Extracting meaningful information from a logistic regression model

Question

Possible warning: basic question ahead.

Let's say that I model whether I wear red shoes depending on the weather. Red shoes, which is my dependent variable, is a dichotomous variable as I either wear them or don't. Weather is a variable with five 'levels' and I'm trying to find the probability that I will wear read shoes.

Let's say I model out this relationship with a logistic regression model in R:

mod = glm(shoes ~ weather, data=mydat, family=binomial(link="logit"))

Now, what I am interested in is finding what are the probabilities for wearing red shoes for each of the five 'levels' in weather. So perhaps I might have a 20% probability of wearing red shoes when cold, 30% when mild, 40% when warm, and so forth.

I'm wondering if modeling is a requirement for finding this information? If so, how does one go from somewhat meaningful regression coefficients to meaningful probabilities in R?

Answer 1

Here is some R code to calculate the desired probabilities.

mydat <- read.csv(url("http://www.ats.ucla.edu/stat/r/dae/binary.csv"))
mod = glm(admit ~ rank, data=mydat, family=binomial(link="logit")) 
predict(mod,newdata=data.frame(rank<-c(1,2,3,4)),type="response")

    1         2         3         4 

0.5125867 0.3691354 0.2456011 0.1533587

All you need to do is supply a new data frame to R with the values that you want to use for the independent variables as above. The function predict(), with the option newdata="dfname", applies the fitted model from the original data set to the new data. The type "response" gives you probabilities rather than logits.

If your predictor is quantitative, then supply an entire range for X and plot the response probabilities. Like this...

mod2 = glm(admit ~ gre, data=mydat, family=binomial(link="logit"))
plot(gre<-400:800,predict(mod2,newdata=data.frame(gre<-c(400:800)),type="response"))