Logistic Regressions Computer Science Worksheet printable pdf download

Logistic Regressions

The goal of logistic regression is to estimate the probability p

of a binary event i given predictor

variables. For example, is success (1) or failure (0) of an animal to reproduce a function of its

age? Or other factors too? Many outcomes can be described in these terms. Logistic regression is

thus flexible, widely used, and fairly simple to run, though some thought is required to express

outcomes as probabilities.

A logistic relationship between p

and the predictor variables is S-shaped, like the population

growth model, where a switch from p

= 0 to p

= 1 takes place somewhere in the middle.

Logistic regression is based on the logit function, which is a log transformation of p

To compute a logistic regression, we again use Generalized Linear Model (glm). A glm is able to

deal with a big problem for lm: error variance that is not evenly distributed across the model.

Here is an example of such a variance problem for lm:

1. Import and attach the

data set. This includes incidence (presence = 1,

islandbird.txt

absence = 0) for a bird species on islands in an archipelago, with given area (km

) and

isolation (km from the nearest island) as predictors.

2. Make simple plots of incidence as function of isolation and of area to see the data. Do

you think both predictor factors affect incidence?

3. Let's first try a linear model that assumes a Gaussian (i.e., normal) error variance. Enter:

liniso2 <- glm(incidence ~ isolation, family=gaussian)

summary(liniso1)

summary(liniso2)

par(mfrow=c(2,2))

plot(liniso1)

See any problems? You should! Thus the problem for analyzing binary data with tools

used so far this semester.

4. Now we try a logistic glm, where we can specify that binomial errors are to be expected

with the binary data. Logistic regression simply assumes response variable observations

are independent. That's it - no need not sweat residual distributions. Now make a new

glm model, with all as in liniso2 but use family=binomial instead, and get a summary. I

assume you call that model logiiso.

Notice how much the coefficients changed simply by assuming a binomial distribution

for the binary data? Coefficients in logistic regression indicate the effect of a one-unit

change in the predictor variable on the log odds of 'success'.

5. How much better is your logistic model than the linear glm (

)? Load the

liniso2

bbmle

package and compute an

with

to find out.

AICctab

weights=TRUE

Logistic Regressions Computer Science Worksheet

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