I have four observational experiments (data sets) that I wish to combine and summarize in a single path analysis model. Each experiment is 3-dimensional but the observables and therefore dimensions/variables are different in each data set. One variable X.1 is common to all datasets. All other variables are present in exactly two experiments.

Here are the experiments and associated variables:

Experiment 1: {X.1, X.2, Y}
Experiment 2: {X.1, X.2, Z}
Experiment 3: {X.1, X.3, Y}
Experiment 4: {X.1, X.3, Z}

For the sake of my study, Y and Z are considered to be the dependent (response) variables in a set of multiple linear regression models (MLRs).

For each data set I minimized the Bayesian Information Criterion (BIC) to select the best MLR model.

These BIC-minimizing models (one for each experiment, same order as above) are as follows:

Y ~ X.1 + X.2
Z ~ X.1
Y ~ X.1 + X.3
Z ~ X.3 

I am looking for a way to create a single path analysis model with two outputs, Y and Z, that unifies all four experiments.

Is there a smart way to get a single path analysis model out of this?

To make such a path model I believe I must first either 1) combine these separate MLR models OR 2) combine the datasets then make a single MLR model. I'm not sure where to start for either of these methods.

Thank you for reading and offering advice.

BTW, there is a little bit of multicollinearity present in these MLR models, but the Variance Inflation Factor is less than 5 for all predictor variables.