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Equivalence of msmt model pt3 2Nov12 - Flash (Large) - 20121102 02.45.48PM
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  1. Manual multi-group analysis
  2. Using the manual procedure, replicate this model
  3. What has changed?
  4. Using the manual procedure, replicate this model
  5. What has changed?
  6. So how do we feel about fit?
  7. Statistical tests of invariance
  8. So how do we feel about fit?
  9. Statistical tests of invariance
  10. Slide 28
  11. Statistical tests of invariance
  12. So how do we feel about fit?
  13. Statistical tests of invariance
  14. So how do we feel about fit?
  15. Statistical tests of invariance
  16. Slide 28
  17. The logic of quest for the noninvariant source
  18. Step 1: Test for invariance of factor loadings relative to each subscale, separately
  19. Step 1: Test for invariance of factor loadings relative to each subscale, separately
  20. Slide 31
  21. Slide 32
  22. Slide 33
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Manual multi-group analysis Constrain measurement model parameters to be equal by right-clicking on the parameters. Label the regression weight B/c we’ve already constrained the weight between item 1 and the factor to be “1” Start with L2 (loading of item on its factor) Checking the “All Groups” box is what constrains the 2 panels for the invariance test Use a sensible labeling system 11/2/2012 23 Using the manual procedure, replicate this model 11/2/2012 24 What has changed? 11/2/2012 25 Parameters for Invariance for Measurement model (now) Parameters for Invariance for Configural model (earlier) MCj01377830000[1] Using the manual procedure, replicate this model 11/2/2012 24 What has changed? 11/2/2012 25 Parameters for Invariance for Measurement model (now) Parameters for Invariance for Configural model (earlier) MCj01377830000[1] So how do we feel about fit? 11/2/2012 26 Statistical tests of invariance ΔΧ2: The difference between Χ2 values for the configural and other models in which the equality constraints have been imposed. The difference is distributed with Χ2 df equal to the difference in df. Invariance is supported with ns results Noninvariance is claimed if the ΔΧ2 is significant (and researchers would follow up with tests exploring for which parameters account for the noninvariance. Chi-Square Distribution table. Because Monte Carlo tests have supported the idea that the ΔΧ2 is too strict… ΔCFI: invariance is shown when ΔCFI < .01 11/2/2012 27 So how do we feel about fit? 11/2/2012 26 Statistical tests of invariance ΔΧ2: The difference between Χ2 values for the configural and other models in which the equality constraints have been imposed. The difference is distributed with Χ2 df equal to the difference in df. Invariance is supported with ns results Noninvariance is claimed if the ΔΧ2 is significant (and researchers would follow up with tests exploring for which parameters account for the noninvariance. Chi-Square Distribution table. Because Monte Carlo tests have supported the idea that the ΔΧ2 is too strict… ΔCFI: invariance is shown when ΔCFI < .01 11/2/2012 27 ΔΧ2 value is statistically significant, p < .025, suggesting model is noninvariant ΔCFI < .01, suggesting that the model is completely invariant Discrepant findings. Byrne said the researcher would decide. She felt it instructive to investigate the source of noninvariance. 11/2/2012 28 Statistical tests of invariance ΔΧ2: The difference between Χ2 values for the configural and other models in which the equality constraints have been imposed. The difference is distributed with Χ2 df equal to the difference in df. Invariance is supported with ns results Noninvariance is claimed if the ΔΧ2 is significant (and researchers would follow up with tests exploring for which parameters account for the noninvariance. Chi-Square Distribution table. Because Monte Carlo tests have supported the idea that the ΔΧ2 is too strict… ΔCFI: invariance is shown when ΔCFI < .01 11/2/2012 27 So how do we feel about fit? 11/2/2012 26 Statistical tests of invariance ΔΧ2: The difference between Χ2 values for the configural and other models in which the equality constraints have been imposed. The difference is distributed with Χ2 df equal to the difference in df. Invariance is supported with ns results Noninvariance is claimed if the ΔΧ2 is significant (and researchers would follow up with tests exploring for which parameters account for the noninvariance. Chi-Square Distribution table. Because Monte Carlo tests have supported the idea that the ΔΧ2 is too strict… ΔCFI: invariance is shown when ΔCFI < .01 11/2/2012 27 So how do we feel about fit? 11/2/2012 26 Statistical tests of invariance ΔΧ2: The difference between Χ2 values for the configural and other models in which the equality constraints have been imposed. The difference is distributed with Χ2 df equal to the difference in df. Invariance is supported with ns results Noninvariance is claimed if the ΔΧ2 is significant (and researchers would follow up with tests exploring for which parameters account for the noninvariance. Chi-Square Distribution table. Because Monte Carlo tests have supported the idea that the ΔΧ2 is too strict… ΔCFI: invariance is shown when ΔCFI < .01 11/2/2012 27 ΔΧ2 value is statistically significant, p < .025, suggesting model is noninvariant ΔCFI < .01, suggesting that the model is completely invariant Discrepant findings. Byrne said the researcher would decide. She felt it instructive to investigate the source of noninvariance. 11/2/2012 28 The logic of quest for the noninvariant source Test for invariance of all factor loadings comprising each subscale, separately. If noninvariance at the subscale level is found, Then, test for invariance of each factor loading (relating only to the factor in question), separately As factor-loading parameters are found to be invariant across groups, their equality constraints are maintained, cumulatively. 11/2/2012 29 http://www.netharuka.com/wp-content/uploads/2009/01/monty-python.jpg Step 1: Test for invariance of factor loadings relative to each subscale, separately Good news! ΔΧ2 is NS ΔCFI is NS Now add DP to the mix 11/2/2012 30 Step 1: Test for invariance of factor loadings relative to each subscale, separately Good news! ΔΧ2 is NS ΔCFI is NS Now add DP to the mix 11/2/2012 30 More good news! ΔΧ2 is NS ΔCFI is NS We now know the source of invariance is in PA Because we’ve isolated PA, add one factor loading at a time. 11/2/2012 31 Still ns Keep going to find out which items contribute to noninvariance 11/2/2012 32 11/2/2012 33 Model description Comparison Χ2 df ΔΧ2 Δdf Statistical significance CFI ΔCFI Configural model; no equality constraints imposed ___ 1962.345 330 ___ ___ ___ .919 ___ Measurement model Model A: All factor loadings constrained equal 2A versus 1 1998.257 349 35.912 19 p < .025 .918 .001 Model B: Factor loadings constrained for only EE 2B versus 1 1969,117 339 6.173 9 NS .919 .000 Model C: Factor loadings constrained for EE and DP only 2C versus 1 1977.807 343 15.462 13 NA .918 .001 Model C: Factor loadings constrained for EE, DP and Item 7 (on PA) 2D versus 1 1980.466 344 18.121 14 NS .918 .001 Model C: Factor loadings constrained for EE, DP, and Items 7, 9 (on PA) 2E versus 1 Model C: Factor loadings constrained for EE, DP, and Items 7, 9, 17 (on PA) 2F versus 1 Model C: Factor loadings constrained for EE, DP, and Items 7, 9, 18 (on PA) 2G versus 1 Model C: Factor loadings constrained for EE, DP, and Items 7, 9, 19 (on PA) 2H versus 1 Model C: Factor loadings constrained for EE, DP, and Items 7, 9, 19, 21 (on PA) 2I versus 1 You can just type your answers right into this table! (please take the time to do this completely; think of it as your homework )