I am conducting multigroup analysis in STATA with 990 participants to determine whether a proposed model differs across two groups (men and women). The model looks at the effect of variable A --> variable B --> variable C --> variable D. Given theoretical support, I have also included pathways from A --> C, A -->D, and B--> D. Additionally, all variables are continuous, the model controls for two covariates at each path (age and socioeconomic status), and the data uses complex sampling weights.
Variable C is comprised of seven items that were measured on different scales (three 5-point and four 6-point scales), so it has to be standardized. When examining the model across all participants, however, standardizing variable C changes the significance of relationship between variables C and D. Specifically, using the summed (unstandardized) seven items for variable C gave a p-value of .036, and using the standardized variable C (after z-scoring and summing all seven items) gives a p-value of .057.
Although a Google search for this question provided mixed suggestions, I came across a recommendation that all of the variables in a model like this should be standardized. My data shows that when both variables C and D are standardized, there is a p-value of .034 (which is closer to what I found after using the summed, unstandardized variable C).
What is the best approach in this situation? Is it best practice to standardize all of the coefficients in the model? Should I only standardize variable C and report p=.057? Thanks in advance for your help!
