# Unit 5: Multiple Logistic Regression

## Learning Objectives

Multiple Logistic Regression

• Use LOG rules for powers and division appropriately as needed to work with logistic models.
• Use the logistic model to predict probabilities or LOG-ODDS.
• State the assumptions of the logistic regression model.
• Derive and appropriately interpret the log-odds-ratio and odds-ratio for comparing levels of a categorical predictor to the reference group.
• Derive and appropriately interpret the log-odds-ratio and odds-ratio for a one-unit increase or a c-unit increase for a continuous predictor.
• Appropriately use SAS output to conduct logistic regression analysis for one predictor and multiple predictors, possibly including interactions.
• Construct confidence intervals for parameter estimates and odd-ratios by hand for comparisons to a reference group for categorical predictors.
• Construct confidence intervals for parameter estimates and odd-ratios by hand for a one-unit or c-unit increase in a continuous predictor.
• Be able to find odd-ratio and confidence intervals in the reverse direction of comparisons given in software output by taking the reciprocal of the values in the output.
• Use contrast and oddsratio statements to test and estimate complex comparisons.
• Appropriately use percent increase or percent decrease interpretations for odd-ratios.

Videos for Unit 5 (Previously labeled Topics 7 and 8)

• Live Topic 7 Part A  (7:50) – Multiple Logistic Regression – Introduction and Model (Slides 1-5)
• Live Topic 7 Part B  (4:13) – Multiple Logistic Regression – Proving how to find the odds ratio for a delta unit increase in X1 (Slide 6)
• Live Topic 7 Part C  (8:37) – Multiple Logistic Regression – Example 1 (Slides 7-13)
• Live Topic 7 Part D  (6:56) – Multiple Logistic Regression – Example 2 (Slides 14-18)
• Live Topic 7 Part E  (3:55) – Multiple Logistic Regression – Confounding (Slides 19-22)
• Live Topic 7 Part F  (5:08) – Multiple Logistic Regression – Interaction (Slides 23-24)
• Live Topic 7 Part G  (5:37) – Multiple Logistic Regression – Interaction (Slides 25-29)
• Live Topic 7 Part H  (3:47) – Multiple Logistic Regression – Interaction, Prediction, ROC curves (Slides 30-44)
• Live Topic 8A  (5:18) – Introduction, Residual Plots, and DFBETAs (Slides 1-11)
• Live Topic 8B  (5:07) – Linearity, Hosmer-Lemshow test of goodness of fit (Slides 12-End)

SAS Code: Unit5.sas (labeled above as topic 7) and Unit5B.sas (labeled above as topic 8)

PowerPoint: Unit5.pptx (labeled above as topic 7) and Unit5B.pptx (labeled above as topic 8)

Optional PowerPoint: PHC6937-SAS-LogisticRegression.pdf (from PHC 6937 – Biostatistical Computing Using SAS for our MS Biostatistics Students)

The following lessons from Penn State STAT 501 are linked in the materials as support materials for Unit 5. Our videos will be the primary instruction for Unit 4 and Unit 5.