19 Questions
Which type of regression is used to model ordinal outcome variables?
Ordinal logistic regression
What is an ordinal variable?
A categorical variable with a clear ordering of the category levels
How many categories are required for using ordinal logistic regression?
3 or more
What does the proportional odds assumption in ordinal logistic regression require?
The coefficients to be the same for each category
What does an ordinal logistic regression model produce in the output?
Multiple intercepts
In an ordinal logistic regression model, how are the odds ratios interpreted?
As the effect of being in a higher category relative to a low category (or vice versa)
What factors are considered in a study on the decision to apply to graduate school?
Parental educational status
What is the purpose of using ordinal logistic regression in the study on the decision to apply to graduate school?
To model the relationship between factors and the decision to apply to graduate school
What assumption is made about the distances between the three points in the study on the decision to apply to graduate school?
The distances are equal
What is the main difference between ordinal logistic regression and multinomial logistic regression?
Ordinal logistic regression models ordered categories, while multinomial logistic regression models unordered categories
Which type of regression is used to model nominal outcome variables?
Multinomial logistic regression
What does the odds ratio of 2.85 indicate for students whose parents attended college?
They are 2.85 times more likely to apply than students whose parents did not go to college
How does the odds of applying differ for public school students compared to private school students?
Public school students are 5.71% less likely to apply than private school students
What does a one unit increase in GPA do to the odds of applying?
Increases the odds by 1.85 times
What is the approximate odds ratio for low SES students selecting the general program instead of the academic program?
3.199
What is the effect of a one unit increase in writing score on the likelihood of selecting the vocational program instead of the academic program?
Decreases the likelihood by 11%
What is the proportional odds assumption in multinomial logistic regression?
The odds of the outcomes are the same for all levels of the predictor variables
What is the interpretation of the odds ratio in the context of parental education?
The odds of applying are 2.85 times higher for students whose parents attended college
What is the difference in the odds of applying between public school students and private school students?
Public school students have 5.71% lower odds of applying than private school students
Study Notes
Ordinal Logistic Regression
- Ordinal logistic regression is used to model ordinal outcome variables.
- An ordinal variable is a categorical variable with a natural order or ranking.
- At least three categories are required for using ordinal logistic regression.
- The proportional odds assumption in ordinal logistic regression requires that the odds of being in a particular category or higher versus being in a lower category are the same across all categories.
Ordinal Logistic Regression Output and Interpretation
- An ordinal logistic regression model produces odds ratios in the output.
- Odds ratios in an ordinal logistic regression model are interpreted as the change in odds of being in a particular category or higher versus being in a lower category.
Study on the Decision to Apply to Graduate School
- Factors considered in the study include parental education, type of school, GPA, SES, and writing score.
- The purpose of using ordinal logistic regression in the study is to model the ordinal outcome variable "decision to apply to graduate school" with multiple categories (e.g., didn't apply, applied to general program, applied to academic program, etc.).
- The assumption is made that the distances between the three points in the study are equal.
Comparison with Multinomial Logistic Regression
- Multinomial logistic regression is used to model nominal outcome variables.
- The main difference between ordinal logistic regression and multinomial logistic regression is that ordinal logistic regression assumes an ordinal outcome variable, while multinomial logistic regression assumes a nominal outcome variable.
Interpretation of Odds Ratios
- An odds ratio of 2.85 indicates that for students whose parents attended college, the odds of applying to graduate school are 2.85 times higher than for students whose parents did not attend college.
- The odds of applying differ for public school students compared to private school students, with public school students having lower odds of applying.
- A one unit increase in GPA increases the odds of applying to graduate school.
- The approximate odds ratio for low SES students selecting the general program instead of the academic program is 0.67.
- A one unit increase in writing score increases the likelihood of selecting the vocational program instead of the academic program.
Multinomial Logistic Regression
- The proportional odds assumption in multinomial logistic regression is not applicable, as it assumes a nominal outcome variable.
- The interpretation of the odds ratio in the context of parental education is that the odds of applying to graduate school are higher for students whose parents attended college.
- The difference in the odds of applying between public school students and private school students is significant, with public school students having lower odds of applying.
Test your knowledge of ordinal and multinomial logistic regression with this quiz! Explore the concepts, applications, and methods used in analyzing relationships between ordinal response variables and explanatory variables. Challenge yourself with questions on modeling, log odds, and more.
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