[Lisrel] using observed variable as outcome & latent var. as predictors

[Tool7]

Hi all,
this time just a quick question:
I'd like to perform SEM in Lisrel with obs. var => lat. var => obs. var. (observed variable influences latent variable which influences other observed variable).
Is this possible? Or can I only use observed variable for the prediction of a latent variable (and would therefore have to do something like obs. var => lat. var => lat var)?
Thanks a lot for your help!

[wandatheavenger]

I can't tell from this whether your first latent variable is indicated by your observed variable or is a separate construct with a hypothesized causal relationship. Either way, I would mirror your final outcome variable up to a latent by simply specifying its loading to 1.0. This won't mess up your analyses at all and will avoid the issue of then having the two variables as indicators of a single latent rather than your actual hypothesized structure (though the two methods might just end up equivalent, I'm not in a position to test it currently).
If the second is the case, I would mirror both the outcome observed variable and predictor variable to latents with a 1.0 loading. This lets you specify all of your path coefficients on the beta and gamma matrices and makes things generally more easy to interpret.

[Tool7]

Thanks a lot for the reply!
I'm not sure whether I got this right, I therefore just specify things quickly.
The model I wanna test is:
x1 (obs variablen) => Y1 (lat. variablen, based on x2, x3, x4) => x5 (obs variable). It's as you said, I'm interested in testing the paths from x1 to Y1 and from Y1 to x5.

With "specifying the loading of the final outcome variable to 1.0.", so x5, do you mean setting the variance = 1 (ie. command: Set variance of x5 equals to 1)? I'm not sure what you mean with "loading". I tried to set the variance of x5 = 1, but it's as you said, and I'm just aware of this now, that SEM interpretes x5 as an indicator of Y1 and does not take the "path-part" from Y1 to x5 into account (the Structural Equations just show Y1=x2, x3, x4 and not x5 = Y1...etc.).

Thanks for your time, I really appreciate it!

[wandatheavenger]

A loading is the path between an indicator variable and its associated latent variable. When fixing paths like this, you need to assign values to both the path itself and the error variance of the indicator, which is determined directly by the path. To do this, I would use the VA (Value Assign) command for, in the case of X1, LX(1,1) to fix that loading to 1. So the command would be as follows: VA 1.0 LX(1,1). To fix the error variance, I would either just fix the entire Theta Epsilon matrix with TE=FI in the MO line. Alternately, VA 0.0 TE(1,1) would do the same thing if you prefer (LISREL has a million ways to do the same thing).

What you will end up doing, then, is testing Ksi1=>Eta1=>Eta2 where Ksi1 has x1 as its only indicator and Eta2 has only x5 as its only indicator. Because these latent variables are exactly the same as your observed variables, the coefficients will be the same. And because of all of the normally estimated terms you are assigning values to, your degrees of freedom will be equal.

As a note, make sure you're talking about your variables correctly. In your model, you will have only one X variable (which you refer to as x1). The other observed variables are Y variables to LISREL, as they will be associated with endogenous latent terms. Out of curiosity, are you using PRELIS or SIMPLIS to do this or the base program? If you're using the base program, I'd strongly suggest you look into specifying models using pattern matrices, as these make not only the initial specification but also debugging a breeze as long as the model isn't too big.

[Tool7]

Thank you again very much for your help! I'm pretty busy today with other work, and will have a close look at your response during the weekend.
Maybe for your understanding: I did take an introductory and advanced course in SEM (no need to say where), but did never encounter the terms Ksi, Eta, etc there, which sure is disappointing, especially considering it now that these term are part of the general understanding of SEM. I did find useful introductory information about these terms now, and want to understand these, before posting a further reply.
As always, one learns most once he's actually doing it oneself. But I really appreciate your information and will give you feedback asap.
Thanks again!

[Tool7]

Hi, thanks again for your input! I’ve gotten myself some information with regards to the different matrices, etc. and understand what you mean with talking about the variables correctly, using the commands VA, TE, etc.
So far I used other commands, so I tried to “translate” your proposition to what I’m used to (at this stage, it’s a little easier for me to understand & to see, what I do).
I did the following:

Observed variables:
x1 y1 y2 y3 y4
Correlation matrix :
…
Sample size: 311
Latent variables: Ksi1 Eta1 Eta2
Relationships:
x1 = 1* Ksi1
y1 = 1* Eta1
y2 = Eta1
y3 = POS Eta1
y4 = Eta2
Eta1 = Ksi1
Eta2= Eta1
Set variance of Eta2 equal to zero.
Path diagram
End of problem

Running the program worked, and the graph actually did show the latent variables, structure equations were also in the output.
However, I got this: “W_A_R_N_I_N_G: Matrix above is not positive definite” referring to the “Covariance Matrix of Latent Variables”. Is this the consequence of setting the variance equals to zero or is there something else to worry about?

I checked and got this information on the web:
“Sometimes researchers specify zero elements on the diagonals of Theta-delta or Theta-epsilon…single measures often lead to identification problems, and analysts may leave the parameter fixed at zero by default. If a diagonal element is fixed to zero, then the matrix will be not positive definite. However, since this is precisely what the researcher intended to do, there is no cause for alarm. The only problem is that these values may cause the solution to fail an admissibility check, which may lead to premature termination of the iterative estimation process. In such cases, it is merely a matter of disabling the admissibility check. In LISREL, for example, this is done by adding AD=OFF to the Output line.”
I did this with “Set AD=OFF”, Lisrel runs well, the same Warning message, however, appears again. Can I just ignore this or does this mean that there are other causes for the non-positive definite matrix?
Thanks a lot!