PSCH 443 Multiple Regression 4 Hierarchical Regression

Introduction to Multiple Regression

• Discussion on methods of multiple regression, emphasizing hierarchical multiple regression.

• Contrast with simultaneous regression where all variables are entered into the model at once.

Simultaneous Regression

• Definition: All predictor variables (IV1, IV2, IV3) are included in the regression equation simultaneously.

• Purpose: To assess the unique effects of predictors after accounting for all other variables.

• Outcome: Allows evaluation of how much variability can be explained by individual predictors controlling for others.

Hierarchical Regression

• Definition: Predictors are entered into the regression model in a specified order determined by the researcher.

• Method: Consists of a series of simultaneous regressions to observe the impact of individual variables or blocks of variables.

• Order of Entry: Should be based on theoretical background and prior research insights.

Example of Variable Entry

• Enter known predictors or background variables first to control for their effects before adding new variables.

• Demographic Variables: Age, gender, race can be entered first to ensure baseline control in predicting outcomes.

Steps in Hierarchical Regression

• First Step: Begin with background variables (e.g., aggressive personality, time spent playing video games).

• Subsequent Steps: Add key variables (like video game violence exposure) and assess additional variability in predicting outcomes.

Case Study: Video Game Violence and Aggression

• Research Context: Study on the relationship between video game violence exposure and aggressive behavior.

• Predictor Variables:

  • Aggressive Personality: As a baseline control.

  • Time Spent Playing Video Games: Irrespective of content.

  • Video Game Violence Exposure: Key variable analyzed for its impact.

• Dependent Variable: Measured aggressive behavior, where higher scores indicate more aggression.

Purpose of Analysis

• To investigate if video game violence explains variability in aggressive behavior after controlling for aggressive personality and gameplay time.

• Assessment Focus: Changes in R-squared values upon adding video game violence as a predictor.

Methodology

• Observing R-squared Changes: Determine the statistical significance of the contribution of the video game violence variable after background controls.

  • Initial model accounts for variance with significant values.

  • Further analysis shows additional variance explained upon adding violent video game exposure.

Correlation Insights

• Examination of correlations among variables to establish logical interrelations.

  • Expect positive correlations: More aggressive personalities might tend to play more violent video games.

• Importance of understanding these correlations before regression analysis.

Hierarchical Regression Results

• Output resembles standard regression results with components like R, R-squared, and adjusted R-squared.

• Introduction of Change Statistics relevant for hierarchical regression:

  • Initial model explained about 17% of variance.

  • Significant change noted when adding video game violence, accounting for an additional 5% of variance.

Coefficient Analysis

• Coefficients' output includes B weights and beta weights.

• Changes from step one to step two reflect the effect of adding new predictors, indicating shared variance.

Conclusion: Reporting Hierarchical Regression Findings

• Focus on meaningful contributions from predictors in explaining variance, especially after including additional variables.

• The hierarchical regression approach enhances understanding of each predictor's impact on the dependent variable.