I added a vignette tspa-interaction.Rmd in the new branch to illustrate how to do 2S-PA, using data from a recent paper. The product indicator approach is pretty tedious to specify.

The 2S-PA approach is actually pretty straightforward: just need to create a product of the factor score variables, and compute the implied error variance using the formula from Hsiao et al. (2021). And the results seem promising: The coefficient estimates are basically the same, but with a larger test statistic. It's possible that the 2S-PA approach has higher statistical power.

@Gengrui-Zhang, would you want to conduct a simulation study comparing the 2S-PA approach and the product indicator approach? It should be a good exercise and you can use a similar design as Hsiao et al. (2021).

@marklhc Hi Mark, I'm happy to conduct a simulation study to compare. I'm also thinking about including the plot for interaction effects. Thanks for the opportunity!

Here's another reference I just found out:

https://journals.sagepub.com/doi/pdf/10.1177/00222437221077266

Consider possible functions to add:

• get_fs_int() generates factor score product indicators
• Add a vignette for continuous indicators (briefly describe simulation results)
• Clean up the branch (or use a different branch)

Discussion on Febr 8, 2024:

• Write a stand-alone function, with input of a data frame of factor scores (and their standard errors). User can specify which columns to compute products. Winnie suggested

Or by default get all pairs of interactions? Allow users to specify the specific pair(s) if they want just one or two