其他產(chǎn)品或模塊共同構(gòu)成一個(gè)完整的系統(tǒng)。各模塊的安裝及更新都可通過其安裝程序非常方便地進(jìn)行。SAS系統(tǒng)具有靈活的功能擴(kuò)展接口和強(qiáng)大的功能模塊，在BASE SAS的基礎(chǔ)上，還可以增加如下不同的模塊而增加不

5、同的功能：SAS/STAT（統(tǒng)計(jì)分析模塊）、SAS/GRAPH（繪圖模塊）、SAS/QC（質(zhì)量控制模塊）、SAS/ETS（經(jīng)濟(jì)計(jì)量學(xué)和時(shí)間序列分析模塊）、SAS/OR（運(yùn)籌學(xué)模塊）、SAS/IML（交互式矩陣程序設(shè)計(jì)語言模塊）、SAS/FSP（快速數(shù)據(jù)處理的交互式菜單系統(tǒng)模塊）、SAS/AF（交互式全屏幕軟件應(yīng)用系統(tǒng)模塊）等等。SAS有一個(gè)智能型繪圖系統(tǒng)，不僅能繪各種統(tǒng)計(jì)圖，還能繪出地圖。SAS提供多個(gè)</p><p

6、><b>　　2．操作方式：</b></p><p>　　SAS是由大型機(jī)系統(tǒng)發(fā)展而來，其核心操作方式就是程序驅(qū)動(dòng)，經(jīng)過多年的發(fā)展，現(xiàn)在已成為一套完整的計(jì)算機(jī)語言，其用戶界面也充分體現(xiàn)了這一特點(diǎn)：它采用MDI（多文檔界面），用戶在PGM視窗中輸入程序，分析結(jié)果以文本的形式在OUTPUT視窗中輸出。使用程序方式，用戶可以完成所有需要做的工作，包括統(tǒng)計(jì)分析、預(yù)測(cè)、建模和模擬抽樣等。但是，這

7、使得初學(xué)者在使用SAS時(shí)必須要學(xué)習(xí)SAS語言，入門比較困難。 SAS的Windows版本根據(jù)不同的用戶群開發(fā)了幾種圖形操作界面，這些圖形操作界面各有特點(diǎn)，使用時(shí)非常方便。但是由于國(guó)內(nèi)介紹他們的文獻(xiàn)不多，并且也不是SAS推廣的重點(diǎn)，因此還不為絕大多數(shù)人所了解。</p><p>　　3．SAS系統(tǒng)基本操作及基本概念 ：</p><p>　　3.1數(shù)據(jù)集（dataset）和庫(kù) 

8、;：</p><p>　　統(tǒng)計(jì)學(xué)的操作都是針對(duì)數(shù)據(jù)的，SAS中容納數(shù)據(jù)的文件稱為數(shù)據(jù)集，數(shù)據(jù)集又包含在不同的庫(kù)（暫且理解為數(shù)據(jù)庫(kù)吧）中。SAS中的庫(kù)分為永久性和臨時(shí)性兩種。顧名思義，存在于永久庫(kù)中的數(shù)據(jù)集是永久存在的（只要你不去刪除它），臨時(shí)庫(kù)中的數(shù)據(jù)集則在你退出SAS后自動(dòng)被刪除。至于SAS中庫(kù)的概念，最簡(jiǎn)單的理解就是一個(gè)目錄，一個(gè)存放數(shù)據(jù)集的目錄。 數(shù)據(jù)集的結(jié)構(gòu)完全等同于我們一般所理解的數(shù)據(jù)表，由

9、字段和記錄所構(gòu)成，在統(tǒng)計(jì)學(xué)中我們習(xí)慣將字段稱為變量，在后面的內(nèi)容中字段和變量我們就理解為同一種東西吧！建立數(shù)據(jù)集的方法很多，編程操作中有專門的數(shù)據(jù)讀入方法來建立數(shù)據(jù)集，但需要將數(shù)據(jù)現(xiàn)場(chǎng)錄入，費(fèi)時(shí)費(fèi)力。如果數(shù)據(jù)量大，我勸各位還是先以其它方法將數(shù)據(jù)集建好，否則程序語句的絕大部分會(huì)浪費(fèi)在數(shù)據(jù)的輸入上。</p><p>　　3.2  SAS程序概述 ：</p><p>　　和其

