Multiple Predictor Linear Model

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Lead Author(s): David Glidden, PhD

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Slide 1: Multiple predictor linear regression

Slide 2: Components of the Linear Model

Slide 3: Systematic part of the model

Slide 4: Interpretation of regression coefficients

Slide 5: Interpretation of regression coefficients

Slide 6: Review: centering predictors

Slide 7: Review: rescaling predictors

Slide 8: Random part of the model

yi =Σ[y|xi]+εi

1. Normally distributed
2. mean zero at every value of x
3. constant variance
4. statistically independent

Slide 9: Assumptions about the predictors

Slide 10: Update of two details

Slide 11: Ordinaryleast squares(OLS)

Slide 12: Multi-predictor linear model for glucose

Multi-predictor linear model for glucose

Slide 13: Interpreting Stata regression output

Interpreting STATA regression output

Slide 14: Summary of model

Slide 15: Confounding

Slide 16: Unadjusted waist/glucose association

Unadjusted waist/glucose association

Slide 17: Adjusted waist/glucose association

Adjusted waist/glucose association

Slide 18: Primary predictor, confounder, and outcome

Primary predictor, confounder and outcome

Adjusting for a confounder

Slide 19: Interpretation of results

Behavior of regression coefficients for this case

Slide 20: Another case: so-called negative confounding

Slide 21: Negative confounding: two scenarios

Negative confounding may arise between predictors that are
  1. Positively correlated, with opposite effects on outcome:
    Example: injury severity, AZT, and seroconversion
  2. Negatively correlated, with similar effects on outcome:
    Example: average BMI decreases with age in HERS
    cohort, but both predict increased SBP

Slide 22: Summary: negative confounding

Slide 23: Confounding is difficult to rule out

Slide 24: Summary

Slide 25: Causal diagrams Mediation

Slide 26: Examining mediation

Slide 27: Mediation

Slide 28: Mediation of BMI by glucose levels

Slide 29: Mediation issues

Slide 30: Negative mediation

Slide 31: Summary: mediation

Slide 32: Interpreting results for log-transformed variables

Slide 33: Log-transformed predictors