ESPHome vs modsem

modsem fits interaction and quadratic effects between latent variables in R, offering both product-indicator approaches (modsem_pi) and distribution-analytic ones (modsem_da, covering LMS and QML). Releases land roughly monthly and are dense pull-request lists. The recent line is dominated by the LMS approach: gradient refactors, parallel E-steps, composite construct support, and careful handling of residual covariances between latent variables.

Two things are being closed at once. The modelling gap — composites and formative constructs, categorical estimators, residual covariances in every direction, multigroup and clustered designs — brings modsem toward what commercial Mplus users expect, and the package's Mplus bridge is maintained alongside it, now with unique file IDs and a cleanup argument. The performance gap is the other: memoised H0, parallel E-step, optimized gradients and Hessians for both LMS and QML, all aimed at the distribution-analytic estimators that are expensive by construction. Convention borrowing from lavaan continues in message formatting and standard-error defaults.

The 1.0.20 and 1.0.21 releases both spent effort on residual covariances between endogenous and exogenous latent variables across estimation, prediction and standardization, and that thread has not obviously closed. The arrival of a second contributor moving MplusAutomation to Suggests suggests dependency trimming continues.