PSCH 443 Multiple Regression 5 Dummy Coding

Understanding Categorical Predictions in Regression

Introduction to Categorical Variables

• Objective: Incorporating categorical variables into regression analyses while keeping the outcome variable continuous.

• Importance of mindful coding of categorical predictors to avoid misinterpretation of numerical values.

Coding Categorical Variables

• Assign numeric values (0 or 1) to represent categories.

  • Example: Gender coding (Male = 1, Female = 0).

  • The choice of coding does not affect results but aids interpretation.

Regression Analysis Example

• Context: Aggression and gender as a background factor.

• Research indicates males generally demonstrate higher levels of aggression.

• Importance of controlling for gender in regression models.

  • Assess how video game violence affects aggression, controlling for gender.

Hierarchical Regression Steps

• Enter gender variable (coded as Male = 1, Female = 0) in the first step of regression.

• Gender (zero for female, one for male) as the referent category helps in evaluating differences in aggressive behavior between genders.

  • Allows examination of how being male affects aggression compared to females.

• Results indicate significant variance in aggression explained by the inclusion of gender in the model.

Interpreting Regression Weights

• Understanding slope as rise over run; one unit change from one category to another reflects a measurable impact on the outcome variable.

• Hierarchical regression shows an increase of 0.738 in aggressive behavior moving from female to male.

• Gender is statistically significant, linked to a 0.258 standard deviation increase in aggression.

Dummy Coding Explained

• Dummy coding allows representation of categorical variables with more than two categories.

• Requires k - 1 dummy variables for k categories.

  • Each category is represented with a binary indicator (1 for membership, 0 for non-membership).

Example of Party Affiliation Analysis

• Using real data from Pew Research on political party affiliation and perceptions of federal tax system fairness.

• Categories: Republican, Democrat, Independent.

• Code two dummy variables for analysis: Independent (1 if member, 0 if not); Republican (1 if member, 0 if not); Democrat as the reference category.

Implementing Regression with Dummy Variables

• Importance of entering all dummy variables simultaneously in regression analysis to avoid errors.

• Democrats serve as the implicit reference category against which other categories are evaluated.

• Regression weights indicate the perceived fairness of the tax system adjusted for party affiliation.

Interpretation of Results

• For Republicans: A 0.675 increase in perceived fairness relative to Democrats.

• For Independents: A 0.2 increase in perceived fairness relative to Democrats.

• Analysis shows both Republicans and Independents perceive the tax system as fairer than Democrats.

Implications for Analysis

• Dummy coding allows effective control and evaluation of categorical variables in regression.

• Understanding the reference category's role is crucial for result interpretation.

• Intercept term in a regression model with only dummy variables equals the mean of the reference group.

• Provides insights into average outcomes across groups by incorporating categorical variables into regression analysis.

Conclusion

• Including categorical variables in regression analysis is useful for controlling variables or testing specific hypotheses.

• Bridges understanding to future discussions on analysis of variance (ANOVA) in the course.