1、Called the link function of the GLM.Selected GLM families and their canonical linkFamilyCanonical linkNamebinomiallogitgaussianidentitypoissonlog1.2 Binary Dependent VariablesModel:In the probit case: equals the standard normal CDFIn the logit case: equals the logistic CDFExample:（1）DataConsidering
2、female labor participation for a sample of 872 women from Switzerland.The dependent variable: participationThe explain variables:income,age,education,youngkids,oldkids,foreignyesandage2.R:library（AER）data（SwissLaborsummary（SwissLabor）participation income age education no :471 Min. : 7.187 Min. :2.00
3、0 Min. : 1.000 yes:401 1st Qu.:10.472 1st Qu.:3.200 1st Qu.: 8.000 Median :10.643 Median :3.900 Median : 9.000 Mean :10.686 Mean :3.996 Mean : 9.307 3rd Qu.:10.887 3rd Qu.:4.800 3rd Qu.:12.000 Max. :12.376 Max. :6.200 Max. :21.000 youngkids oldkids foreign Min. :0.0000 Min. :0.0000 no :656 1st Qu.:0
4、.0000 1st Qu.:0.0000 yes:216 0.0000 Median :1.0000 0.3119 Mean :0.9828 0.0000 3rd Qu.:2.0000 3.0000 Max. :6.0000 （2） Estimationswiss_prob=glm（participation.+I（age2）,data=SwissLabor,family=binomial（link=probit）summary（swiss_prob）Call:glm（formula = participation . + I（age2）, family = binomial（link = ）
5、, data = SwissLabor）Deviance Residuals: Min 1Q Median 3Q Max -1.9191 -0.9695 -0.4792 1.0209 2.4803 Coefficients: Estimate Std. Error z value Pr（|z|） （Intercept） 3.74909 1.40695 2.665 0.00771 * income -0.66694 0.13196 -5.054 4.33e-07 *age 2.07530 0.40544 5.119 3.08e-07 *education 0.01920 0.01793 1.07
6、1 0.28428 youngkids -0.71449 0.10039 -7.117 1.10e-12 *oldkids -0.14698 0.05089 -2.888 0.00387 * foreignyes 0.71437 0.12133 5.888 3.92e-09 *I（age2） -0.29434 0.04995 -5.893 3.79e-09 *-Signif. codes: 0 * 0.001 * 0.01 * 0.05 . 0.1 1 （Dispersion parameter for binomial family taken to be 1） Null deviance:
7、 1203.2 on 871 degrees of freedomResidual deviance: 1017.2 on 864 degrees of freedomAIC: 1033.2Number of Fisher Scoring iterations: 4（3） VisualizationPlotting participation versus ageplot（participationage,data=SwissLabor,ylevels=2:1）（4） EffectsAverage marginal effects:The average of the sample margi
8、nal effects:fav=mean（dnorm（predict（swiss_prob,type=link）fav*coef（swiss_prob）（Intercept） income age education youngkids oldkids foreignyes I（age2） The average marginal effects at the average regressor:av=colMeans（SwissLabor,-c（1,7）av=data.frame（rbind（swiss=av,foreign=av）,foreign=factor（c（no,yesav=pre
9、dict（swiss_prob,newdata=av,type=av=dnorm（av）avswiss*coef（swiss_prob）-7foreignswiss: （Intercept） income age education youngkids oldkids I（age2） Foreign:（5） Goodness of fit and predictionPseudo-R2:as the log-likelihood for the fitted model, as the log-likelihood for the model containing only a constan
10、t term. swiss_prob0=update（swiss_prob,formula=.1）1- as.vector（logLik（swiss_prob）/logLik（swiss_prob0）1 0.1546416Percent correctly predicted:table（true=SwissLabor$participation,pred=round（fitted（swiss_prob） predtrue 0 1no 337 134yes 146 25567.89%ROC curve:TPR（c）:the number of women participating in th
11、e labor force that are classified as participating compared with the total number of women participating.FPR（c）:the number of women not participating in the labor force that are classified as participating compared with the total number of women not participating.ROCRpred=prediction（fitted（swiss_pro
12、b）,SwissLabor$participation）plot（performance（pred,acctprfprabline（0,1,lty=2） Extensions: Multinomial responsesFor illustrating the most basic version of the multinomial logit model, a model with only individual-specific covariates,.BankWagesIt contains, for employees of a US bank, an ordered factor job with levels custodial, admin（for administration）, and manage （for management）, to be modeled as afunction of education （in years） and a factor minority indicating minority status. There also exists a factor gender, but since there are no women in the category custo
