Measurement Bias Detection Through Factor Analysis Barendse, M. T., Oort, F. J. Werner, C. S.,...
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Transcript of Measurement Bias Detection Through Factor Analysis Barendse, M. T., Oort, F. J. Werner, C. S.,...
Measurement Bias Detection Through Factor Analysis
Barendse, M. T., Oort, F. J. Werner, C. S., Ligtvoet, R., Schermelleh-Engel, K.
Defining measurement bias
• Violation of measurement invariance
Where V is violator• If V is grouping variable, then MGFA is suitableIntercepts – uniform biasFactor loadings – non-uniform bias (vary with
t)
Restricted Factor Analysis (RFA)
• Advantages of RFA over MGFA:V can be continuous or discrete, observed or
latentInvestigate measurement bias with multiple Vs.More precise parameter estimates and larger
power• Disadvantage of RFA:Not suited for nonuniform bias (interaction term)
Approaches for non-uniform bias
• RFA with latent moderated structural equations (LMS)
---- Simulation (categorical V) showed at least as good as MGFA
• RFA with random regression coefficients in structural equation modeling (RSP)
---- performance unknown
This paper…• Compared methods:MGFA RFA with LMSRFA with RSP• Measurement biasUniformNonuniform• ViolatorDichotomousContinous
Data generation (RFA)
• True model:
• Uniform bias: . Nonuniform bias: • T and v are bivariate standard normal
distributed with correlation r• e is standard normal distributed• u is null vector
0b 0c
Simulation Design
For continuous V:• Type of bias (only on item 1): No bias (b=c=0), uniform bias(b=0.3,c=0), nonuniform bias (b=0,c=0.3), mixed bias (b=c=0.3)• Relationship between T and V Independent (r=0), dependent (r=0.5)
Simulation Design
For dichotomous V:• V=-1 for group 1 and v=1 for group 2• Model can be rewritten into
• Relationship between T and V: Correlation varies!
.)()(
,)()()2(
)1(
detcabux
detcabux
)1,4.0(~
)1,4.0(~)2(
)1(
NT
NT
The MGFA method
• When v is dichotomous, regular MGFA• When v is continuous, dichotomize x by V• Using chi-square difference test with df=2Uniform : interceptsNonuniform: loadings
The RFA/LMS method
• V is modeled as latent variable:Single indicatorFix residual variance (0.01)Fix factor loading• Three-factor model: T, V, T*V• Robust ML estimation• Chi-square test with S-B correction: : uniform bias : nonuniform bias
0b0c
RFA/RSP method
• Replacing with , where is a random slope.
• Robust ML estimation• Chi-square test with S-B correction: : uniform bias : nonuniform bias
0b
0c
Single & iterative procedures• Single run procedure: test once for each item• Iterative procedure: 1)Locate the item with the largest chi-square
difference2)Free constrains on intercepts and factor
loadings for this item and test others3)Locate the item with the largest chi-sqaure
difference 4)…5)Stops when no significant results exist or half
are detected as biased
Results of MGFA – single run
• Shown in Table 2.• Conclusion:1.better with dichotomous than with
continuous V; 2.non-uniform bias is more difficult to detect
than uniform bias; 3.Type I error inflated.
Results of MGFA – iterative run
• Shown in Table 3.• Conclusion:1.Iterative procedure produces close power as
single run does.2.Iterative procedure produces better
controlled Type I error rate.
Results of RFA/LMS & RFA/RSP - single run
• Shown in Table 4 and Table 5.• Conclusion:1.LMS and RSP produce almost equivalent
results. 2. larger power than MGFA with continuous V.3.More severely inflated Type I error rates
Results of RFA/LMS & RFA/RSP - iterative run
• Shown in Table 6.• Conclusion:1.Power is close to the single run2.Type I error rates are improved
Results of estimation bias - MGFA
• Shown in Table 7.• Conclusion:1.Bias in estimates is small2.Bias in SD is non-ignorable3.Smaller bias in estimates for dichotomous V
(dependent T&V)
Results of estimation bias - RFA
• Shown in Table 8 & 9• Conclusion:1.Similar results for LMS and RSP2.Small bias in estimates3.Non-ignorable bias in SD4.Smaller SE than MGFA5.Smaller bias in estimates than MGFA with
dependent T&V, continuous V.