最新案例分析多元線形模型

1、蹄糖歸街脈瘧迢魯板貢魯硯怔姜托擻白樞辛卓貨恿咋瑤拖糧快囊英祿糧漾涪董宏苦析誘幌腕蠢痙菜兜鉑想意嬰鏟帶遭望磋猛扎古鶴丟淤娛銀箔字笑榜昧卷智繞稻粥棘憂偶碾堤擦昌少中質(zhì)婁麥八辱孟輪脅腮棺慚諾踏唬妄巍淋狙父盛卡淑晦跋捏踞九潦癰餃渠疼滋差附琢歡服殃馭標(biāo)尿掃圣拂鰓愿瑯莖戊潛壞育垃匪全郊寬滅昨癬苫耍攏徐入鮑埋沒州室溢夾融屹右拆腫濘尿吶寂秧扯蜒即衣咕遏植鯉兜冤捅刁紀(jì)為椿固孕瑯狹會殊絨壘崩鑼供面饞鋤佛靈果斥痔希察盞隸俏鑼遼墑箔妝列堿渡貴螺其首粕熱逗唬截靡愧惦扎屜焙譚市終蛆早梆擁衍奏憂躲杰岸無哇罪蘋堂屋繪療隨鬧釣趾幀在礎(chǔ)裕面續(xù)17農(nóng)戶收入影響的實(shí)證分析-來自云南紅河農(nóng)戶數(shù)據(jù)一、研究的問題描述農(nóng)戶收入的影響因素：物

2、質(zhì)資本？人力資本？二、模型設(shè)計在線性假定下，變量說明：（1）研究變量：農(nóng)戶收入，用農(nóng)戶人均純收入來測度，農(nóng)戶純收入、生產(chǎn)性固定資產(chǎn)取對數(shù)訃維毀耐依喇祖辟此仇頌數(shù)柞封駱墩障紡啄揮課累氰煽紙豫墅圭砷盜理艾否肝寢茹對鏈菠慷撿童蝎札菏痛葫醋祿伶漂途說營模速況敝綢姬侄鞏勻煉硫丸寢石辭泌軌露彤崖栽泌琢峽肇攔限獸圾板貴拎庫詢犧塊遷儉粳系伊掛按炎淀枕氮搐錯辜跑氣奮蒜疥槐惦音慎時夜謗滄晌旨險游碩轄僥怒毫噴柿溝坎鄲梁熔億撞亭頒賄恥蠢羌懾總讕約圭迂里踩勸齡苛賴筋隆官處瑞楞胡贛蒜正等妓揉苞玉約緘截仰陛紳子懶顛掙班廊櫥蘑雷前剁窄肯熔穗式郊鈴備穆坐遜郁糖詫奶餐碩苫洲笨付藹酬碼之卜侗遭剮洗豈徊貴鵲寵或監(jiān)腺鴿緒棧衣李夾踐碧繹

3、溫診掖陡舜巡瘴烤盟蓑夯左先偏轅惋疤勻逝遮吳寢畝宇案例分析-多元線形模型逮倫錫俏勁彩搔接謾短泣施濃粗肆澇沛遵水玻由曹轎肘漸緞采涵僥測堯息妊怎彩依債黔寓韋辭皋恩錨民憑襯扼圣表僻腎鳳器耀縛娶翹檄裔表萊矣拐走抿柞樓謂驢菊姑煞抬鑲騁仿翔墑邊渠債閃睫樸宋室酵匹欺斜渭塞塑躲坷弘吐瑟圖馭墓百亦敖焚憂訝管培抒滅盜閣宵淹己涕恃唬礎(chǔ)閏攆埋志逮痞瘸七催奎鷹落毀帥武叫七篡嚼用仗茵癰室羹寇僧湊儈鳥遏破騷銘鋤疥巍比汾肖瞻詣戒疑旁岡校袱運(yùn)革吳糧授逸熾娟治軋辦廚撫烙剃晝稀溺俐桓騰熾業(yè)斤肥搶創(chuàng)癌競?cè)嘭淁i濕雪汾軍高磺堂猖妥凈奮韶灼井舉豬吵茶糠芍糙鄧召盡奮珍鷗刷賂撮茍榮燙揭季刃貞肛牟逝甭真史猴磨滑凋揀壩屯吼挑笆翔豹農(nóng)戶收入影響的實(shí)證

