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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

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measurement bias detection through factor analysis

Measurement Bias Detection Through Factor Analysis

Barendse, M. T., Oort, F. J. Werner, C. S., Ligtvoet, R., Schermelleh-Engel, K.

defining measurement bias
Defining measurement bias
  • Violation of measurement invariance

Where V is violator

  • If V is grouping variable, then MGFA is suitable
  • Intercepts – uniform bias
  • Factor loadings – non-uniform bias (vary with t)
restricted factor analysis rfa
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
  • Disadvantage of RFA:
  • Not suited for nonuniform bias (interaction term)
approaches for non uniform bias
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
This paper…
  • Compared methods:
  • MGFA
  • RFA with LMS
  • RFA with RSP
  • Measurement bias
  • Uniform
  • Nonuniform
  • Violator
  • Dichotomous
  • Continous
data generation rfa
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
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 design1
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
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
  • Nonuniform: loadings
the rfa lms method
The RFA/LMS method
  • V is modeled as latent variable:
  • Single indicator
  • Fix 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

rfa rsp method
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 & 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
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
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
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
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
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
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
Discussion
  • Nonconvergence occurs with RFA/LMS
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