Hi. I running a path model to examine the relationship between x and y while including covariates and mediators. I would like to account for a non-linear relationship between x and y, as indicated when I examine the relationship using ordinary regression. Do you have any recommendations on how to best account for a non-linear relationship? I have tried to include X^2 in the model, having it modeled just as X is and allowing the two to covary. However the model is non-positive definite when I do this.
I have also considered including an additional term for piecewise regression. Would it follow the normal X term and do they covary?
Any advice that you could provide would be very helpful!
I would like to test a threshold model (in which the relationship between X and Y gets significantly stronger above a certain value of X) using piecewise/segmented regression. Also I would prefer the threshold value to be estimated from the data instead of fixing one a priori. Can this be done in Mplus?
You can try mixture modeling as in User's guide example 7.1. This would be our recommendation for you.
You can also do piece wise segmentation - where you would manually select the threshold value and choose the one with the best likelihood (from a grid of threshold values). If you decide to do that you can still compare the model to the mixture model using BIC.