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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.

• Violation of measurement invariance

Where V is violator

• If V is grouping variable, then MGFA is suitable

• Intercepts – uniform bias

• 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)

• 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

• Compared methods:

• MGFA

• RFA with LMS

• RFA with RSP

• Measurement bias

• Uniform

• Nonuniform

• Violator

• Dichotomous

• Continous

• 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

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)

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!

• When v is dichotomous, regular MGFA

• When v is continuous, dichotomize x by V

• Using chi-square difference test with df=2

• Uniform : intercepts

• 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

• Replacing with , where is a random slope.

• Robust ML estimation

• Chi-square test with S-B correction:

: uniform bias

: nonuniform bias

• 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

• 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.

• Shown in Table 3.

• Conclusion:

• Iterative procedure produces close power as single run does.

• Iterative procedure produces better controlled Type I error rate.

• 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

• Shown in Table 6.

• Conclusion:

• Power is close to the single run

• Type I error rates are improved

• 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)

• 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.

• Nonconvergence occurs with RFA/LMS

• Summary: