Using residuals in crosslagged path models
Hi there!
I'm currently in the process of figuring out how best to evaluate changes in three factors from one time point to the next (measured 6 months between) in a cross-lagged path model. In addition, one variable was measured 6 months prior to the two primary measurement waves. The study is openly exploratory, as little is known about the relationships we are exploring from earlier research. The variable names are substituted for surrogate concepts - so do not cite me on these models.
The thought was to control for the covariance between each factor at time point 1, and evaluate whether these factors predict changes in one another beyond that initial covariance.
As far as I can tell, allowing exogenous factors (T1 = Timepoint 1) to covary does not take into account their covariance when predicting the factors at a later time point? See the path model here.
Well, I think I may have gone rogue - but if the SEMbuilder does not allow to control for initial covariance in later prediction, I thought it might be worth the shot to do it myself.
So I used the regress-command for each of the three T1-variables, with Injury (T0), and the other two variables as predictors, to generate a residual score for each variable - which should then be free(r) of confounding from the initial covariation (?). Using these residual scores as T1-variables to predict later scores should do what I want, right?
'Lo and behold, the following model is produced. The correlation between the variables at T0 and T1 is now 0, and the model supports more temporally dynamic relations between the concepts.
But I am sure there is something very basic I am misunderstanding here. Anyone more knowledgeable willing to comment on which of the procedures seems more correct?
Thanks for any and all help in advance!
I'm currently in the process of figuring out how best to evaluate changes in three factors from one time point to the next (measured 6 months between) in a cross-lagged path model. In addition, one variable was measured 6 months prior to the two primary measurement waves. The study is openly exploratory, as little is known about the relationships we are exploring from earlier research. The variable names are substituted for surrogate concepts - so do not cite me on these models.
The thought was to control for the covariance between each factor at time point 1, and evaluate whether these factors predict changes in one another beyond that initial covariance.
As far as I can tell, allowing exogenous factors (T1 = Timepoint 1) to covary does not take into account their covariance when predicting the factors at a later time point? See the path model here.
Well, I think I may have gone rogue - but if the SEMbuilder does not allow to control for initial covariance in later prediction, I thought it might be worth the shot to do it myself.
So I used the regress-command for each of the three T1-variables, with Injury (T0), and the other two variables as predictors, to generate a residual score for each variable - which should then be free(r) of confounding from the initial covariation (?). Using these residual scores as T1-variables to predict later scores should do what I want, right?
'Lo and behold, the following model is produced. The correlation between the variables at T0 and T1 is now 0, and the model supports more temporally dynamic relations between the concepts.
But I am sure there is something very basic I am misunderstanding here. Anyone more knowledgeable willing to comment on which of the procedures seems more correct?
Thanks for any and all help in advance!
