How are parameter standard errors estimated?
Asymptotic estimated standard errors for parameter estimates are obtained from the matrix of second partial derivatives of all independent model parameters towards the log-likelihood (Hessian matrix). The Hessian is inverted, and all elements multiplied times -1. This gives the asymptotic variance/covariance matrix; taking the square roots of the diagonal elements gives the asymptotic estimated standard errors. Derivatives can be calculated either analytically, or numerically–i.e., by evaluating how much the log-likelihood changes when adding and/or subtracting a small value (delta) to/from model parameter values. Parameter standard errors can also be estimated using the parametric bootstrap method. This method resamples (constructs multiple simulated data sets) using the expected frequencies of a given latent class model. Specifically, for a set of observed data, one first estimates a latent class model, second, calculates the expected frequencies given the parameter estimates so obt