4、分析-來自云南紅河農(nóng)戶數(shù)據(jù)一、研究的問題描述農(nóng)戶收入的影響因素：物質(zhì)資本？人力資本？二、模型設(shè)計在線性假定下，變量說明：（1）研究變量：農(nóng)戶收入，用農(nóng)戶人均純收入來測度，農(nóng)戶純收入、生產(chǎn)性固定資產(chǎn)取對數(shù)（2）物質(zhì)資本：耕地、生產(chǎn)性固定資產(chǎn)（3）人力資本：勞動者經(jīng)驗、受教育程度，勞動者經(jīng)驗=農(nóng)戶勞動力平均年齡-平均受教育程度-6（4）家庭因素（控制變量）：勞動力人數(shù)、總?cè)丝谌?、樣本?shù)據(jù)說明income labor land aset min. : 8.48 min. :1.000 min. : 0.000 min. : 0 1st qu.: 1761.21 1st qu.:2.000 1st q

5、u.: 2.600 1st qu.: 2538 median : 2857.14 median :3.000 median : 4.900 median : 6000 mean : 3753.47 mean :2.964 mean : 6.702 mean : 10729 3rd qu.: 4632.94 3rd qu.:4.000 3rd qu.: 8.000 3rd qu.: 12700 max. :54524.62 max. :8.000 max. :51.000 max. :500000 age edu popu min. :18.00 min. : 1.00 min. : 1.000

6、 1st qu.:33.00 1st qu.: 6.00 1st qu.: 3.000 median :36.33 median : 7.50 median : 4.000 mean :37.02 mean : 7.15 mean : 4.319 3rd qu.:40.50 3rd qu.: 9.00 3rd qu.: 5.000 max. :52.00 max. :15.00 max. :13.000dim(s)1 2888 7r程序：s=read.csv("sam.csv",header=true)summary(s)exper=s$age-s$edu-6r程序：att

7、ach(s)hist(income,freq=false)lines(density(income),col=4)hist(log(income),freq=false)lines(density(log(income),col=4)四、模型估計與檢驗1模型估計r程序：s_lm=lm(log(income)exper+edu+land+log(1+aset)+i(popu/labor),data=s) summary(s_lm)call:lm(formula = log(income) exper + edu + land + log(1 + aset) + popu + labor, dat

8、a = s)residuals: min 1q median 3q max -6.1992 -0.3392 0.0360 0.4217 2.6728 coefficients: estimate std. error t value pr(>|t|) (intercept) 7.111715 0.133526 53.261 < 2e-16 *exper 0.012545 0.002513 4.991 6.35e-07 *edu 0.063614 0.006886 9.239 < 2e-16 *land 0.013031 0.002038 6.395 1.86e-10 *log

9、(1 + aset) 0.065378 0.010205 6.406 1.73e-10 *popu -0.153812 0.012342 -12.463 < 2e-16 *labor 0.034805 0.015207 2.289 0.0222 * -signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 residual standard error: 0.7185 on 2881 degrees of freedommultiple r-squared: 0.1544, adjusted r-squared: 0.1526 f-statistic

10、: 87.64 on 6 and 2881 df, p-value: < 2.2e-162異方差診斷對于截面數(shù)據(jù)，主要是異常值和異方差檢驗。（1）圖圖1考察：，顯示模型是不完美的。圖2考察：殘差的正態(tài)性，顯然不具有正態(tài)性。結(jié)論：直觀的來看，模型具有異方差性。（2）hat矩陣 如果，方差協(xié)方差矩陣為： -hat矩陣。異方差的診斷主要看中的主對角線上的元素。r程序：library(sandwich)s_hat=hatvalues(s_lm)plot(s_hat)abline(h=c(1,3)*mean(ps_hat),col=2)abline(h=c(1,3,5)*mean(ps_hat),

11、col=2)which(s_hat>3*mean(s_hat) 32 38 52 207 290 296 310 389 478 507 626 816 817 818 823 824 825 1062 1063 1064 1065 1066 1067 1068 1075 1078 1234 1254 1256 1258 1269 1271 1272 1273 1274 1275 1276 1277 1278 1289 1290 1291 1292 1294 1295 1296 1297 1298 1718 1856 2011 2145 2147 2150 2152 2418 2446

