Latent factor loadings

Agree with @Joshua_Pritikin , assuming the sign of the factor loadings can be overly restrictive, with low factor loadings could lead to truncated posterior. I see more as something you want to test ratter than assume. For example this is a common constraint in IRT for the slopes. A less restrictive model would need some sign adjustment (like blavaan) or very careful consideration of priors, as it can lead to non-positive definite matrices

@mike-lawrence About blavaan, the idea of estimating the parameters from the unconstrainted model is to “take advantage” of factor indeterminancy. Meaning that all the parameters can switch direction across iterations and the model would be the same (same model implied covariances, log-likelihood). So, it estimates the model without worrying about the sign direction, and in the generated quantities block changes the iterations that swicthed direction. This improved efficiency as the actual estimation doesnt have extra constraints, and the generated quantities is very fast. For example the constraint of having 1 factor loadings being positive can lead to rejecting some interations and slow down the estimation
The same way the factor scores are now estimated in the generated quantities, whch makes it faster and exclude them of the parameter estimation process

In this previous trend I presented a simpler model that follows the same approach https://discourse.mc-stan.org/t/non-convergence-of-latent-variable-model/12450/13?u=mauricio_garnier-villarre
With Stan I have tried the different approaches and this has been more efficient

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