I want to model the following:
DV: Y at time 3
IVs: X at time 1, X at time 2, change of X from time 1 to time 2
Which is the most appropriate way (preferably in SPSS).
I am afraid I cannot use multiple linear regression due to multicollinearity, right?
Thanks a lot!
There are several biased Multiple Linear Regression methods that allow you to estimate Model parameters in presence of Multicollinearity, e.g Principal Component Regression and Ridge Regression, these models purposefully invoke bias in estimation to reduce the variance in the estimator.
In case of your research problem It seems your third variable is just a linear combination of first two, do you really need to invoke this regressor into your model? It is not providing any new information in this linear framework and you can simply work with a full rank model by model respecification in this case , perhaps in a nonlinear Regression modeling problem it would be more appropriate and informative about the process.
Yes, the model you described will have the 'singularity' issue. Your third predictor is a linear combination of the first and the second predictor. You need to exclude one of your predictors from the model.
But for a better model I guess you'll need an ARIMAX approach here.
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