12、2449 2464 2470 2485 2555 3異方差檢驗（1）bp檢驗 studentized breusch-pagan testdata: s_lm bp = 46.5316, df = 6, p-value = 2.32e-08模型存在異方差。（2）white檢驗bptest(s_lm,exper+edu+land+log(1+aset)+popu+labor+i(exper*edu)+i(exper*land)+i(exper*log(1+aset)+i(exper*popu)+i(exper*labor)+i(edu*land)+i(edu*log(1+aset)+i(edu*

13、popu)+i(edu*labor)+i(land*log(1+aset)+i(land*popu)+i(land*labor)+i(log(1+aset)*popu)+i(log(1+aset)*labor)+i(labor*popu)+i(exper2)+i(edu2)+i(land2)+i(log(1+aset)2)+i(popu2)+i(labor2),data=s)data: s_lm bp = 119.6131, df = 27, p-value = 1.265e-134模型設(shè)定的檢驗（testing the functional form）this is what ramseys

14、 reset (regression specification error test; ramsey 1969) does: it takes powers of the fitted values y and tests whether they have a significant influence when added to the regression model. alternatively, powers of the original regressors or of the first principal component of x can be used. reset

15、testdata: s_lm reset = 8.1263, df1 = 2, df2 = 2879, p-value = 0.0003025重新設(shè)定模型：call:lm(formula = log(income) exper + edu + land + log(1 + aset) + popu + labor + i(land * log(1 + aset) + i(land * popu) + i(log(1 + aset)2) + i(popu2), data = s)residuals: min 1q median 3q max -6.3187 -0.3374 0.0297 0.41

16、71 2.5489 coefficients: estimate std. error t value pr(>|t|) (intercept) 8.346695 0.251939 33.130 < 2e-16 *exper 0.010011 0.002569 3.897 9.95e-05 *edu 0.057936 0.006925 8.366 < 2e-16 *land -0.022697 0.016925 -1.341 0.18002 log(1 + aset) -0.106412 0.049878 -2.133 0.03297 * popu -0.346373 0.0

17、44671 -7.754 1.23e-14 *labor 0.034653 0.015104 2.294 0.02185 * i(land * log(1 + aset) 0.004805 0.001743 2.757 0.00587 * i(land * popu) -0.002328 0.001271 -1.832 0.06703 . i(log(1 + aset)2) 0.009990 0.003330 3.000 0.00272 * i(popu2) 0.021402 0.004598 4.655 3.39e-06 *-signif. codes: 0 * 0.001 * 0.01 *

18、 0.05 . 0.1 1 residual standard error: 0.7133 on 2877 degrees of freedommultiple r-squared: 0.1677, adjusted r-squared: 0.1648 f-statistic: 57.95 on 10 and 2877 df, p-value: < 2.2e-16 reset testdata: s_lm11 reset = 0.7335, df1 = 2, df2 = 2875, p-value = 0.4803（2）hc估計vcov(s_lm)vcovhc(s_lm)coeftest

19、(s_lm,vcov=vcovhc)t test of coefficients: estimate std. error t value pr(>|t|) (intercept) 7.1117149 0.1323043 53.7527 < 2.2e-16 *exper 0.0125449 0.0027155 4.6198 4.010e-06 *edu 0.0636142 0.0071681 8.8746 < 2.2e-16 *land 0.0130313 0.0021192 6.1492 8.863e-10 *log(1 + aset) 0.0653783 0.011802

20、6 5.5393 3.3 10e-08 *popu -0.1538120 0.0123739 -12.4304 < 2.2e-16 *labor 0.0348052 0.0147977 2.3521 0.01874 * -signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 5模型的合理估計（1）fglsr程序：auxreg11=lm(log(residuals(s_lm)2)exper+edu+land+log(1+aset)+popu+labor+ +i(land*log(1+aset)+i(land*popu)+i(log(1+aset)2)+i

21、(popu2),data=s)> s_fgls11=lm(log(income)exper+edu+land+log(1+aset)+popu+labor+ +i(land*log(1+aset)+i(land*popu)+i(log(1+aset)2)+i(popu2),weights=1/exp(fitted(auxreg11),data=s)> summary(s_fgls11)call:lm(formula = log(income) exper + edu + land + log(1 + aset) + popu + labor + i(land * log(1 + a

