Bidirectional relationship with longitudinal data: what's the best model?

#1
N=1000+. I have about 3-4 repetitive measures of a few numerical variables and categorical variables.

How do I test the hypothesis that x (numerical) increases with y (numerical) and z incidence (categorical) over time, in the same time that both y and z are also affected by the increase in x? In summary, X is fueled by y and z, but both of them are boosted by increase in X over time.

I cannot say that y and z are independent, right? Do I need to perform 3 different models? 1) x as dependent, 2) y as dependent, 3) z as dependent?

What would be the best model to test this kind of hypothesis?

Thanks!
 
#2
you want to do an autoregressive model (time series) for a system of equations.

such that Y = intercept + X + Z + error
and X = intercept + Y + Z + error

correct? That's a little bit of a tougher model to work with since its non-recursive.

You might get more mileage out of something like =
Y = intercept + X + Z + error
X = intercept + Z + Error
 
#3
you want to do an autoregressive model (time series) for a system of equations.

such that Y = intercept + X + Z + error
and X = intercept + Y + Z + error

correct? That's a little bit of a tougher model to work with since its non-recursive.

You might get more mileage out of something like =
Y = intercept + X + Z + error
X = intercept + Z + Error
Thank you for your input. I'll read more about it. I did not think about a forecast model. Can I do a forecast model using repetitive measures for each subject?
 
#4
Thank you for your input. I'll read more about it. I did not think about a forecast model. Can I do a forecast model using repetitive measures for each subject?
yes, there are a number of different approaches depending on what you are asking.

If you want to know if the system of equations remains the same over time, you test for a stability coefficient.

if you want to treat the time as a "nuisance" you treat it as psuedo replication in something like a mixed model

if you want to look at the change over time, you can use a latent growth curve model.