controlling for baseline david a. kenny december 15, 2013
TRANSCRIPT
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Controlling for Baseline
David A. Kenny
December 15, 2013
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VariablesOutcome 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.
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3
Equation
Y2 = a + Y1 + bX + e
X and Y1 as predictors
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Comparable AnalysesAnalysis 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)
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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) .
The estimated equals where is the reliability of the pretest (controlling for X).
Not enough of the “gap” is subtracted.
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Solutions to the Measurement Error Problem
Known Reliability Solutions
Lord-Porter Correction
Williams & Hazer Strategy
Reliability Estimation Solution
Latent Variable Analysis with Multiple Indicators
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Known ReliabilityReliability or 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 by (- rXY12)/(1 - rXY1
2).
Williams & Hazer uses the reliability of Y1 so no adjustment is necessary.
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Lord-Porter CorrectionReliability or Y1 controlling for X or must
be known.
Regress Y1 on X (and covariates) and compute the predicted score (P) and the residual (R)
Compute: Y1ʹ = P + R (is the reliability)
Regress
Y2 on Y1ʹ and X
Hardly ever done, but does not require a SEM program.
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Williams & HazerError variance of for the T1 latent variable is
fixed to sY12(1- where is the known
reliability of Y1.
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Latent VariableMultiple 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.
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MoreTechnically 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.