Model for a latent exogenous variable and all other observed variables : SEM? MR?

Question

Suppose I have one independent variable(IV), one dependent variable(DV), and two control variables(CVs). If they are all observed variables, a multiple regression is the way to see the effect of the IV on the DV.

Then, what if the independent variable is a latent variable measured by several observed indicators? Because there is only one latent variable, it seems like I have only a measurement model, without a structural model. Then, can I say I'm using a SEM to investigate the relationship? or I would be better go with a multiple regression by creating a scale score for the latent variable?

Answer 1

A structural model is a description - you look at a model, and describe some of it as structural and some of it as measurement, but sometimes (as in your case) it's not so clear.

You have a structural model if you want to think about it as a structural model, it's the effects of the predictors on the latent. You can think of the predictors as being latents with one indicator (and no error variance). In the days of the original LISREL you HAD to do it this way.

If you want a name for your model, it's a MIMIC model - a multiple indicator multiple cause. The first link I find when I google "SEM mimic" is lipas.uwasa.fi/~sjp/Teaching/sem/lectures/semc8.pdf, which has a path diagram on page 2.