Standard errors of estimated latent variable scores with estimated structural parameters

The authors propose a concise formula to evaluate the standard error of the estimated latent variable score when the true values of the structural parameters are not known and must be estimated. The formula can be applied to factor scores in factor analysis or ability parameters in item response theory, without bootstrap or Markov chain Monte Carlo methods. The proposed method is valid when both the number of items and the number of subjects are large. However, simulation results suggest that the proposed method provides valid estimates for standard errors of latent abilities even when the numbers of items and subjects are not large.