SPSS Data Analysis Examples: Logit Regression



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SPSS Data Analysis Examples
Logit Regression

Examples

Example 1: Suppose that we are interested in the factors that influence whether or not a political candidate wins an election. The outcome (response) variable is binary (0/1); win or lose. The predictor variables of interest are: the amount of money spent on the campaign, the amount of time spent campaigning negatively and whether or not the candidate is an incumbent. Because the response variable is binary we need to use a model that handles 0/1 variables correctly.

Example 2: We wish to study the influence of age, gender and exercise on whether or not someone has a heart attack. Again, we have a binary response variable, whether or not a heart attack occurs.

Example 3: How do variables, such as, GRE (Graduate Record Exam scores), GPA (grade point average), and prestige of the undergraduate program effect admission into graduate school. The response variable, admit/don't admit, is a binary variable.

Description of the Data

For our data analysis below, we are going to expand on Example 3 about getting into graduate school. We have generated hypothetical data, which can be obtained by clicking on logit.sav. You can store this anywhere you like, but our examples will assume it has been stored in c:\data. First, we read the data file into SPSS.

get file = "C:\data\logit.sav".

This hypothetical data set has a binary response (outcome, dependent) variable called admit. There are three predictor variables: gre, gpa and topnotch, which is a binary predictor in which 1 indicates that the undergraduate institution was "top notch" and 0 indicates that it is not.

descriptives /variables=gre gpa.

frequencies /variables = topnotch.

Some Strategies You Might Try

OLS regression: This analysis is problematic because the assumptions of OLS are violated when using a binary response variable.
Hotelling's T²: The 0/1 outcome is turned into the grouping variable and the former predictors are turned into outcome variables.
This will produce an overall test of significance but will not give individual coefficients for each variable, and it is unclear the extent to which each "predictor" is adjusted for the impact of the other "predictors".
Probit regression: Probit analysis will produce results similar logit regression. The choice of probit versus logit regression depends largely on individual preferences.

Using the Logit Model

Before running logit, check to see if any cells (created by the crosstab of our categorical and response variables) are empty or particularly small. If this occurs, there may be difficulty running the logit model.

crosstabs /tables=admit by topnotch.

None of the cells are too small or empty (has no cases), so we will run our logit model.

logistic regression admit with gre topnotch gpa.

This shows the number of observations and the coding for the outcome variable, admit.

Block 0: Beginning Block

This shows the results from running an empty model, which is generally boring. The next set of results are for the model we specified.

Block 1: Method = Enter

The likelihood ratio chi-square of 21.85 with a p-value of 0.0001 tells us that our model as a whole fits significantly better than the empty model (Model 0). The -2 log likelihood (478.13) was used to to compare the fit of this model with Model 0. The R Square values shown might appear to be just like those you get with OLS, but these are forms of "pseudo" R square values which can vary considerably depending on the measure you select.

This classification table is usually boring.

The above table gets into the heart of the results. It shows the coefficients (B), their standard errors, the Wald Chi-Square statistic, associated p-values, and odds ratio (Exp(B)). Both gre and gpa are statistically significant while topnotch is not. The interpretation of the coefficients can be awkward. For example, for a one unit increase in gpa, the log odds of being admitted to graduate school (versus not being admitted) increases by .668. For this reason, many researchers prefer to exponentiate the coefficients and interpret them as odds-ratios. For example, we can say that for a one unit increase in gpa, the odds of being admitted to graduate school (versus not being admitted) increased by a factor of 1.949. Since GRE scores do not increase by a single unit (they increase only in units of 10), a one unit increase is meaningless. We can take the odds ratio and raise it to the 10th power, e.g. 1.002 ^ 10 = 1.02, and say for a 10 unit increase in GRE score, the odds of admission to graduate school increased by a factor of 1.02.

Sample Write-up of the Analysis

Below is one way of describing these results.

A logit regression was used to predict admission to graduate school from GRE score, GPA, and whether the student was from a top notch university. GRE score and GPA were significant predictors of admission to graduate school, but being from a top notch university was not related to admission to graduate school. For every one unit increase in GPA, the odds of admission (versus non-admission) increased by a factor of 1.95, while for every ten unit increase in GRE score, such odds increased by a factor of 1.02.

Cautions, Flies in the Ointment

Perfect prediction: Perfect prediction means that only one value of a predictor variable is associated with only one value of the response variable. If this happens, SPSS will usually issue a note in the log file.
Sample size: Both logit and probit models are likely to require more cases than OLS regression because they use maximum likelihood techniques.
Empty cells or small cells: You should check for empty or small cells by doing a crosstab between categorical predictors and the outcome variable. If a cell has very few cases (a small cell), the model may become unstable or it might not run at all.
Diagnostics: Diagnostics still have to be done to check that the assumptions of the logit analysis have not been violated, but these are different from the diagnostics done in OLS regression. They are essentially the same as those done for probit regression.

SPSS Data Analysis Examples Logit Regression