multigroup model

[rpsychologist]

Notes on the multigroup model.

The current model is estimating all parameters freely per game.

I guess what we want is to constrain some groups, e.g. add this to the lavaan call

group.equal = c("residuals", "residual.covariances", "lv.variances", "lv.covariances"),

https://github.com/digital-wellbeing/gametime-longitudinal/blob/f501fb5a4683210043c01b8d43fdd606774533ff/Analysis/Analysis.Rmd#L1024-L1031

A multigroup model + meta-analysis is probably the best approach.

I manage to fit multilevel RICLPM in Stan, and then compared it to a multigroup SEM + MA. This simulation can be found here https://github.com/digital-wellbeing/gametime-longitudinal/tree/analysis/Models/RICLPM-2L-stan

I also checked the frequentist properties of the whole lavaan multigroup + MA pipeline, the results are OK.

https://github.com/digital-wellbeing/gametime-longitudinal/blob/970625c1cad867c004e88095a83f08ec3930362d/Models/RICLPM-2L-stan/multilevel.Rmd#L517-L540

variable	mean(est)	theta	RB(est)	mean(se)	sd(est)	RB(se)	CI_cover
betafree[1]	0.593	0.66	-0.101	0.151	0.154	-0.017	0.910
betafree[2]	0.196	0.22	-0.110	0.149	0.145	0.026	0.930
betafree[3]	0.491	0.55	-0.107	0.149	0.146	0.024	0.916
betafree[4]	0.314	0.33	-0.047	0.149	0.161	-0.073	0.920
sd_1[1]	0.470	0.50	-0.059	0.109	0.103	0.058	0.954
sd_1[2]	0.460	0.50	-0.079	0.110	0.109	0.009	0.936
sd_1[3]	0.464	0.50	-0.072	0.108	0.107	0.012	0.922
sd_1[4]	0.455	0.50	-0.090	0.110	0.112	-0.023	0.910

Other options

• We can get the vcov matrix for the full model, so pooling the estimates as a linear contrast would be easy. Essentially a fixed effects approach.
• We could also fit a single model and use cluster-robust standard errors.

[mvuorre]

Awesome work! Yes we need to equate some if not all other parameters across games as you said. I'll work that in now. Then we'll work with the multi-group lavaan models + meta analyses.

[mvuorre]

I think we've answered this one and I'll proceed with meta-analysing the game-independent models.

[mvuorre]

Hooray