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Published on: July 3, 2020
Limited Information Parameter Estimates for Latent or Mixed Manifest and Latent Variable Models
Abstract:
We argue for separate analyses of the measurement and structural portions of latent or mixed manifest and latent variable models. We present limited information (single equation) procedures for estimating parameters in the structural portion of these models. These include parameter estimation procedures for recursive or nonrecursive relations, and procedures for testing zero-effect hypotheses. We then compare full and limited information estimates in a Monte Carlo analysis of sample correlation matrices that contained structural model misspecifications. Both full and limited information estimates identified misspecified nonzero effects reasonably well. However, limited information estimates were far superior in detecting misspecified zero-effect hypotheses. We recommend limited information parameter estimation procedures over full information techniques for (a) testing specific causal hypotheses and (b) locating specific structural model misspecifications.
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Prediction Intervals
However, the point estimate is most likely not the exact value of the population parameter, but close to it. After calculating point estimates, we construct interval estimates, called confidence intervals or prediction intervals. This prediction interval comprises a range of values unlike the point estimate and is a better predictor of the observed sample value, y.

