Probit Model

 require(aod)

require(ggplot2)

mydata <- read.csv("https://stats.idre.ucla.edu/stat/data/binary.csv")

## convert rank to a factor (categorical variable)

mydata$rank <- factor(mydata$rank)

## view first few rows

head(mydata)

summary(mydata)

xtabs(~rank + admit, data = mydata) #

myprobit <- glm(admit ~ gre + gpa + rank, family = binomial(link = "probit"), 

                data = mydata)

## model summary

summary(myprobit)

confint(myprobit)

wald.test(b = coef(myprobit), Sigma = vcov(myprobit), Terms = 4:6)

l <- cbind(0, 0, 0, 1, -1, 0) #FOR 4:6 IS 6 VALUE TAKEN

wald.test(b = coef(myprobit), Sigma = vcov(myprobit), L = l)

newdata <- data.frame(gre = rep(seq(from = 200, to = 800, length.out = 100), 

                                4 * 4), gpa = rep(c(2.5, 3, 3.5, 4), each = 100 * 4), rank = factor(rep(rep(1:4, 

                                                                                                            each = 100), 4)))

head(newdata)

newdata[, c("p", "se")] <- predict(myprobit, newdata, type = "response", se.fit = TRUE)[-3]

ggplot(newdata, aes(x = gre, y = p, colour = rank)) + geom_line() + facet_wrap(~gpa)

## change in deviance

with(myprobit, null.deviance - deviance)

## change in degrees of freedom

with(myprobit, df.null - df.residual)

## chi square test p-value

with(myprobit, pchisq(null.deviance - deviance, df.null - df.residual, lower.tail = FALSE))

logLik(myprobit)