10、它計(jì)算機(jī)語言一樣，SAS語言（稱為SCL語言，SAS Component Language）也有其專有的詞匯（即關(guān)鍵字）和語法。關(guān)鍵字、名字、特殊字符和運(yùn)算符等按照語法規(guī)則排列組成SAS語句，而執(zhí)行完整功能的若干個(gè)SAS語句就構(gòu)成了SAS程序。 SAS程序包括多個(gè)步驟和一些控制語句，一般情況下均包括數(shù)據(jù)步和過程步，一個(gè)或多個(gè)、數(shù)據(jù)步或過程步，它們之間任何形式的組合均可成為一段SAS程序，只要能完成一個(gè)完整

11、的功能。通常情況下SAS程序還包括一些全程語句，用以控制貫穿整個(gè)SAS程序的某些選項(xiàng)、變量或程序運(yùn)行的環(huán)境。  SAS程序的語句一般以關(guān)鍵字開始，以一個(gè)分號(hào)結(jié)束，一條語句可占多行（SAS每看到一個(gè)分號(hào)，就將其以前、上一個(gè)分號(hào)以后的所有東東當(dāng)作一條語句來處理，而不管他們處在多少個(gè)不同的行中）。SAS語句對(duì)字母的大小寫不敏感，你可以根據(jù)個(gè)人習(xí)慣決定字母的大寫或小寫。 </p><p>　　

12、4. Logistic回歸：</p><p>　　Logistic回歸是一類統(tǒng)計(jì)模型稱為廣義線性模型。這一模型包括單一回歸，包括普通的回歸和方差分析，以及多元統(tǒng)計(jì)等變數(shù)和對(duì)數(shù)線性回歸。一個(gè)很好使用線性模型的例子為萊斯蒂。</p><p>　　Logistic回歸允許一個(gè)預(yù)測(cè)離散成果，如組成員，來自于一組變量，可能是連續(xù)的，離散的，二分，或混合任何這些。一般情況下，因變量是二分變量，如在場(chǎng)/

13、缺席或成功/失敗。判別分析是用來預(yù)測(cè)組成員只有兩個(gè)群體。然而，判別分析只能用連續(xù)獨(dú)立變量。因此，在獨(dú)立的變量是一個(gè)絕對(duì)的，或混合的連續(xù)和明確情況，Logistic回歸是首選。</p><p><b>　　4.1 模型：</b></p><p>　　因變量的logistic回歸通常是二分變量，就是因變量值為1是事件發(fā)生，值為0是事件不發(fā)生。這種類型的變量被稱為伯努利（或

14、二元）變量。雖然不是常見的，也不是在事件中討論，應(yīng)用Logistic回歸也已擴(kuò)大到情況下，因變量是兩個(gè)以上的情況下，這種情況被稱為多項(xiàng)式或多級(jí)[ Tabachnick和費(fèi)德爾（ 1996年）使用的術(shù)語polychotomous ] 。 </p><p>　　如前所述，獨(dú)立的或預(yù)測(cè)變量Logistic回歸可以采取任何形式。也就是說， Logistic回歸是不作任何假設(shè)的分布的獨(dú)立變量。他們不必正態(tài)分布，線性關(guān)系或平

15、等的差額在每個(gè)組之間的關(guān)系，預(yù)測(cè)和因變量不是一個(gè)線性函數(shù)的logistic回歸，代替他的是，Logistic回歸函數(shù)的使用是對(duì)數(shù)函數(shù)的變換：</p><p>　　這里=截距項(xiàng)，=自變量的預(yù)測(cè)系數(shù)。 </p><p>　　另一種形式的Logistic回歸方程為：</p><p>　　Logistic回歸的目的是正確預(yù)測(cè)出一個(gè)模型，這個(gè)模型適用與大哥事件發(fā)生概率的預(yù)測(cè)。

16、為了實(shí)現(xiàn)這一目標(biāo)，建立一個(gè)模型，這個(gè)模型包括一個(gè)因變量和多個(gè)自變量，多個(gè)自變量被用于預(yù)測(cè)因變量的結(jié)果。在模型建立過程中幾個(gè)不同的選擇被利用。變量在指定的順序可進(jìn)入模型由研究員或logistic回歸可以測(cè)試適合的模式后，每一個(gè)系數(shù)為增加或刪除，呼吁逐步回歸。</p><p>　　逐步回歸被使用在研究探索階段，但我們不建議用于理論測(cè)試（梅納爾1995年） 。理論測(cè)試是測(cè)試各個(gè)變量之間關(guān)系的變數(shù)。探索性測(cè)試是測(cè)試給定觀

17、測(cè)值各個(gè)變量之間的關(guān)系，因此，逐步回歸的目標(biāo)是發(fā)現(xiàn)因變量與各個(gè)自變量之間的關(guān)系。 </p><p>　　向后逐步回歸似乎是首選方法探索分析，在分析，首先是全部或飽和模型和變量排除在模型中的一個(gè)反復(fù)的過程。合適的模型進(jìn)行測(cè)試后，消除每個(gè)變量，以確保該模型仍能充分符合數(shù)據(jù).當(dāng)沒有變量可以從模型中刪除時(shí)，整個(gè)統(tǒng)計(jì)分析工作就完成了。</p><p>　　這里是logistic回歸的兩種主要用途。首

18、先是預(yù)測(cè)組成員。由于Logistic回歸計(jì)算概率或失敗之上的概率，分析結(jié)果是以優(yōu)勢(shì)率形式進(jìn)行的。例如， Logistic回歸經(jīng)常被用于流行病學(xué)研究，分析結(jié)果是在控制其他的風(fēng)險(xiǎn)因素前提下啦預(yù)測(cè)癌癥的發(fā)病率。 Logistic回歸還提供了變量之間關(guān)系的只是（例如，吸10包煙癌癥的發(fā)病率將高于你在棉礦中工作的癌癥發(fā)病率）。這個(gè)過程，系數(shù)測(cè)試幾個(gè)不同的技術(shù)，所有這些將在下文討論。</p><p>　　4.2 Wald檢驗(yàn)

19、： </p><p>　　Wald檢驗(yàn)是用來測(cè)試的統(tǒng)計(jì)意義的每一個(gè)自變量的系數(shù)（ B）在該模型中是否是為0。Wald檢驗(yàn)計(jì)算的Z是通過以下的公式得出的：</p><p>　　Z值再平方，產(chǎn)生了瓦爾德統(tǒng)計(jì)與卡方分布。然而，一些作者已查明了使用Wald檢驗(yàn)的缺陷。梅納（ 1995 ）警告說，系數(shù)不變，標(biāo)準(zhǔn)誤差增大，降低了Wald統(tǒng)計(jì)值。萊斯蒂指出，最大似然度對(duì)于大規(guī)模樣本要比使用Wald測(cè)試更

20、有效。 </p><p>　　4.3 最大似然度檢驗(yàn)： </p><p>　　最大似然使用的比例，以最大化的價(jià)值，似然函數(shù)為充分模型（L1）的最大化價(jià)值的似然函數(shù)的簡(jiǎn)單的模型（ L0 ） 。的似然比檢驗(yàn)統(tǒng)計(jì)量等于：</p><p>　　這個(gè)記錄的可能性轉(zhuǎn)變職能產(chǎn)生的卡方統(tǒng)計(jì)。這是推薦的檢驗(yàn)統(tǒng)計(jì)時(shí)使用的模式，通過建設(shè)落后的逐步消除。 </p><p

