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Unformatted text preview: Logistic Regression, Part IIIPage 1 Logistic Regression, Part III: Hypothesis Testing, Comparisons to OLS [This handout steals heavily from the SPSS Advanced Statistics User Guide. Also, Linear probability, logit, and probit models, by John Aldrich and Forrest Nelson, paper # 45 in the Sage series on Quantitative Applications in the Social Sciences; and Applied Logistic Regression Analysis Second Edition by Scott Menard, paper # 106 in that series.] WARNING: As Menard more or less points out, notation is wildly inconsistent across authors and programs when it comes to Logistic regression. Im trying to more or less follow Menard, but youll have to learn to adapt to whatever the author or statistical program happens to use. Overview. In this handout, well examine hypothesis testing in logistic regression and make comparisons between logistic regression and OLS. Well use both SPSS and Stata in this handout. A separate handout provides more detail about using Stata. The optional appendix to this handout provides more detail on how some of the key calculations are done. There are a number of logical analogs between OLS and Logistic regression, i.e. the math is different but the functions served are similar. I will summarize these first, and then explain each of them in more detail: OLS Regression Logical Analog in Logistic Regression Total Sums of Squares -2LL , DEV , D 0 Error/ Residual Sums of Squares -2LL M , DEV M , D M Regression/Explained Sums of Squares Model Chi Square, L 2 , G M Global F Model Chi Square, L 2 , G M Incremental F Test Chi-Square Contrast/ Incremental chi-square contrast Incremental F Test and Wald test of the same hypotheses give identical results Chi-square contrast between models and a Wald test of the same hypotheses generally do NOT give exactly identical results. Logistic Regression, Part IIIPage 2 Using the same data as before, here is part of the output we get in SPSS when we do a logistic regression of Grade on Gpa, Tuce and Psi. Block 1: Method = Enter Omnibus Tests of Model Coefficients 15.404 3 .002 15.404 3 .002 15.404 3 .002 Step Block Model Step 1 Chi-square df Sig. Model Summary 25.779 .382 .528 Step 1-2 Log likelihood Cox & Snell R Square Nagelkerke R Square The more or less corresponding output from Stata is . use http://www.nd.edu/~rwilliam/stats2/statafiles/logist.dta, clear . logit grade gpa tuce psi Iteration 0: log likelihood = -20.59173 Iteration 1: log likelihood = -13.496795 Iteration 2: log likelihood = -12.929188 Iteration 3: log likelihood = -12.889941 Iteration 4: log likelihood = -12.889633 Iteration 5: log likelihood = -12.889633 Logistic regression Number of obs = 32 LR chi2(3) = 15.40 Prob > chi2 = 0.0015 Log likelihood = -12.889633 Pseudo R2 = 0.3740 [Rest of output deleted] Global tests of parameters . In OLS regression, if we wanted to test the hypothesis that all s = 0 versus the alternative that at least one did not, we used a global F test. In logistic regression,...
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- Spring '11