Odds Ratio


ADM 7213

Homework Assignment 6

 

 

  1. Coefficients

 

Now let’s do the simple interpretation, since that is more intuitive.

 

  1. If the regression coefficient is positive, this means that an increase in

the independent variable ___________ the probability that Y=1

  1. If a coefficient is positive, then its odds ratio will always be greater than __
  2. If the regression coefficient is negative, this means that an increase in

the independent variable ___________ the probability that Y=1

  1. If a coefficient is negative, then its odds ratio will always be less than ____
  2. The odds ratio for negative coefficients is bounded by zero and ___
  3. The odds ratio for positive coefficients is bounded by one and positive _________________
  1. Rules for Odds Ratio Interpretation

 

  1. Rules for Interpreting Odds Ratios on Dummy Variables

 

The mantra is this: The odds of the numerator case are OR times the odds of the denominator case.

 

  • If OR>1: For example, OR=1.2. We would say that the odds of the outcome are (OR-1)*100= 20% larger in for the numerator group.
  • If OR<1:  For example, an OR=0.2. We would say that the odds of the outcome are (1-OR)*100=80% smaller in the numerator group compared to another.

 

  1. Rules for Interpreting Odds Ratios on Continuous Variables

 

The mantra is this: A one unit change in X is associated with a OR change in the odds of the outcome

 

  • If OR>1: For example, OR=1.2. We would say that a one unit change in x is associated with a (OR-1)*100= 20% increase in the odds of the outcome.
  • If OR<1:  For example, OR=0.95. We would say that a one unit change in x is associated with a (1-OR)*100=5% decrease in the odds of the outcome.

 

 

  1. Titanic Data

 

Here are estimates for the following using logistic regression using Odds Ratios

 

Survived = b0 + b1 male +b2 fare + b3 age + b4 fam_size

 

For this regression, Odds Ratios are reported instead of raw coefficients.

 

 

  1. Interpretation of odds ratio b1 (male)

 

  • Is this a dummy variable or continuous variable? So, you should use the

 

interpretation for a ______________ variable.

 

 

  • Is the odds ratio greater than 1 or less than 1? So, you should use the

 

interpretation for an odds ratio _____ ________ 1.

 

  • What is the interpretation of the odds ratio b1?

 

 

 

  • What is the p value for b1 ?

 

 

 

  • How many stars for b1?

 

 

  1. Interpretation of odds ratio b2 (fare)

 

  • Is this a dummy variable or continuous variable? So, you should use the

 

interpretation for a ______________ variable.

 

 

  • Is the odds ratio greater than 1 or less than 1? So, you should use the

 

interpretation for an odds ratio _____ ________ 1.

 

  • What is the interpretation of the odds ratio b2?

 

 

 

  • What is the p value for b2 ?

 

 

 

  • How many stars for b2?

 

 

 

  • Logistic Regression in Real Research

 

Please download and read the following article:

 

David J. Houston, “Walking the Walk” of Public Service Motivation: Public Employees and Charitable Gifts of Time, Blood, and Money, Journal of Public Administration Research and Theory, Volume 16, Issue 1, January 2006, Pages 67–86, https://doi.org/10.1093/jopart/mui028

 

Note that in the logistic regression tables, odds ratios are reported in parenthesis to the right of the raw coefficients)

 

Look at Table 3, Model 1.

 

  • According to model 1, the odds ratio for public employees is 1.372.

 

  1. Is this a dummy variable or continuous variable? So, you should use the

 

interpretation for a ______________ variable.

 

 

  1. Is the odds ratio greater than 1 or less than 1? So, you should use the

 

interpretation for an odds ratio _____ ________ 1.

 

  1. What is the interpretation of the odds ratio?

 

 

 

 

  • According to model 1, the odds ratio for years of education is 1.086

 

  1. Is this a dummy variable or continuous variable? So, you should use the

 

interpretation for a ______________ variable.

 

 

  1. Is the odds ratio greater than 1 or less than 1? So, you should use the

 

interpretation for an odds ratio _____ ________ 1.

 

  1. What is the interpretation of the odds ratio?

 

 

 

 

  • According to model 1, the odds ratio for church attendance is 2.481

 

  1. Is this a dummy variable or continuous variable? So, you should use the

 

interpretation for a ______________ variable.

 

 

  1. Is the odds ratio greater than 1 or less than 1? So, you should use the

 

interpretation for an odds ratio _____ ________ 1.

 

  1. What is the interpretation of the odds ratio?

 

 

 

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