1

I have done Principal Component Analysis for a scale comprising multiple latent variables. Is it necessary to do Confirmatory Factor Analysis before doing Structure Equation Modelling?

Nabeela
  • 13
  • 3

2 Answers2

1

Discussions of whether you should use PCA to model exploratory latent variables (or not) aside, the short answer here is: typically, yes. PCA has given you a data-driven exploratory model, but in advance of modelling the structural associations between latent variables, editors, reviewers, and readers will typically want to see that the measurement model the data "gave" you replicates, when you deliberately fit it (with a discriminating pattern of factor loadings) in a separate sample.

There are a couple of notable exceptions to this standard practice, the first of which (ESEM) might be something for you to consider:

Exploratory Structural Equation Modeling

Want to model the structural parameters of exploratory latent constructs? ESEM (Asparouohov & Muthén, 2009) may be for you! However, ESEM uses common factor measurement models--not PCA models as you have done. It's also worth noting that at this point, accessible software capable of ESEM is relegated to Mplus, and to a more limited extent, Revelle's psyc package for R. There's also a gap in the simulation literature with respect to ESEM models; whereas much is known about evaluating the fit of traditional SEM/CFA models, ESEM models (which are deliberately less parsimonious) have received little attention.

Parcelling

At some point in time, a measurement model may be so widely replicated that it no longer seems worth fitting the full measurement model in all of its complexity (which can degrade model fit). Researchers in this position may wish to parcel their indicators (see Little et al., 2002 for a discussion), so that their latent variables are locally just-identified, and thereby, their measurement does not substantially detract from the fit of the overall model. Instead, overall model fit is primarily driven by the adequacy of the representation of the structural associations between latent variables.

In your case, however, parcelling would not be appropriate because your measurement model is still entirely untested--it hasn't been fit with a confirmatory approach even once, so parcelling would be very questionable. Further, parcelling isn't a practice without its critics--even under the strict conditions I've characterized (and described in Little et al. 2002). I'd recommend those interested in the parceling debate to read the recent review by Sterba and Rights (2017), but in a nutshell, they take issue with the extent to which how a researcher decides to combine indicators in parcels can influence model fit, tests of structural parameters, etc.

References

Asparouhov, T., & Muthén, B. (2009). Exploratory structural equation modeling. Structural Equation Modeling, 16, 397-438. doi: 10.1080/10705510903008204

Little, T.D., Cunningham, W. A., Shahar, G., & Widaman, K. F. (2002). To parcel or not to parcel: Exploring the question, weighing the merits. Structural Equation Modeling, 9, 151-173. doi: 10.1207/S15328007SEM0902_1

Sterba, S. K., & Rights, J. D. (2017). Effects of parcelling on model selection: Parcel-allocation variability in model ranking. Psychological Methods, 22, 47-68. doi: 10.1037/met0000067

jsakaluk
  • 5,006
  • 1
  • 20
  • 45
  • Thanks for rich information. I have tested measurement model by CFA. Goodness of fit thresholds were met through several indicators like df, chi-square, probability, CFI RESEA GFI etc – Nabeela Jul 17 '17 at 19:16
  • convergent and discriminent validity does not reached at minimum required threshold in Amos. Now what should i do with these variables – Nabeela Jul 17 '17 at 19:18
  • Re: "I have tested measurement model by CFA", have you done this in a new sample of data? – jsakaluk Jul 17 '17 at 19:21
  • convergent is however permissible but discriminent is too low. It may be because the factors are related to almost same construct. there are different types of Thinking errors in scale – Nabeela Jul 17 '17 at 19:21
  • No. It was same data. for which PCA was done – Nabeela Jul 17 '17 at 19:22
  • it is newly developed tool. "first time administered" – Nabeela Jul 17 '17 at 19:23
  • 1
    Ah. Well, you need a new sample to do the CFA. Running the confirmatory model on the same data that generated the Exploratory model is inadvisable. Think of it this way: the data told you "here's what the factor structure might look like", and then you went and ran a model asking the very same data, "Does the factor structure look like this?". Thus, your current CFA is not particularly informative. – jsakaluk Jul 17 '17 at 19:25
  • Also @Nabeela (since you are new to the site)if you found my original answer helpful, you might consider up-voting it (via the up arrow next to it) and accepting it (via the check mark next to it). – jsakaluk Jul 17 '17 at 19:29
0

Yes, confirmatory factor analysis must be done for the internal consistency of the paragraphs of the questionnaire, and to also indicate what paragraphs negatively affected the scale.

Karolis Koncevičius
  • 4,282
  • 7
  • 30
  • 47
numsmk
  • 1