Linear statistical models 2008 Binary and binomial responses The response probabilities are modelled as functions of the predictors Link functions: the.

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Presentation transcript:

Linear statistical models 2008 Binary and binomial responses The response probabilities are modelled as functions of the predictors Link functions: the probit link: the logit link: the log-log link:

Linear statistical models 2008 Binary and binomial responses the probit link: the logit link: the log-log link:

Linear statistical models 2008 Link functions

Linear statistical models 2008 Probit analysis

Linear statistical models 2008 Probit analysis proc GENMOD data=linear.rotenone; model Affected/insects=logconc /link=probit dist=bin; run;

Linear statistical models 2008 Logit (logistic) regression proc GENMOD data=linear.rotenone; model Affected/insects=logconc /link=logit dist=bin; run;

Linear statistical models 2008 Multiple logistic regression Model building principles  Significance testing  Forward selection  Backward selection  Stepwise selection  Best subset selection  Cross-validation

Linear statistical models 2008 Odds and odds ratios

Linear statistical models 2008 Odds ratios proc GENMOD data=linear.oddsratio; class smoker; freq frequency; model survived=smoker/link=logit dist=bin; run;

Linear statistical models 2008 Odds ratios where x is one for smokers and 0 for non-smokers

Linear statistical models 2008 Count data and contingency tables and log-linear models Expected frequency: Log-linear models are models of the log expected frequency (log is used as link function)