I have run a series of 4 nested cross-lagged panel models exploring the temporal ordering between subjective age and health (2 variables for each model). I have 4 types of health and each type was test separately. Furthermore, I conducted separate analysis for younger and older people. In other words:

• Health1young: Models 1-4
• Health2young: Models 1-4
• Health3young: Models 1-4
• Health4young: Models 1-4
• Health1old: Models 1-4
• Health2old: Models 1-4

Health3old: Models 1-4

• Health4old: Models 1-4

My research question asks "is the strength of the subjective age-health relationship the same for each health dimension?" In other words, for the younger group, is the strength of the relationship the same for each type of health? What about for the older group?

I have run all the models (in Mplus) and I have b and Beta weights for the paths. I can see the numbers are different, but I don't know if they are (the all mighty) statistically significantly different. How could I compare the coefficients to be able to answer my research question?

How would I go about testing between groups (young vs. old) to see if the strength of the relationship is different for young vs. old?

Is there a simple formula to compute these by hand? Do I need to run a new set of analyses? If so, guidance for conducting those analyses would be helpful (in Mplus, SPSS, or Excel for extra points).

Thank you!