Logit Labmaterial borrowed from tutorial by

William B. KingCoastal Carolina

see: ww2.coastal.edu/kingw/statistics/R-tutorials/logistic.html

# Start by loading MASS library# Note: Functions and datasets to support Venables and Ripley, 'Modern Applied Statistics with S’

library("MASS")

#Load data set for analysisdata(menarche)

#View structure of datastr(menarche)

# There are 3 variables with 25 observations:Age: average age of each cohort, i.e., partitioned by ageTotal: total number of girls in each cohortMenarche: number of girls that have reached menarche

# Get summary statisticssummary(menarche)# See ranges for each variable along with distributions info

# Plot dataplot(Menarche/Total ~ Age, data=menarche)

# Wow! Looks like a really good data set for logistic regression

# What does the logistic regression command look like?glm. out = glm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(logit), data=menarche)

# So what is glm??glm

# we see that this is a generalized linear model function.

# Lets parse the commandglm. out = glm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(logit), data=menarche)

# glm – generalized linear model

# What is cbind(Menarche, Total-Menarche) ~ Age?# Type incbind(Menarche, Total-Menarche)

# Why do you get an error?

# You get an error because Menarche & Total are variables in a frame and# not top-level variables.

# Recall the plot command we used:plot(Menarche/Total ~ Age, data=menarche)

# Notice: data = menarche. This specifies the data frame# this is equivalent toplot(menarche$Menarche/menarche$Total ~ menarche$Age)

# What is cbind(Menarche, Total-Menarche)?# when data=menarche, cbind(Menarche, Total-Menarche) is# cbind(menarche$Menarche, menarche$Total-menarche$Menarche)# Type it incbind(menarche$Menarche, menarche$Total-menarche$Menarche)

# We see that these are the Y values of the points representing the dichotomy# Thus cbind(Menarche, Total-Menarche) ~ Age, # are the Y ~ X values that are arguments to the model

# What about family=binomial(logit)?# This tells the glm function to fit the data using the logit model

# Altogetherglm. out = glm(cbind(Menarche, Total-Menarche) ~ Age, family=binomial(logit), data=menarche)

# Ok, let’s examine the result of fitting the data with the logit modelplot(Menarche/Total ~ Age, data=menarche)lines(menarche$Age, glm.out$fitted, type="l", col="red")title(main="Menarche Data with Fitted Logistic Regression Line")

#Good fit!!!

# Check the statisticssummary(glm.out)

# Observe that the Estimated coefficient of Age is 1.63197# Recall that the response variable is log odds so# so the change in odds is exp(1.632) = 5.11 times.

# Interpretation: for every year increase in age the odds of having reached# menarche increase by exp(1.632) = 5.11 times.