Measurement Models and CFA; Chi-square and RMSEA

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Measurement Models andCFA Chi-square and RMSEA

• Ulf H. Olsson
• Professor of Statistics

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CFA and ML
k is the number of manifest
variables. If the observed variables
comes from a multivariate normal
distribution, and the model holds in the
population, then
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Testing Exact Fit
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Problems with the chi-square test

• The chi-square tends to be large in large samples
  if the model does not hold
• It is based on the assumption that the model
  holds in the population
• It is assumed that the observed variables comes
  from a multivariate normal distribution
• gt The chi-square test might be to strict, since
  it is based on unreasonable assumptions?!

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Alternative test- Testing Close fit
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How to Use RMSEA

• Use the 90 Confidence interval for EA
• Use The P-value for EA
• RMSEA as a descriptive Measure
• RMSEAlt 0.05 Good Fit
• 0.05 lt RMSEA lt 0.08 Acceptable Fit
• RMSEA gt 0.10 Not Acceptable Fit

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Other Fit Indices

• CN
• RMR
• GFI
• AGFI
• Evaluation of Reliability
• MI Modification Indices

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Model evaluation

• Does the model fit the data
• Chi-square RMSEA and other descriptive measures
• Are the measures reliable?
• Are the paths (coeffisients) significant?
• Is it possible to improve fit?
• Modification indices