21、>　　4.4 霍斯默- Lemshow擬合優(yōu)度檢驗(yàn)： </p><p>　　該霍斯默- Lemshow統(tǒng)計(jì)評(píng)估擬合優(yōu)度，創(chuàng)造10命令群體的主題，然后比較實(shí)際的人數(shù)在各組（觀察）的數(shù)量預(yù)測(cè)的Logistic回歸模型（預(yù)測(cè)） 。因此，檢驗(yàn)統(tǒng)計(jì)量是卡方統(tǒng)計(jì)與理想的結(jié)果非意義，這表明該模型預(yù)測(cè)并沒有顯著不同的觀察。 </p><p>　　排列的10個(gè)團(tuán)體的基礎(chǔ)上創(chuàng)建自己的估計(jì)概率;那些估計(jì)概

22、率低于0.1形成一組，依此類推，直至與概率0.9至1.0 。每一類又分為兩組，根據(jù)實(shí)際觀察到的結(jié)果變量（成功，失?。?。預(yù)期的頻率為每一個(gè)細(xì)胞都得到model.If模式是好的，那么大多數(shù)的主題成功屬于較高風(fēng)險(xiǎn)和那些失敗的風(fēng)險(xiǎn)較低。</p><p><b>　　科技外文文獻(xiàn)</b></p><p>　　SAS Statistical Analysis Software

23、And Logistic Regression</p><p>　　I. Overview: SAS is called the Statistics Analysis System, the first from the University of North Carolina's two post-graduate preparation of biostatistics, and in 1

24、976 the Institute of SAS software is established e, the formal SAS software launched. SAS is a large-scale decision support for integrated information systems, but the software system functions limited to the first stati

25、stical analysis, since the statistical analysis is still an important part of its core functionality. the curr</p><p>　　SAS is a combination of SAS software system, which is a combination of multiple functio

26、nal modules, the basic part of BASE SAS module. BASE SAS module is the core of the SAS system,which assume the main task of data management and user management environment for the conduct of the user of language processi

27、ng, call the other SAS modules and products. In other words, SAS systems, we start the BASE SAS module, which in addition has its own data management, programming and computing descriptive stat</p><p>　　2. o

28、peration</p><p>　　SAS was developed from the mainframe system, the core operation is the process-driven, after many years of development, SAS has now become a complete set of computer language, and its user

29、interface is also fully embodied the characteristics: It uses MDI (Multiple Document interface), the user input program in the PGM window, the results of the analysis in the form of text output in the OUTPUT window. usin

30、g the program, users can complete all the work, including statistical analysis, forecasting</p><p>　　3.the basic operation and basic concepts of SAS</p><p>　　3.1 Dataset (dataset) and the datab

31、ase </p><p>　　Statistics are for the operation of the data, files which is filled with SAS data is named dataset. in the capacity as the data sets, data sets also included in different library (for the time

32、being it understood as a database). SAS in the library is divided into two types of permanent and temporary. As the name suggests, the existence of a permanent library in the data set is permanent (as long as you do not

33、delete it), temporary library in the data sets from the SAS you automatically be delete</p><p>　　3.2 SAS language </p><p>　　And other computer languages, SAS Language (known as the SCL language

34、, SAS Component Language) also has its proprietary terms (ie keywords) and grammar. Keywords, names, special characters and operators, such as the composition in accordance with the grammar rules with SAS statements, and

35、 the implementation of the full functionality of a number of SAS statements constitute the SAS procedure. SAS procedures, including a number of steps and a number of control statements, the general case, in</p>

36、;<p>　　4.Logistic Regression</p><p>　　Logistic regression is part of a category of statistical models called generalized linear models. This broad class of models includes ordinary regression and ANOV

37、A, as well as multivariate statistics such as ANCOVA and loglinear regression. An excellent treatment of generalized linear models is presented in Agresti (1996). </p><p>　　Logistic regression allows one to

38、predict a discrete outcome, such as group membership, from a set of variables that may be continuous, discrete, dichotomous, or a mix of any of these. Generally, the dependent or response variable is dichotomous, such as

39、 presence/absence or success/failure. Discriminant analysis is also used to predict group membership with only two groups. However, discriminant analysis can only be used with continuous independent variables. Thus, in i

