Announcement

Collapse
No announcement yet.
X
  • Filter
  • Time
  • Show
Clear All
new posts

  • Bi-factor Model in Stata

    Hello,

    I have used the SEM builder to specify a Bi-factor model in Stata with two latent factors - one factor has three indicators and the other factor has four indicators and a general factor where all the indicators of the two factors map onto the general factor. The results returned = not concave. This suggests that the model is unidentified, (am I correct?)

    I have two additional questions:

    1) Can I successfully run a bifactor model in Stata and can anyone point me to some general information which will allow me to locate specific goodness of fit indices and factor rotation relevant to Stata?

    2) Any ideas on why the model does not run? (and perhaps provide some supporting information to help clarify the problem.

    Many thanks in advance for any responses.
    Gill

  • #2
    Originally posted by Gill Francis View Post
    This suggests that the model is unidentified, (am I correct?)
    Put a limit, say 5, on the number of iterations via the -iterate()- option and look at the footnotes. See if there is something like "Note: The LR test of model vs. saturated is not reported because the fitted model is not full rank."

    Can I successfully run a bifactor model in Stata and can anyone point me to some general information which will allow me to locate specific goodness of fit indices and factor rotation relevant to Stata?
    I dont' know what a Bi-factor model is, but I don't see any problem in principle for a straightforward confirmatory factor analysis model with two latent factors having three to four indicator variables each and a covariance between the latent factors, but spare on the indicator variable covariances and crossloadings.

    I'm not sure whether factor rotation is relevant to confirmatory factor analysis, at all, let alone to CFA in Stata. (Although MPlus now has some kind of hybrid EFA/CFA thing that I've never looked into--maybe that's what you're talking about?)

    Any ideas on why the model does not run? (and perhaps provide some supporting information to help clarify the problem.
    Most textbooks on SEM that I've seen have a chapter on identifiability and how to guestimate whether a model is identified.

    Comment


    • #3
      To add to Joseph's helpful comments, note that you can have a theoretically identified model but get "not concave" results. Note also, not concave is ok if later iterations don't include it. Read the SEM documentation - it includes fit statistics etc.

      Comment


      • #4
        Originally posted by Joseph Coveney View Post
        Put a limit, say 5, on the number of iterations via the -iterate()- option and look at the footnotes. See if there is something like "Note: The LR test of model vs. saturated is not reported because the fitted model is not full rank."

        I dont' know what a Bi-factor model is, but I don't see any problem in principle for a straightforward confirmatory factor analysis model with two latent factors having three to four indicator variables each and a covariance between the latent factors, but spare on the indicator variable covariances and crossloadings.

        I'm not sure whether factor rotation is relevant to confirmatory factor analysis, at all, let alone to CFA in Stata. (Although MPlus now has some kind of hybrid EFA/CFA thing that I've never looked into--maybe that's what you're talking about?)

        Most textbooks on SEM that I've seen have a chapter on identifiability and how to guestimate whether a model is identified.
        I apologize if the image below is too big, but this is a bifactor model in SEM diagram format. Imagine the 9 blue boxes are each a question on depression (the Patient Health Questionnaire, or PHQ-9, specifically). The red ovals are the latent variables - the general factor is depression, and there are two sub-factors (I think there's a technical term for them, but I forget it right now). You'll note that there's no covariance between any latent factor - that's a feature of the bifactor model, not me forgetting to draw them. The general factor is orthogonal to the sub-factors.

        I believe Joseph is right that factor rotation isn't relevant in confirmatory SEM, i.e. it's a concept that doesn't apply. Perhaps Gill was asking about the correlation structure of the latent variables. As stated above, in the standard bifactor model, I believe all latent variables are orthogonal (i.e. covariance constrained to zero). Could you estimate a covariance between just the two group factors? Maybe, but I think that's no longer the standard bifactor model.

        Last, I assume Gill is using linear SEM. I am not as familiar with linear SEM, but I believe the usual fit indices reported in -estat gof- apply no matter what the model structure (ie. unidimensional, bifactor, or any other structure).


        Please use the code delimiters to show code and results - use the # button on the formatting toolbar, between the " (double quote) and <> buttons.

        Please use the command -dataex- to show a representative sample of data; it is installed already if you have Stata 14.2 or 15.1, else you can install it by typing

        Code:
        ssc install dataex

        Comment


        • #5
          Thank you, Weiwen, for the explanation. On that impetus, I searched the list's archives and found this. Bifactor models were (and still are) fitted from exploratory factor analysis, and so Gill's question about factor rotation might have stemmed from encountering that somewhere.

          I get the impression that, although it is certainly possible with only two (Weiwen's example shows this), things work out more smoothly with at least three "specific" ("group") factors. In order to learn a little more about how they work, I've been simulating data for bifactor modeling and with only two specific factors (in addition to the general factor) and 500 observations, -sem- converged when, for example, each of the two factors has six indicator variables, but it seemed fragile: variance for one of the two specific latent factors was not accurately estimated, and using the same dataset -sem- would not converge after limiting the number indicator variables for the two specific factors to four and five.

          The didactic literature makes a point of comparing a bifactor model to the corresponding second-order CFA, and for that you'll need at least three first-order latent factors to identify the second-order factor (or to impose equality constraints on the second-order factor loadings).

          Comment

          Working...
          X