1. Controlling for Baseline
David A. Kenny

2. Variables Outcome variable Y Baseline measure: Y1
Follow-up measure: Y2
Causal variable X measured at time 1
The question is how to measure the effect of X on Y2 and control for Y1.

3. Equation
Y2 = a + bY1 + bX + e
X and Y1 as predictors

4. Comparable Analyses Analysis of Covariance with Y1 as a covariate.
Control for Y1, but make the outcome change or Y2 – Y1
Residualized change (or gain) score analysis
Regress Y2 on Y1 and compute residuals
Regress X on Y1 and compute residuals
(usually not done)
Regress the first residual on the second
Reduce df by 1. (usually not done)

5. b

6. Measurement Error in Y1
Assume Y1 mediation of the Z (the assignment variable) to Y2.
The measurement error in Y1 attenuates (pushes it toward zero) b.
The estimated b equals br where r is the reliability of the pretest (controlling for X).
Not enough of the “gap” is subtracted.

7. Solutions to the Measurement Error Problem
Known Reliability Solutions
Lord-Porter Correction
Williams & Hazer Strategy
Reliability Estimation Solution
Latent Variable Analysis with Multiple Indicators

8. Known Reliability Reliability or r must be known.
Perhaps use an internal consistency estimate.
Lord-Porter uses the reliability of Y1 controlling for X not the reliability of Y1.
Must adjust r by (r - rXY12)/(1 - rXY12).
Williams & Hazer uses the reliability of Y1 so no adjustment is necessary.

9. Lord-Porter Correction
Reliability or Y1 controlling for X or r must be known.
Regress Y1 on X (and covariates) and compute the predicted score (P) and the residual (R)
Compute: Y1ʹ = P + rR (r is the reliability)
Regress
Y2 on Y1ʹ and X
Hardly ever done, but does not require a SEM program.

10. Williams & Hazer
Error variance of for the T1 latent variable is fixed to sY12(1- r) where r is the known reliability of Y1. b

11. Latent Variable Multiple indicators of latent Y at each time
Set up a Latent Variable Model
Test to see that the loadings are the same at each time. To be safely identified, need at least 3 indicators at each time.
Correlate errors of the same indicator at different times.

12. b

13. More
Technically need only a Time 1 latent variable and no Time 2 latent variable.
If latent variables at two times, do not necessarily need temporally invariant loadings though you do with CSA.