This lab is intended as a lead-in to logistic regression. I will go over logistic regression in more depth on Tuesday in class. We will do this lab together in class, because it led to a lot of questions last year. I want you to hand in the answers to each of these questions next week.
Logistic regression is quite easy to perform, and it is not that hard once you get your head straight, but it does take some head straightening because it involves a different way of looking at things. This exercise is intended to give you some experience with logistic regression, and to help you understand just what the resulting models are all about. We will use a data set from Howell and Huessy (1985) on children who did, and did not, show behavior associated with Attention Deficit Disorder (ADD). The data are in a file named ADDfull.sav, and the variables are:
- ADDSC Average of three measures of ADD-like behavior in elementary school
- Gender 1 - male, 2 = female
- Repeat 1 = repeated at least one grade, 0 = did not repeat
- IQ IQ from a group-administered IQ test
- EngL Level of English in 9th grade 1 = college prep, 2 = general, 3 = remedial
- EngG Grade in 9th grade English
- GPA Grade point average in 9th grade
- SocProb Serious social problems in 9th grade 1 = yes, 0 = no
- DropOut 1 = dropped out before completing school, 2 = did not drop out
This data file is not the one in the book. It is a larger file, based on the full 359 cases.
We will use these data to see if we can predict Social Problems in 9th grade from the children’s level of ADD-like behavior in elementary school, their gender, and their subsequent GPA in 9th grade.
We will start out with Gender, which is actually a lousy predictor. I chose this because it is a dichotomous predictor.
The first thing to do is to get a plain old CrossTab (contingency table) of Gender against SocProb. It is located under Statistics/Descriptives. Be sure to ask it to include a chi-square test.
Using this printout, what are the odds of SocProb|male, the odds SocProb|female, the odds ratio, and the inverted odds ratio?
Now use logistic regression with SocProb as the dependent variable and Gender as the independent (covariate) variable.
What is the chi-square test on a model with Gender included, versus one with only the constant? (You can't answer this question with the current version of SPSS, but you can find it in the answers that go with this lab. I left it in because it makes a good point.)
What is the coefficient for Gender?
That is the ln(odds ratio). Calculate the odds ratio ( eln(odds ratio), and relate that to what you already know.
Do you see why I started with a dichotomous predictor?
Now we will move on to a continuous predictor. Continuous predictors work the same way as dichotomous ones, but it is a bit harder to draw parallel's with what you already know. It seems reasonable to assume that we want to know if ADDSC alone can predict future SocProb scores, so use that as your sole predictor.
Does ADDSC significantly predict SocProb using logistic regression? How do you know?
What is the logistic regression equation? What does it mean?
Use that equation to make a prediction for someone with an ADDSC score of 40, 50, 51, 60, 70, 80, 90, & 100. Crudely sketch out these predicted values in terms of odds and then probabilities. (Remember, p = odds/(1 + odds).) (You can get these plots in Excel or Word using Graph, and can put them all on the same graph.)
Why are we interested in eln(odds), and what does it tell us?
What do these predicted values in terms of odds stand for?
What does the difference between the prediction for 50 and 51 tell you?
Write a sentence or two telling me what you have found.
Now add GPA to the model.
Is that model an improvement on the previous model?
How are you best going to test whether GPA adds significant explanatory power?
Write out the model and calculate ln(odds), odds, and p that a person with an ADDSC score of 45 and a GPA of 2.5 will exhibit social problems.
What do you think this model has to say about causal relationships?
Why might you want to look at the model in this incremental way, rather than just starting with both ADDSC and GPA as predictors? (Hint: Think about Wald.)
Would you give the same answer to this question if you also included birthweight as a predictor at the same time as you included GPA?
How would your answer to the question about incremental change differ if you were using standard linear regression rather than logistic regression?
Finally, design an experiment that you might imagine doing that would use logistic regression.
A new page containing the answers to these questions can be found at Logistic Regression Lab Answers. Do not look at that until after you have done this work.
Last revised: 04/03/02