We are trying to implement a multiple correspondence analysis (MCA) model. I was looking for metrics to assess the quality of an MCA to evaluate our model. Sadly, I didn’t find much literature about the topic (how to implement an MCA) but I found these 3 papers about factor analysis:
This paper recommends 3 metrics:
- The “factor determinacy index”
- Test for construct replicability
- Explained common variance
This paper gives a more detailed approach on how they implemented their exploratory factor analysis :
- First, it tests the adequacy of the sample and data for factor analysis using the Kaiser-Meyer-Olkin (KMO), Bartlett’s Test of Sphericity, communality, testing for ceiling and floor effects, Test of Sampling Adequacy and more…
- Then it proceeds to test the model using robust diagonally weighted least squares (RDWLS), the Kaiser’s criteria (Eigenvalue ≥1), the scree test, the cumulative variance explained rule (>40%), the robust parallel analysis, the Comparative Fit Index (CFI), the goodness of fit index (GFI), the weighted root mean square residual (WRMR), the root mean square error of approximation (RMSEA), the non-normed fit index (NNFI), the χ2…
This paper distinguishes between
- Exploratory factor analysis that requires: Kaiser’s criterion, scree test the cumulative variance
- Confirmatory Factor Analysis that requires: The chi-square test, Comparative Fit Index, Root Mean Square Error of Approximation
My first question is; are these metrics correct? These papers all relate to factor analysis, so can I really use the metrics they recommend for an MCA? If yes, which metrics, because these papers differ quite a bit?
Second, the SAS paper recommends the use of only 3 metrics for an EFA. But the second paper used many more metrics, even though it implements an EFA. Which one should I trust? Are 3 metrics enough or should I also check the CFI, RMSEA, WRMR, the Chi-square etc…
My final question is about the Chi-square test. My intuition about the Chi-square test is that when we reject the null hypothesis, it means that the variables are not independent. Does this implicitly mean there is a common factor (hence its use in MCA for testing for common factors)? So if I am correct, we need to reject the null hypothesis to test for the existence of at least one factor; is my understanding correct ?
Thank you very much,