bmuthen posted on Friday, October 25, 2002 - 11:39 pm
In some applications it may be more natural to let a factor be defined as being influenced by indicators, rather than influencing the indicators. An example is SES. Mplus handles this modeling by the following model statements.
Anonymous posted on Wednesday, June 09, 2004 - 7:09 pm
Would you elaborate on the substantive meaning of this parameterization ?
If the latent variable (LV) "causes" the indicators, isn't the interpretation of this particular parameterization that the correlation between the indicators is rendered spurious in the presence of the "true cause" of the indicators, LV. Examples of the this type of model would be: intelligence, conservativism, etc.
I'm guessing the the model you're suggesting suggests that the LV is "caused" by the indicators, but that correlation between the indicators is still permitted ? Is this correct. I fail to see the connection between this parameterization and (in your example) SES.
bmuthen posted on Thursday, June 10, 2004 - 5:44 pm
Yes, having the arrows point to a factor instead of from a factor can be thought of as the LV being "caused" by the indicators and correlations between the indicators are not modeled, but are free. The interpretation in the context of SES might be that a person's education, income, and job status produce the person's SES (the LV). A regular factor analysis model would in contrast say that a person has a latent SES (an inborn need?, a life style requirement?) that influences the education and job he/she gets. The substantive theory would guide the choice. As a layman, I think the former view is a bit more compelling in the context of SES, although I can imagine a complex combination of the two formulations perhaps being closer to the truth.
In this case, is it true that the "f@0;" from above is only required for identification if you only have 1 y variable in the by statement? Jarvis, MacKenzie, and Podsakoff talk about being able to uniquely estimate the variance in f if F is a predictor of 2 or more latent variables.
bmuthen posted on Friday, November 05, 2004 - 1:19 pm
Hmmm, I didn't think the residual variance of the formative factor f (f predicted by x) would be identified even if f predicts a second f, f2 say, with f2 having a residual variance and multiple indicators (y say). I am not familiar with the paper you mention. Seems like there is no information for the f residual variance since the x covariances are already saturated by this model, the x-y covariances don't involve that parameter, and although the y covariances identify only the variance of f2 it cannot be separated into the f2 and f residual variances. But maybe I am missing something - you can try it out and see what Mplus says.
What would be a suitable way of getting factor scores for the formative factor? Would it be fine to save the factor scores as you do with factors with reflective indicators? Any suggestions would be appreciated.
bmuthen posted on Monday, November 15, 2004 - 6:58 pm
Yes, factor scores can be obtained for any latent variable in the Mplus model.
In reply to the previous discussion, yes, you can estimate the variance of the emergent variable. The theory and math behind this is discussed fairly extensively in a 1993 Psych Bulletin paper by MacCallum and Browne as well as in an as of yet unpublished paper by Bollen and Davis, "Causal indicator models: identification, estimation, and testing." The Bollen and Davis paper is especially useful for showing the necissary conditions for the identification of these models. One of those conditions is that the emergent variable must emit two paths.
hai hong li posted on Thursday, September 28, 2006 - 8:17 pm
I am a new user of Mplus. I am trying to incorporate causal indicators (formative measures - not MIMIC) into a sem model. It's not clear how to write the code for this kind of problems although I've gone through all related discussions in the discussion board.
Suppose for example we have a model with six measured variables, x1-x6, x1-x3 are causal (formative) indicators of F1, and x4-x6 are reflective indicators of F2, and there is a path from F1 to F2. Could you help me with the coding of such a model?
1. Yes. See Examples in Chapter 5 and the Topic 1 course handout.
2. The model implied covariances for the binary indicators can be obtained by asking for RESIDUAL in the OUTPUT command.
3. I think these are part of Sample Statistics. This is because when there are covariates in the model, the sample statistics used for model estimation for WLSMV are the threholds, probit regression coefficients, and residual correlations.
Erin P posted on Tuesday, January 24, 2012 - 12:45 am
I'm having a hard time specifying two models. I'm not sure that all of my variances are specified properly
Any suggestions would be appreciated.
MODEL 1 (induced variable model): F1 ON y1-y3; F2 BY y4; F1 BY F2; y1 WITH y2 y3; y2 WITH y3; F1@0; y4@0;
MODEL 2 (common factor model): F1 BY y1-y3; F2 BY y4@1; F2 ON F1; y4@0;
I am running a formative factor model with three indicators pointing to the latent construct. I am using the categorical function and complex sampling options. I have missing data and am using the default, FIML. I have been trying to figure out what the default estimation is for this model? I have looked in the manual but cannot find it. Also, is this the appropriate estimation method for this kind of model? Thank you.
Weight = NANALWT; Stratification=Stratum; Subpopulation = cbclpop=1; missing are all .;
ANALYSIS: TYPE=COMPLEX; interations=50000; PARAMETERIZATION=Theta; MODEL: par_imp by; par_imp on mhprob@1 drugs alcohol; par_imp@o; alcohol drugs mhprob on poverty; total on pds_at2r par_imp pds_ng2r; pds_at2r pds_ng2r on par_imp ; alcohol with drugs; mhprob with alcohol; mhprob with drugs;
Thank you Dr. Muthen. I have one more follow up question. With a WLSMV estimation, i get a warning.
Chi-sqaure cannot be used for chi-square difference testing in a regular way. My understanding of difftest is that this is used in testing multigroup models, which I am not conducting. I am on the other hand, running a formative factor model (please see message above for code). Should the chi-square value not interpreted?