40、nstances where the indepen</p><p>　　4.1 The Model:  </p><p>　　The dependent variable in logistic regression is usually dichotomous, that is, the dependent variable can take the value 1 wit

41、h a probability of success , or the value 0 with probability of failure 1-. This type of variable is called a Bernoulli (or binary) variable. Although not as common and not discussed in this treatment, applications

42、of logistic regression have also been extended to cases where the dependent variable is of more than two cases, known as multinomial or polytomous [Tabachnick </p><p>　　As mentioned previously, the independe

43、nt or predictor variables in logistic regression can take any form. That is, logistic regression makes no assumption about the distribution of the independent variables. They do not have to be normally distributed, linea

44、rly related or of equal variance within each group.The relationship between the predictor and response variables is not a linear function in logistic regression, instead, the logistic regression function is used, which i

45、s the logit transforma</p><p>　　Where  = the constant of the equation and,  = the coefficient of the predictor variables. An alternative form of the logistic regression equation is:</p><

46、;p>　　The goal of logistic regression is to correctly predict the category of outcome for individual cases using the most parsimonious model. To accomplish this goal, a model is created that includes all predictor vari

47、ables that are useful in predicting the response variable. Several different options are available during model creation. Variables can be entered into the model in the order specified by the researcher or logistic regre

48、ssion can test the fit of the model after each coefficient is added </p><p>　　Stepwise regression is used in the exploratory phase of research but it is not recommended for theory testing (Menard 1995). Theo

49、ry testing is the testing of a-priori theories or hypotheses of the relationships between variables. Exploratory testing makes no a-priori assumptions regarding the relationships between the variables, thus the goal is t

50、o discover relationships.   </p><p>　　Backward stepwise regression appears to be the preferred method of exploratory analyses, where the analysis begins with a full or saturated model and variables are

51、eliminated from the model in an iterative process. The fit of the model is tested after the elimination of each variable to ensure that the model still adequately fits the data.When no more variables can be eliminated fr

52、om the model, the analysis has been completed.   </p><p>　　There are two main uses of logistic regression. The first is the prediction of group membership. Since logistic regression calculates the proba

53、bility or success over the probability of failure, the results of the analysis are in the form of an odds ratio. For example, logistic regression is often used in epidemiological studies where the result of the analysis

54、is the probability of developing cancer after controlling for other associated risks. Logistic regression also provides knowledge of the </p><p>　　4.2 Wald Test: </p><p>　　A Wald test is used t

55、o test the statistical significance of each coefficient () in the model. A Wald test calculates a Z statistic, which is:  </p><p>　　This z value is then squared, yielding a Wald statistic with a chi-squ

56、are distribution. However, several authors have identified problems with the use of the Wald statistic. Menard (1995) warns that for large coefficients, standard error is inflated, lowering the Wald statistic (chi-square

57、) value. Agresti (1996) states that the likelihood-ratio test is more reliable for small sample sizes than the Wald test.</p><p>　　4.3 Likelihood-Ratio Test: </p><p>　　The likelihood-ratio test

58、 uses the ratio of the maximized value of the likelihood function for the full model (L1) over the maximized value of the likelihood function for the simpler model (L0). The likelihood-ratio test statistic equals:  

59、 </p><p>　　This log transformation of the likelihood functions yields a chi-squared statistic. This is the recommended test statistic to use when building a model through backward stepwise elimination.  

60、;    </p><p>　　4.4 Hosmer-Lemshow Goodness of Fit Test:   </p><p>　　The Hosmer-Lemshow statistic evaluates the goodness-of-fit by creating 10 ordered groups of subjects and then

61、compares the number actually in the each group (observed) to the number predicted by the logistic regression model (predicted). Thus, the test statistic is a chi-square statistic with a desirable outcome of non-significa

62、nce, indicating that the model prediction does not significantly differ from the observed.   </p><p>　　The 10 ordered groups are created based on their estimated probability; those with estimated probab

63、ility below 0.1 form one group, and so on, up to those with probability 0.9 to 1.0. Each of these categories is further divided into two groups based on the actual observed outcome variable (success, failure). The expect