Is it possible to take a latent variable (for example Marketing) as for a composite variable which can be measured through its components ( for example promotional expenditure, price discounts etc). We can always argue that Marketing is itself a measured variable but if we take it as a composite function of all the activities that comprises of marketing then is it possible to use it as a latent variable? Will it violate any principles of SEM or factor analysis ?

A quick response will be highly helpful as I'm reaching the deadline of my project submission and I'm stuck due to this problem.

Thank you in advance.

Could you clarify what you mean by "composite variable?"

but I also have questions with regard to modeling composite variables. For clarification, according to Kline (2016)

^{1}, a composite is a latent variable with causal indicators (a formative measurement model), where the factor's disturbance variance is fixed to zero (i.e., it is dropped from the model). That is a linear combination of the indicators. A composite model is is illustrated in Figure 14.3(c).I'd be interested to know if this affect how the model is estimated with regards to which model parameters can be fixed when the causal indicators are ordinal. For example, would theta parameterization where all residual variances are fixed to zero be problematic if the variance of their common latent/composite variable is fixed to zero?

Kline, R. B. (2016). Principles and practice of structural equation modeling (4th ed.). The Guilford Press. www.guilford.com ↩︎

Generally, when we speak about latent variables (or factors), we are referring to latent variables that have at least some one-headed arrows that go from the latent variables to observed variables. Identification of these conventional factor models has been well-known and readily discussed for decades. More recently, models that have latent variables with one-headed arrows going from the observed variables to the latent variables have gained a large amount of attention.

Both kinds of models have observed variables and latent variables, but they have totally different identification criteria and many terms do not translate across both kinds of models. For example, consider "residual variances". In conventional factor models (arrows from latents to observed), the observed variables have residual variances. These residual variances relate to how much of the observed variable variance relates to the latent variable. By contrast in "formative" factor models (arrows from observed variables to latents), the observed variables have variances, but no residual variances. Consequently, the notion of a "theta" "parameterization" does not apply to these models. The variances of the observed variables do not relate to the quality of "measurement". I would go so far as to say "formative" factor models are not measurement models in any sense that I presently understand.

My general advice is this: be thoughtful about your model and particularly about the predictions your model makes about the data. "Factor" models with arrows going from the observed variables to the latents imply very different things about the data than factor models with arrows going from the latents to the observed variables. They also have very different identification criteria when all the observed variables are continuous. "Formative" factor models are generally quite hard to identify even in the best circumstances. They are even harder to identify when you have ordinal data.