1 Chapter 2: Logistic Regression and Correspondence Analysis 2.1 Fitting Ordinal Logistic Regression Models 2.2 Fitting Nominal Logistic Regression Models 2.3 Introduction to Correspondence Analysis

2 Chapter 2: Logistic Regression and Correspondence Analysis 2.1 Fitting Ordinal Logistic Regression Models 2.2 Fitting Nominal Logistic Regression Models 2.3 Introduction to Correspondence Analysis

Objectives Define a cumulative logit. Fit an ordinal logistic regression model. Interpret parameter estimates. Compute odds ratios. 3

When Do You Use Ordinal Logistic Regression? 4 Nominal Ordinal Binary Two Categories Three or More Categories Response Variable Type of Logistic Regression Binary Nominal Ordinal Yes No

Cumulative Logits 5 Response Log Logit(1) Logit(2) Number of Cumulative Logits = Number of Levels -1

Proportional Odds Assumptions 6 Predictor X Logit(i) Logit(2)= a 2 +BX Logit(1)= a 1 +BX Equal Slopes

Sample Data Set 7 PREDICTORSPREDICTORS OUTCOMEOUTCOME > Gender Income Age MODEL

8 This demonstration illustrates the concepts discussed previously. Examining Distributions

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10 Exercise This exercise reinforces the concepts discussed previously.

11 Chapter 2: Logistic Regression and Correspondence Analysis 2.1 Fitting Ordinal Logistic Regression Models 2.2 Fitting Nominal Logistic Regression Models 2.3 Introduction to Correspondence Analysis

Objectives Explain a generalized logit. Fit a nominal logistic regression model. Interpret the parameter estimates. Compute odds ratios. 12

When To Use Nominal Logistic Regression? 13 Nominal Ordinal Binary Two Categories Three or More Categories Response Variable Type of Logistic Regression Binary Nominal Ordinal Yes No

Generalized Logits 14 Response Log Logit(1) Logit(2) Number of Generalized Logits = Number of Levels -1

Generalized Logit Model 15 Logit(i) Predictor X Different Slopes and Intercepts Logit(i) Predictor X Logit(2)=a 2 +B 2 X Logit(1)=a 1 +B 1 X Different Slopes and Intercepts

2.01 Multiple Choice Poll Suppose a nominal response variable has four levels. Which of the following statements is true? a.JMP will compute three generalized logits. b.Logit(1) is the log odds for level 1 occurring versus level 4 occurring. c.JMP will compute a separate intercept parameter for each logit. d.JMP will compute a separate slope parameter for each logit. e.All of the above are true. 17

2.01 Multiple Choice Poll – Correct Answer Suppose a nominal response variable has four levels. Which of the following statements is true? a.JMP will compute three generalized logits. b.Logit(1) is the log odds for level 1 occurring versus level 4 occurring. c.JMP will compute a separate intercept parameter for each logit. d.JMP will compute a separate slope parameter for each logit. e.All of the above are true. 18

Sample Data Set 19 PREDICTORSPREDICTORS OUTCOMEOUTCOME > Gender Income Age MODEL

20 This demonstration illustrates the concepts discussed previously. Nominal Logistic Regression Model

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22 Exercise This exercise reinforces the concepts discussed previously.

23 Chapter 2: Logistic Regression and Correspondence Analysis 2.1 Fitting Ordinal Logistic Regression Models 2.2 Fitting Nominal Logistic Regression Models 2.3 Introduction to Correspondence Analysis

Objectives Explain how correspondence analysis can help you study data. Perform a simple correspondence analysis. Interpret a correspondence plot. 24

What Is Correspondence Analysis? Correspondence analysis is a data analysis technique that enables you to display the associations between the levels of two or more categorical variables graphically extract information from a frequency table with many levels for the rows and columns. 25

Row and Column Profiles Row and column percentages are used to obtain row and column profiles. 26 AB C Gives Row Profile Gives Column Profile Row % Column %

Row Profiles Row percentages are used to obtain row profiles. 27 AB C Row % Row Profile = Row%/100

Column Profiles Column percentages are used to obtain column profiles. 28 AB C Column % Col Profile = Column%/100

Rows 1 and 2 have similar profiles. Their points are close together and fall in the same direction away from the origin. The profile for Row 7 is different. Its point is closer in and falls in a different direction away from the origin. Correspondence Plot 29

Row 8 and Column D fall in approximately the same direction from the origin, and are relatively close to one another. Association 30

2.02 Multiple Answer Poll In correspondence analysis, which of the following are true? (Choose all answers that apply.) a.Row points that fall far from each other but in the same direction away from the origin indicate that they have similar profiles. b.Column points that fall close together and in the same direction away from the origin indicate that they have similar profiles. c.Row and column points that fall in the same direction away from the origin indicate that they have an association. 32

2.02 Multiple Answer Poll – Correct Answers In correspondence analysis, which of the following are true? (Choose all answers that apply.) a.Row points that fall far from each other but in the same direction away from the origin indicate that they have similar profiles. b.Column points that fall close together and in the same direction away from the origin indicate that they have similar profiles. c.Row and column points that fall in the same direction away from the origin indicate that they have an association. 33

Sample Data Set 34 ACTION MYSTERY COMEDY SPORTS ROMANCE SCI-FI HORROR DRAMA FAMILY AGE GENDER MOVIES

Analysis Approaches You want to perform an analysis that takes into account the three variables Movie, Age, and Gender. There are several approaches. You can analyze a two-way table where the rows correspond to the levels of Movie and the columns correspond to combinations of the levels of Age and Gender treat Gender as a stratification variable and analyze males and females separately. 35

36 This demonstration illustrates the concepts discussed previously. Correspondence Analysis

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38 Exercise This exercise reinforces the concepts discussed previously.

2.03 Quiz Ice cream brands A through D are tested by a panel, and rated from 1through 9 (with 9 as the best score). What can you conclude from the Correspondence Analysis? 40