attach$($L$)$

L $<-$ as$.$data.frame$($L$)$

#Likelihood function

logL $<-$ function$($b$,$X$,$Y$)\{$

b$0\}<-\backslash$textrm$\{$b$\}[1$

b$1<-$ b$[2]$

logn $<-$ sum$(($log$($ exp$($b$0+$b$1$X$))))($log$(1-$exp$($b$0+$b$1$X$)))))$ #Likelihood

return $(-$logn$)$

$\}$

#optimization to get ML parameters

pm$2$L $<-$ optim$($c$(2,-1),$logL$,$Y$=$L$Y,x=L$X$,$hessian$=$TRUE$)$

#compute marginal effect

probhat $<-$ exp$($pm$2$Lpar$[1]+pm2$Lpar$[2]*$L$x$par$[1]+$pm$2$Lpar$[2]*L$X$))$

dFdxL $<-$ mean$(($probhat$*(1-$probhat$))*$pm$2$L$par$[2])$

#check whether identical to starting point of our analytical calculations last week:

$1/100*$sum$($pm$2$Lpar$[1]-$pm$2$Lpar$[2]*L$X$))^(-2)*$exp$(-$pm$2$Lpar$[1]-pm2$Lpar$[2]*$L$X$))$ #relevant element of Jacobian

J$1<-1/100$pm$2$L$par$[2]*$L

J $<-1/100*$sum$(($exp$(-$pm$2$Lpar$[1]-pm2$Lpar$[2]*$L$x$par$[1]-$pm$2$Lpar$[2]*L$X$))+$pm$2$L

#multiply Jacobian by variance covariance matrix,

sqrt$($matrix$($c$($J$1,$J$),$ nrow$=1,$ncol$=2)\%\%$matrix$($c$($J$1,$J$),$ nrow$=2,$ncol$=1))$

tstat$<-$ dFdxL$/$sqrt$($matrix$($c$($J$1,$J$),$ nrow$=1,$ncol$=2)\%\%$matrix$($c$($J$1,$J$),$ nrow$=2,$ncol$=1))$

$2*(1-$pnorm$($abs$($tstat$)))$stddFdxL $<-$ abs$($J$)*$sqrt$($diag$($solve$($pm$2$L$hessian$))[2])$

#derive z$-$statistic $($marginal effect divided by sandard deviation of marginal effect$)$

dFdxL$/$stddFdxL; tdFdxL $<-$ dFdxL$/$stddFdxL

#compute p$-$value corresponding to size of that test statistic. $($know that the test statistic is asymptotically

$2*(1-$pnorm$($abs$($tdFdxL$)))$

#check computations with built$-$in command.

#marginal effect:

library$($VGAM$)$

a $<-$ glm$($Y~X$,$ family $=$ binomial$($link $=$ "logit"$),$ data$=$L$)$#know that distribution of Y is equal to a binomial dist

summary$($a$)$library$($mfx$)$

logitmfx$($Y~X$,$ data$=$L$,$ atmean$=$FALSE$)$

#slight differences in betahats, coefficients & marginal effects lead to different standard errors via delta meA $<-$ read.table$("/$Documents$/$Daten R$/$Microeconometrics$/$Logit$.$csv$",$header$=$TRUE,sep$="$;$")$

attach$($A$)$

A $<-$ as$.$data.frame$($A$)$

#programme probit function

probit $<-$ function$($theta$,$X$,$Y$)\{$beta$1<-$ theta$[2]$linpred $<-$ beta$0+$beta$1*$Xcolnames$($results$)<-$c$("$b$","$se$","$t$","$p$")$

rownames$($results$)<-$c$("$Constant$","$X$1")$

print$($results$,$digits$=3)$

library$($VGAM$)$

a $<-$ glm$($Y~X$,$ family $=$ binomial$($link $=$ "probit"$),$data$=$A$)$

summary$($a$)$mean$($dnorm$($pm$2$par$[1]+$pm$2$par$[2]*$X$)*$pm$2$par$[2])$;dFdx $<-$mean$($dnorm$($pm$2$par$[1]+$pm$2$par$[2]**$X$)**$pm$2$par$[2])$

$1$ibrary$($VGAM$)$

library$($mfx$)$# look at the documentation of the package.

library$($ProbMarg$)$

a $<-$ glm$($Y~X$,$ family $=$ binomial$($link $=$ "probit"$),$data$=$A$)$

#margeff$($a$)$

probitmfx$($Y~X$,$data$=$A$,$ atmean$=$FALSE$)$

mean$($margEffects $($a$,$method$=$"probit",specs$=$A$)[,1])$

summary$($pnorm$($pm$2$par$[1]+pm2$par$[2]*$X$))$

mean $($pnorm$($pm$2$par$[1]+pm2$par$[2]*$X$))$ #compute significance of marginal effect via delta rule

J $<-1/100*($sum$($dnorm$($pm$2$par$[1]+pm2$par$[2](-$pm$2$par$[1]-pm2$par$[2]*$X$)$pm$2$par$[1]+$pm$2$$par

stddFdx $<-$ abs$($J$)*$sqrt$($diag$($solve$($pm$2$$hessian$))[2])$

dFdx$/$stddFdx; tdFdx $<-$ dFdx$/$stddFdx

$2*(1-$pnorm$($abs$($tdFdx$)))$hatPY $<-$ pnorm$($pm$2$par$[1]+$pm$2$par$[2]*$X$)$

hatY $<-$ ifelse$($hatPY$>=0\mathrm{.}5,1,0)$

TRUEFP $<-$ ifelse$($hatY$==$Y$,1,0)$

CountR$2<-$ sum$($TRUEFP$)/$length$($Y$)$

use similar r codes like this for the above question