model ratio between 2 variables

[Shajar]

I have a situation where in theory the ratio between 2 variables n/d is an important attribute of my system  - it is a result of some other variables and observable cause of others. But both n & d has independent predictors. What is the right way to model such a relation?

Here is a model to make the question clearer (without latent variables for this example)

n ~  a+b

d ~ c + d

e ~ n/d

n/d ~ n + d    #???? Since n/d is not exogenous I want to model it, but it will be correct for n but not for d.

 

Thanks!

[Terrence Jorgensen]

What is the right way to model such a relation?

I would try a general Bayesian program, like JAGS or Stan, where you are free to define the model you want to fit, rather than try to squeeze your theory into LISREL matrices.

But if you want to use lavaan for some reason, you could just define n/d as a new variable in your data.frame, and include it as another variable in your model.  In principle, it is not very different from defining a product between 2 variables to model an interaction effect, but the product is n * 1/d instead of n*d.  You can allow the n/d variable to correlate with the residuals of n and d, or regress n/d on n and d like your syntax already does, but I don't know if that resolves the endogeneity problem.  You could ask on SEMNET, since this isn't really a lavaan issue; there are a lot of causal-modelers on there who are more well versed in that literature and could probably help.

Terrence D. Jorgensen

Assistant Professor, Methods and Statistics

Research Institute for Child Development and Education, the University of Amsterdam

http://www.uva.nl/profile/t.d.jorgensen

[Shajar]

Thanks Terrence for your prompt response!

I am too deep in the project to switch tool... I will try use in the model only the ratio (already defined as a separate variable) and predicting variables predicts the ratio and not the original variables. 

I will ask SEMNET as you suggest. Thanks!