CHAPTER 19 Other Useful Kinds of Regression 273

follow one of several different distribution functions, such as normal, expo-

nential, binomial (as in logistic regression), or Poisson.»

» ^{With LM, the linear combination becomes the predicted value of the outcome,}

but with GLM, you can specify a link function. The link function is a transforma-

tion that turns the linear combination into the predicted value. As we note in

Chapter 18, logistic regression applies exactly this kind of transformation: Let’s

call the linear combination V. In logistic regression, V is sent through the

logistic function 1

1

/

e ^V to convert it into a predicted probability of

having the outcome event. So if you select the correct link function, you can

use GLM to perform logistic regression.

GLM is the Swiss army knife of regression. If you select the correct link function,

you can use it to do ordinary least-squares regression, logistic regression, Poisson

regression, and a whole lot more. Most statistical software offers a GLM function;

that way, other specialized regressions don’t need to be programmed. If the soft-

ware you are using doesn’t offer logistic or Poisson regression, check to see

whether it offers GLM, and if it does, use that instead. (Flip to Chapter 4 for an

introduction to statistical software.)

Running a Poisson regression

Suppose that you want to study the number of fatal highway accidents per year in

a city. Table  19-1 shows some made-up fatal-accident data over the course of

12 years. Figure 19-1 shows a graph of this data, created using the R statistical

software package.

Running a Poisson regression is similar in many ways to running the other com-

mon kinds of regression, but there are some differences. Here are the steps:

1.

As with any regression, prepare your predictor and outcome variables in

your data.

For this example, you have a row of data for each year, so year is the experi-

mental unit. For each row, you have a column containing the outcome values,

which is number of accidents each year (Accidents). Since you have one

predictor — which is year — you have a column for Year.

2.

Tell the software which variables are the predictor variables, and which

one is the outcome.