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Confirmatory factor analysis GHQ 12. From Shevlin/Adamson 2005:

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Presentation on theme: "Confirmatory factor analysis GHQ 12. From Shevlin/Adamson 2005:"— Presentation transcript:

1 Confirmatory factor analysis GHQ 12

2

3 From Shevlin/Adamson 2005:

4 Model 2 – 2 factor Politi et al, F1F2

5 Specifying the model F F2 F1F2 F1 by ghq02* ghq05 ghq06 ghq09 ghq10 ghq11 ghq12; F2 by ghq01* ghq03 ghq04 ghq07 ghq08 ghq12; F1 with F2;

6 Mplus syntax for ‘model 2’ Variable: Names are ghq01 ghq02 ghq03 ghq04 ghq05 ghq06 ghq07 ghq08 ghq09 ghq10 ghq11 ghq12 f1 id; Missing are all (-9999) ; usevariables = ghq01 ghq03 ghq05 ghq07 ghq09 ghq11 ghq02 ghq04 ghq06 ghq08 ghq10 ghq12; categorical = ghq01 ghq03 ghq05 ghq07 ghq09 ghq11 ghq02 ghq04 ghq06 ghq08 ghq10 ghq12; idvariable = id; Analysis: estimator = WLSMV; model: F1 by ghq02* ghq05 ghq06 ghq09 ghq10 ghq11 ghq12; F2 by ghq01* ghq03 ghq04 ghq07 ghq08 ghq12; F1 with F2;

7 TESTS OF MODEL FIT Chi-Square Test of Model Fit Value * Degrees of Freedom 32** P-Value * The chi-square value for MLM, MLMV, MLR, ULSMV, WLSM and WLSMV cannot be used for chi-Square difference tests. MLM, MLR and WLSM chi-square difference testing is described in the Mplus Technical Appendices at See chi-square difference testing in the index of the Mplus User's Guide. ** The degrees of freedom for MLMV, ULSMV and WLSMV are estimated according to a formula given in the Mplus Technical Appendices at See degrees of freedom in the index of the Mplus User's Guide. Chi-Square Test of Model Fit for the Baseline Model Value Degrees of Freedom 13 P-Value CFI/TLI CFI TLI Number of Free Parameters 50 RMSEA (Root Mean Square Error Of Approximation) Estimate WRMR (Weighted Root Mean Square Residual) Value 2.067

8 Results for ‘model 2’ MODEL RESULTS Two-Tailed Estimate S.E. Est./S.E. P-Value F1 BY GHQ GHQ GHQ GHQ GHQ GHQ GHQ F2 BY GHQ GHQ GHQ GHQ GHQ GHQ F1 WITH F

9 Results for ‘model 2’ Two-Tailed Estimate S.E. Est./S.E. P-Value Thresholds GHQ01$ GHQ01$ GHQ01$ GHQ03$ GHQ03$ GHQ03$ GHQ05$ GHQ05$ GHQ05$ GHQ07$ GHQ12$ GHQ12$ GHQ12$ Variances F F

10 Graphs

11 Distribution of factors

12 Scatterplot of factors

13 Model 1Model 2Model 3Model 4Model 5Model 6 χ² test of Model Fit Value * * * * * DF33**32**33**32**33** P-Value< χ² test of Model Fit (Baseline Model) Value DF13 P-Value< CFI TLI # Params RMSEA WRMR

14 What happened to model 4? WARNING: THE RESIDUAL COVARIANCE MATRIX (THETA) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR AN OBSERVED VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO OBSERVED VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO OBSERVED VARIABLES. CHECK THE RESULTS SECTION FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE GHQ03. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THE MODEL MAY NOT BE IDENTIFIED. CHECK YOUR MODEL. PROBLEM INVOLVING PARAMETER 39. THE CONDITION NUMBER IS 0.221D-15. FACTOR SCORES WILL NOT BE COMPUTED DUE TO NONCONVERGENCE OR NONIDENTIFIED MODEL.

15 Use tech1 to establish what para-39 is LAMBDA F1 F2 ________ ________ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ GHQ Lambda is the matrix of factor loadings There is a problem with the loading of GHQ03 on the second factor

16 You could actually tell this from the output: MODEL RESULTS Estimate F1 BY GHQ GHQ GHQ GHQ GHQ GHQ GHQ F2 BY GHQ GHQ GHQ GHQ GHQ GHQ F1 WITH F This problem stems from the fact that the third item is loading on both factors. This does not always lead to problems (see other models fitted here) but in this case it has done. It does not appear possible to replicate this model using the current dataset If the aim was not replication, but merely to test one’s own theories, then removing the loading from one of the factors would solve the problem. Depending on your theories on the underlying mechanism, this may or may not be desirable.

17 Conclusions Based on the level of CFI/TLI, the fit of models 2, 3 and 6 was acceptable (>0.95), however the RMSEA values were too high (> 0.1) If one were forced to choose between these 3 models, one could argue that model 3 is superior due to parsimony (fewer parameters) and better separation of factors (no double loading) It is interesting to note that model 3 has the simplest interpretation (pos/neg item wording) whilst model 2 which is subtly different has been given a more theoretical interpretation. Researchers from different disciplines may interpret the same factor model in different ways – e.g. to support their own theories. It’s a good idea to establish whether you agree with this interpretation.


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