Measurement Bias Detection Through Factor Analysis

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# Measurement Bias Detection Through Factor Analysis - PowerPoint PPT Presentation

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 suitable Intercepts – uniform bias

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### 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 suitable
• Intercepts – uniform bias
Restricted Factor Analysis (RFA)
• Advantages of RFA over MGFA:
• V can be continuous or discrete, observed or latent
• Investigate measurement bias with multiple Vs.
• More precise parameter estimates and larger power
• 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 LMS
• RFA with RSP
• Measurement bias
• Uniform
• Nonuniform
• Violator
• Dichotomous
• Continous
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
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!

The MGFA method
• When v is dichotomous, regular MGFA
• When v is continuous, dichotomize x by V
• Using chi-square difference test with df=2
• Uniform : intercepts
The RFA/LMS method
• V is modeled as latent variable:
• Single indicator
• Fix residual variance (0.01)
• Three-factor model: T, V, T*V
• Robust ML estimation
• Chi-square test with S-B correction:

: uniform bias

: nonuniform bias

RFA/RSP method
• Replacing with , where is a random slope.
• Robust ML estimation
• Chi-square test with S-B correction:

: uniform bias

: nonuniform bias

Single & iterative procedures
• Single run procedure: test once for each item
• Iterative procedure:
• Locate the item with the largest chi-square difference
• Free constrains on intercepts and factor loadings for this item and test others
• Locate the item with the largest chi-sqaure difference
• Stops when no significant results exist or half are detected as biased
Results of MGFA – single run
• Shown in Table 2.
• Conclusion:
• better with dichotomous than with continuous V;
• non-uniform bias is more difficult to detect than uniform bias;
• Type I error inflated.
Results of MGFA – iterative run
• Shown in Table 3.
• Conclusion:
• Iterative procedure produces close power as single run does.
• 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:
• LMS and RSP produce almost equivalent results.
• larger power than MGFA with continuous V.
• More severely inflated Type I error rates
Results of RFA/LMS & RFA/RSP - iterative run
• Shown in Table 6.
• Conclusion:
• Power is close to the single run
• Type I error rates are improved
Results of estimation bias - MGFA
• Shown in Table 7.
• Conclusion:
• Bias in estimates is small
• Bias in SD is non-ignorable
• Smaller bias in estimates for dichotomous V (dependent T&V)
Results of estimation bias - RFA
• Shown in Table 8 & 9
• Conclusion:
• Similar results for LMS and RSP
• Small bias in estimates
• Non-ignorable bias in SD
• Smaller SE than MGFA
• Smaller bias in estimates than MGFA with dependent T&V, continuous V.
Discussion
• Nonconvergence occurs with RFA/LMS