PSCH 443 Multiple Regression 3 Evaluating Assumptions Part 2

Assumptions in Regression Analysis

• Normality

  • Refers to the assumption that predictor and outcome variables are normally distributed.

  • Essential to check for normal distribution before conducting regression analyses.

• Multivariate Normality

  • Involves combining individual variables in the regression equation.

  • Errors in prediction should also be normally distributed (centered around zero).

  • If errors are normal, we can assess the multivariate normality assumption effectively.

  • Use SPSS to plot residuals against a normal curve for evaluation.

Evaluating Normality

• Residual Analysis

  • Showcases whether predicted values closely align with observed values.

  • Examine plots; deviations indicate flaws in the data.

• Example of Normal PP Plot

  • Data points should ideally follow a straight line. Deviations signal potential issues.

Consequences of Violating Assumptions

• Impact of Non-Normality

  • Affects parameter estimates and may complicate interpretation.

  • Increased error can diminish statistical significance in results.

  • Results may still be interpretable if one predictor is statistically significant, even amidst assumption violations.

Linear Relationships

• Linearity Assumption

  • Assumes a straight-line relationship between predictors and outcomes.

  • Consider potential curvilinear relationships at the conceptual level before analysis.

Homoscedasticity

• Refers to the uniformity of residual variation across predicted values.

• Plot residuals against predicted values; expect a random scatter of dots.

• Detecting Violations

  • Heteroskedasticity: Identified by a triangular pattern; variability increases in one direction.

  • Non-Linearity: Curvilinear relationships invalidate linear regression assumptions.

Independence of Errors

• Errors of prediction need to be independent, especially in repeated measures or longitudinal designs.

• Durbin-Watson Statistic

  • Helps assess autocorrelation among prediction errors. A result near 2 indicates independence.

Suppressor Effect

• Occurs when predictors correlate in a way that influences each other's predictive power

• Notable features include:

  • Absolute value of a beta weight exceeds its univariate correlation.

  • Changes in beta weights may indicate suppression when variables are added or removed.

Avoiding Errors

• Conduct bivariate correlation analyses to prepare for regression.

• Keep an eye on correlation size and direction to identify potential issues early.

• Basic checks ensure proper interpretation and prevent misleading results in reporting.