# Structural Equation Model - Construct Operationalization

I'm building a Structural Equation Model and I'm trying to operationalize my Dependent Variable, the construct of "Investor Behaviour" (= whether or not an investor is willing to invest in a startup). Would it be possibile to operationalize this construct by using as variables 8 different scenarios, obtained via fractional factor design (each one of them made of the following three attributes, combined differently: expert/non expert team, tested/not tested product and tested/not tested market fit)? For each scenario, I will ask to the investor if he/she is willing to invest or not, on a likert scale from 1 to 7?

For instance, one scenario would be: 1) Are you willing to invest in a startup wth a non expert team, but a tested product with a tested market fit? Put a x between 1(not at all) and 7 (for sure) below.

... and so on for each scenario...

Basically, at the end I would have, depending on 8 different scenario, 8 numerical variables, that I could use to operationalize the "Investor Behaviour" construct and insert into my Structural Equation Model. Is that possibile or I'm missing something? Any suggestion?

Thank you in advance, Fed

## 1 Answer

This is certainly possible; participant responses to your eight scenarios, rated on a 7-point scale, would make fine indicators for an SEM. However, it seems that you are already anticipating three "first-order" latent variables, pertaining to investment behavior based on (1) expertise, (2) product tested-ness, and (3) market tested-ness. As such, you might want to consider specifying a second-order latent variable model (see Beaujean, 2014, for a conceptual description), in which your scenario responses load onto their respective first-order latent variables, which subsequently load onto a second-order "investor behavior" factor.

If you were going to pursue the second-order latent variable modeling strategy, I'd encourage you to consider ensuring that you have at least three indicators (i.e., scenarios) per first-order latent variable, so that each of them would be just-identified (if not over-identified).

The measurement model in lavaan would look something like this (using a marker-variable method of scale-setting):

library(lavaan)
investor.model<-' expertise=~x1+x2+x3
prod.test=~x4+x5+x6
mark.test=~x7+x8+x9
inv.beh=~expertise+prod.test+mark.test'
summary(output.investor<-cfa(investor.model, data=df), fit.measures=TRUE)


Note that this second-order latent variable model model will fit the data equally as well as a model in which only the first-order latent variables were specified. If you want to see, just remove inv.beh=~expertise+prod.test+mark.test from the script. I recommend the second-order model simply because it seems to better represent the theoretical model for investor behavior you seem to be outlining above.

References

Beaujean, A. A. (2014). Latent variable modeling using R: A step-by-step guide. New York, NY: Routledge.