Thank you for reading this question.
In my data the age was captured in categories (e.g., "under 20 years", "21-30 years"). Since those categories lead to some kind of inaccuracy I'm not sure if "age" has to be modeled as manifest variable with or without a disturbance term. The point is: Does measuring in categories produce an error which is modeled in SEM or not?
Moreover, if "age" is modeled as a manifest variable it belongs to the measurement model but since my hypotheses include "age" doesn't it also belong to the structural model?
Thank you for your help!
Wouldn't it be a solution to run a multi-group analysis using age groups for grouping and compare the effects across them instead of including age as variable in one model? (I'm not familiar with amos, but for me it looks like age is treated like continious even it's jsut ordered categorical in this case?); beside the advantage of testing invariance across the age groups, in this model you could test, if the direct and indirect effect of you latents are the same in the different groups; in addition this would fix your problem with the error term.
Best
I am not sure how you intend to incorporate age (i.e. two categories) in your CFA or structural model. As I read many papers using SEM, age and other demographic variables are generally used as mediating/moderating variables in multi-group analysis (where those variables can be part of your hypotheses). You may consult this paper:
Byrne, B. M. (2004). Testing for multigroup invariance using AMOS graphics: A road less traveled. Structural Equation Modeling, 11(2), 272-300.
Thank you! I will read it.
Sorry, if I wasn't clear enough. Age is supposed to determine three latent variables and thus work as a moderator for the relations between them.
"Age is supposed to determine three latent variables"...is confusing to me. However, if age is used to test its moderating effect on the relations between latent variables, then the paper I suggested provides a step-by-step guide to perform the analysis in AMOS.
I attached the model. The point is: is the disturbance term e4 necessary when age has been measured in categories, or not? Based on literature I think it has to be deleted.
Wouldn't it be a solution to run a multi-group analysis using age groups for grouping and compare the effects across them instead of including age as variable in one model? (I'm not familiar with amos, but for me it looks like age is treated like continious even it's jsut ordered categorical in this case?); beside the advantage of testing invariance across the age groups, in this model you could test, if the direct and indirect effect of you latents are the same in the different groups; in addition this would fix your problem with the error term.
Best
@ Khan Taufique: Ok, perfect. Thank you.
(My idea was the error term has to be there because for example someone who is 22 will be shown in the data to be 21-30 - which is inaccurate.)
@ Manuel Heinrich: Thank you! I just had the same idea but wasn't sure it will make sense - will try it.
What Manuel suggests is exactly what I tried to mean in my first answer. AMOS is just one of many CB-SEM software that can be used to do this kind of multi-group analysis.
error term is only belong to the endogenous construct. In your case, you have to delete e4 at age variable. You still can adapt categorical variable and continuos variable simultaneously using SEM. But i prefer Mplus software since the estimator (Mean and Variance adjusted weighted least square) used can treat the categorical variable.
Ok, thank you. Now I just have to find out how to tranfer AMOS to Mplus ;)
Hi Anja,
Manuels proposal would require that age functions as a moderator (i.e., the model coefficients are different for different age groups). If this is how you regard age, than that's the way to go.
If, however, age is a predictor or contol variable, you have to incorporate it in your model. Your question in this regard touches two issues: a) maniftest vs. latent and b) categorical variables
a) Yes, age is a latent variable, because your MEASURE of age is just an error-prone indicator. That is, you should set up a single-indicator model with the loading fixed to one (this is done as a default), and a fixed error. Normally, people fix the error to 0, hence, implying that the measurement error is zero. This procedure leads to EQUATING the measure with the latent variable. An alternative (which is proposed by Leslie Hayduk) is to fix the error to a reasonable value. As age should be almost perfectly measured, the difference may be neglible, but nonetheless more thoughful. Perhaps 2% part of the variance.
b) There is an easy and a more sophisticated version. The easy is: if the measure as almost equal intervals, use it directly. If not (the sophisticated one), use estimators such as DWLS or WLSMV. I don't know however, if AMOS is able to do this.
I would strongly recommend switching to lavaan (www.lavaan.org) which is a R package. I have written a small book in German language that introduces lavaan to newbies and also treats the latent variable and measurement theory implied in SEM.
Best,
Holger
Hi Holger,
thank you for your answer. I think I understand the problem way better now.
If I got it right this time, "age" is a predictor in my model for 3 latent variables. I checked it and no, of course AMOS does not provide those estimators. Think I have to switch to lavaan or Mplus. Hope this is something I can manage within 3 weeks.
Best wishes,
Anja
Hi, no worries. Write me an email if you have problems!
Best,
Holger
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