Formative model with an observed dependent variable ("friends")
TITLE: Hodge-Treiman social status modeling DATA: FILE = htmimicn1.dat; TYPE = COVARIANCE; NOBS = 530; VARIABLE: NAMES = church member friends income occup educ; USEV = friends-educ; MODEL: f BY friends*; ! defining the factor; same ! as regressing friends on ! f f@0; f ON income@1 occup educ; OUTPUT: TECH1 STANDARDIZED;
Formative model with a latent dependent variable ("fy")
TITLE: Hodge-Treiman social status modeling DATA: FILE = htmimicn1.dat; TYPE = COVARIANCE; NOBS = 530; VARIABLE: NAMES = church members friends income occup educ; USEV = church-educ; MODEL: fy BY church-friends; f BY fy*; f@0; f ON income@1 occup educ;
I followed the second code segment (for latent DV "fy") and drew the directions of the variable and indicators.
Can I clarify that this is a 2nd-order model, with "fy" as 1st-order factor having income, occup and educ as formative indicators, and "fy" being a reflective latent variable (indicator) of the 2nd-order factor "f"?
Just a quick question. In the Formative model with a latent dependent variable model above you set the path between income and f to one. But if that path is set to one, we cannot conclude anything about the significance of that specific path. My question is; since we cannot say anything about the significance of the path between income and f, how can we conclude that income is a formative indicator of f?
I saw the same model under Indicator Arrows Pointing to a Factor discussion but setting one of the paths between formative indicators and factor to one is not explained there neither.
One of the paths needs to be fixed to a non-zero number for model identification. It does not necessarily need to be income.
Gareth posted on Tuesday, September 04, 2007 - 3:50 am
In the example "Formative model with a latent dependent variable ("fy")", how would I include a covariate (e.g. age) that I hypothesize should be related to either or both of the formative and latent variables?
For example, f ON age implies that age is part of the formative variable, which I don't want:
The residual variance cannot be identified. The formative approach essentially is like forming a factor by a weighted sum of the indicators where the weights are estimated, but measurement error is not parsed out.
I used the input and data from the example above. I only changed the path which is restricted to 1. The standardized estimates for F BY FY are the same in the three cases, but I cannot assess definitely, if the coefficient is significant.
Any nominal variable with more than two categories must be turned into a set of dummy variables. Formative factors are specified using ON. Variables on the right-hand side of ON are covariates in a regression and must be binary (dummy) or continuous as in regular regression.
Hi Linda and thanks for your thought. Letís assume an indentified model where the formative measured latent has 3 cause indicators and is directly connected to 2+ endogenous variables . In order to set a scale for the formative latent one has following options (e.g., Edwards, 2001, p.161): 1. either fix the paths leading to or from the formative construct to 1 (like the examples above with SES - but not necessarily with zeta set to 0) or 2. fix the variance of the construct to unity, thereby standardizing the construct.
I would prefer the second option because I want to test the S.E. for all paths. Frankeet al. (2008) show that the effects in the model change depending on the scaling method (They used lisrel and I have read somewhere that it is also possible with ramon but I was curios about mplus).
You can constrain the variance of the construct to unity using Model Constraint, where you express the variance of the construct in terms of model parameters and the formative indicators' sample covariance matrix and set the construct variance at 1.
Note that in Mplus you can test all paths even if you fix a slope at 1 - this is because Mplus gives you SEs also for the standardized coefficients.
Because different scaling settings lead to different results I think it might be more straightforward to set the construct residual variance at zero, acknowledging that we don't have information on it.
Many thanks! (I will try to model the variance using the model constraint. I was using version 4.1 where the stdxy; option is not implemented; it seems that the consequences of different scalings could be a good case for a new monte carlo study )
Lewina Lee posted on Monday, August 27, 2012 - 3:33 pm
Dear Drs. Muthen,
I'm building an SEM involving a formative indicator (CMAT1) predicting a latent outcome variable (LPOS). When I ran the model specifying one of the composite paths to 1 (CMAT1 on AGE @1 MARRY EDU;) and freely estimating the link between the outcome variable and the composite variable (LPOS on CMAT1;), as in METHOD 1 below, the model would not converge.
However, when I slightly changed the model so that I freely estimated all the composite paths (CMAT1 on AGE MARRY EDU;) but set the link between the composite indicator and the outcome variable to 1 (LPOS ON CMAT1 @1;), as in METHOD 2 below, the model was identified.
I see that METHOD 2 is slightly different than what you have adviced here and in your handout, am I doing anything wrong?
(MARRY is a dichotomous variable, if that may make any difference).
Thank you, Lewina
***METHOD 1*** LPOS by LSAT MCS; CMAT1 by; CMAT1 on AGE @1 MARRY EDU; CMAT1 @0; LPOS on CMAT1;
***METHOD 2*** LPOS by LSAT MCS; CMAT1 by; CMAT1 on AGE MARRY EDU; CMAT1 @0; LPOS on CMAT1 @1;
I wonder if the problem is that lpos is not identified. Try playing with that.
Lewina Lee posted on Tuesday, August 28, 2012 - 8:35 am
Thanks, Linda. Would you consider METHOD 1 & METHOD 2 above equivalent? If METHOD 2 allows the model to converge (despite the slight departure from your suggested approach in the handouts & on this forum), can I go along with the results?