Additional approaches to incorporate

[stonegold546]

Would be good to see how current program structure holds up for different models, i.e. can we retain same helper functions for different models etc ...

• Expand the model support, i.e. reflect the diversity of models offered by (b)lavaan
  • Basically follow (b)lavaan all the way through
  • Time consuming ...
• Regular model with no modelled residual covariance structure
• Has global-local (generalized double Pareto) priors for non-specified cross-loadings if simple_struc = FALSE
• Alternative priors for estimating residual covariances, initial approach is normal (ridge-style)
  • LKJ
  • Lasso #10
  • Horseshoe
    • Easy enough to implement, but parameter growth problem!
  • Generalized double Pareto (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3903426/)
    • Is global-local (heavily shrinks weak signals and frees strong signals) and has simple form
• Wu & Browne (2015): https://doi.org/10.1007/s11336-015-9451-3
  • Generalized matrix beta type-II approach (Wishart->Inverse-Wishart) that similarly assumes minor factor influences, referred to as adventitious error.
  • Issues calculating log-likelihood if using GMB dist, instead of sampling Inv-Wishart
• [x] Uanhoro (2022): https://doi.org/10.1080/10705511.2022.2142128
  • Meta-analytic SEM approach (using Wu & Browne above as basis) that estimates error covariance structure.
  • [ ] Add moderators
  • [ ] Add missing data
  • Sent to bayesianmasem
• Serious approach for modelling error in mean structures?
  • Would be useful for growth-curve models.
  • Current thinking: error in mean structures is already reflected in the residual variance parameter -- no need to model concurrently.
  • Practical approach is to compare saturated and unsaturated mean structures for fit.
• Practical (or not too slow) approach for modelling error in non-continuous data?
  • Would be useful to have options for binary and ordinal, but these take too long.
  • Any credible moments-based (two-step) approaches so it does not take forever? Hotelling T-square?
  • Bring Archakov et al. approach over from bayesianmasem
• Non-complete data
• Standard multi-group models, so multi-group parameters ...
  • Or maintain that meta-analytic (hierarchical) approach is actually preferable especially once we have many groups?