1 chapter 2: logistic regression and correspondence analysis 2.1 fitting ordinal logistic regression...
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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
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Chapter 2: Logistic Regression and Correspondence Analysis
2.1 Fitting Ordinal Logistic Regression Models2.1 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.
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When Do You Use Ordinal Logistic Regression?
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Nominal
Ordinal
BinaryTwo
Categories
Threeor More
Categories
Response VariableType of
Logistic Regression
Binary
Nominal
Ordinal
Yes No
Cumulative Logits
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Response
Log
Log
Logit(1)
Logit(2)
Number of Cumulative Logits = Number of Levels -1
Proportional Odds Assumptions
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Predictor X
Logit(i) Logit(2)= a2+BX
Logit(1)= a1+BX
Equal Slopes
Sample Data Set
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PREDICTORS
OUTCOME
>100
75-100
50-74
25-49
0-24
5
4
3
2
1
Gender
Income
Age
MODEL
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This demonstration illustrates the concepts discussed previously.
Examining Distributions
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Exercise
This exercise reinforces the concepts discussed previously.
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Chapter 2: Logistic Regression and Correspondence Analysis
2.1 Fitting Ordinal Logistic Regression Models
2.2 Fitting Nominal Logistic Regression Models2.2 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.
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When To Use Nominal Logistic Regression?
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Nominal
Ordinal
BinaryTwo
Categories
Threeor More
Categories
Response VariableType of
Logistic Regression
Binary
Nominal
Ordinal
Yes No
Generalized Logits
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Response
Log
Log
Logit(1)
Logit(2)
Number of Generalized Logits = Number of Levels -1
Generalized Logit Model
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Logit(i)
Predictor X
Different Slopes and
Intercepts
Logit(i)
Predictor X
Logit(2)=a2+B2X
Logit(1)=a1+B1X
Different Slopesand
Intercepts
2.01 Multiple Choice PollSuppose 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.
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2.01 Multiple Choice Poll – Correct AnswerSuppose 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.
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Sample Data Set
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PREDICTORS
OUTCOME
>100
75-100
50-74
25-49
0-24
5
4
3
2
1
Gender
Income
Age
MODEL
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This demonstration illustrates the concepts discussed previously.
Nominal Logistic Regression Model
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Exercise
This exercise reinforces the concepts discussed previously.
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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 Analysis2.3 Introduction to Correspondence Analysis
Objectives Explain how correspondence analysis can help
you study data. Perform a simple correspondence analysis. Interpret a correspondence plot.
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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.
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Row and Column Profiles
Row and column percentages are used to obtain row and column profiles.
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A B C
1
4
19.5527.39
25.9123.27
54.5525.53
217.2724.20
28.84
29.49
25.31
26.12
53.49
53.00
24.47
24.47
317.6724.20
17.5124.20
28.1825.31
54.5525.53
GivesRow Profile
Gives Column Profile
Row %Column %
Row Profiles
Row percentages are used to obtain row profiles.
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A B C
1
4
19.55 25.91 54.55
2 17.27
28.84
29.49
53.49
53.00
3 17.67
17.51
28.18 54.55
Row %
Row Profile = Row%/100
Column Profiles
Column percentages are used to obtain column profiles.
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A B C
1
4
27.39 23.27 25.53
2 24.20
25.31
26.12
24.47
24.47
3 24.20
24.20
25.31 25.53
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
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Row 8 and Column D fall in approximately the same direction from the origin, and are relatively close to one another.
Association
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2.02 Multiple Answer PollIn 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.
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2.02 Multiple Answer Poll – Correct AnswersIn 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.
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Sample Data Set
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ACTION
MYSTERY
COMEDY
SPORTS
ROMANCE
SCI-FI
HORROR
DRAMA
FAMILY
AGE
GENDER
MOVIES
Analysis ApproachesYou 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.
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This demonstration illustrates the concepts discussed previously.
Correspondence Analysis
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Exercise
This exercise reinforces the concepts discussed previously.
2.03 QuizIce 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?
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