Asymptotic Standard Error Sample Clauses

Asymptotic Standard Error. Estimation of the proposed latent trajectory models was done via the EM algorithm. One limitation of the EM algorithm is that it does not automatically provide standard errors. A variety of approaches have been proposed to assess the standard errors of the parameter estimates obtained via the EM algorithm[49, 56, 53]; however, many of these approaches rely heavily on likelihood theory and are not applicable in the current context. Thus, we propose two options for approximating the standard errors of the parameter estimates that can be implemented within the proposed framework. The first option is to use a bootstrap approach to standard error approximation, where the number of latent classes is held fixed and the bootstrap samples are drawn in the unit of individuals to accommodate repeated measures over time[13]. Since a bootstrap approach to estimation can be computationally intensive even for relatively simple problems, bootstrapping the standard errors for the parameter estimates involved in a finite mixture of estimating functions can be computationally burdensome. As an alternative, we propose an analytical approach based on a sandwich variance estimate. Let Γg (yi; ψ) =  ∂ logπg (xi;α) ∂α hg (yi; θ)  . Note that the complete-data estimating function is given by ∑ ∑