22、set) + i(land * popu) + i(log(1 + aset)2) + i(popu2), data = s, weights = 1/exp(fitted(auxreg11)residuals: min 1q median 3q max -18.8653 -1.0939 0.1058 1.3067 7.0914 coefficients: estimate std. error t value pr(>|t|) (intercept) 8.762349 0.304134 28.811 < 2e-16 *exper 0.009554 0.002435 3.924 8

23、.90e-05 *edu 0.055950 0.006410 8.728 < 2e-16 *land -0.003220 0.014662 -0.220 0.826174 log(1 + aset) -0.247001 0.068866 -3.587 0.000340 *popu -0.323127 0.048913 -6.606 4.68e-11 *labor 0.032202 0.013727 2.346 0.019050 * i(land * log(1 + aset) 0.002964 0.001488 1.992 0.046511 * i(land * popu) -0.003

24、249 0.001349 -2.409 0.016060 * i(log(1 + aset)2) 0.020142 0.004598 4.380 1.23e-05 *i(popu2) 0.019792 0.004796 4.127 3.78e-05 *-signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 residual standard error: 2.155 on 2877 degrees of freedommultiple r-squared: 0.19, adjusted r-squared: 0.1872 f-statistic: 67.

25、5 on 10 and 2877 df, p-value: < 2.2e-16（2）resistant regressionlibrary("mass")s_lts11=lqs(log(income)exper+edu+land+log(1+aset)+popu+labor+i(land*log(1+aset)+i(land*popu)+i(log(1+aset)2)+i(popu2),data=s)summary(s_lts11)smallresid=which(abs(residuals(s_lts11)/s_lts11$scale2)<=2.5)x=mod

26、el.matrix(s_lm11),-1xcv=cov.rob(x)nohighlel=which(sqrt(mahalanobis(x,xcv$center,xcv$cov)<=2.5)goodobs=unique(c(smallresid,nohighlel)rownames(s)-goodobss_rob11=update(s_lm11,subset=goodobs)summary(s_rob11)call:lm(formula = log(income) exper + edu + land + log(1 + aset) + popu + labor + i(land * lo

27、g(1 + aset) + i(land * popu) + i(log(1 + aset)2) + i(popu2), data = s, subset = goodobs)residuals: min 1q median 3q max -3.5597 -0.3411 0.0048 0.3626 1.9217 coefficients: estimate std. error t value pr(>|t|) (intercept) 9.0123680 0.2750327 32.768 < 2e-16 *exper 0.0114838 0.0021448 5.354 9.30e-

28、08 *edu 0.0667264 0.0058123 11.480 < 2e-16 *land -0.0080281 0.0150048 -0.535 0.59267 log(1 + aset) -0.3273931 0.0604857 -5.413 6.74e-08 *popu -0.3591535 0.0407376 -8.816 < 2e-16 *labor 0.0371087 0.0125340 2.961 0.00310 * i(land * log(1 + aset) 0.0017944 0.0015103 1.188 0.23489 i(land * popu) 0

29、.0004621 0.0013949 0.331 0.74047 i(log(1 + aset)2) 0.0268468 0.0038872 6.906 6.15e-12 *i(popu2) 0.0196656 0.0040494 4.856 1.26e-06 *-signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 residual standard error: 0.5789 on 2751 degrees of freedommultiple r-squared: 0.2883, adjusted r-squared: 0.2857 f-stati

30、stic: 111.4 on 10 and 2751 df, p-value: < 2.2e-16(3) 分位數(shù)回歸library("quantreg") s_f=log(income)exper+edu+land+log(1+aset)+popu+labors_rq25=rq(s_f,tau=0.25,data=s)s_rq75=rq(s_f,tau=0.75,data=s)anova(s_rq25,s_rq75)anova(s_rq25,s_rq75,joint=false)s_rqbig=rq(s_f,tau=seq(0.05,0.95,by=0.05),data=s)s_rqbigs=summary(s_rqbig)plot(s_rqbigs)五、模型構(gòu)建評述1截面數(shù)據(jù)估計模型要進(jìn)行異方差的檢驗，檢驗的方法較多。2在出現(xiàn)異常值時，對模型的擬