The overall goal for Phases I and II of the proposed research is to create statistical software that can take into account the complex survey complications of sampling weights, stratification, and clustering in the estimation of the following multivariate outcome models for categorical, continuous, and combinations of categorical and continuous observed variables: linear, probit, and logistic regression; path analysis; exploratory and confirmatory factor analysis; latent class analysis and latent transition analysis; growth modeling for observed and latent variables; growth mixture modeling for observed and latent variables; multilevel modeling; continuous- and discrete-time survival models with covariates; and combinations of these models. The specific aims of Phase I are: (1) develop and implement algorithms for a Monte Carlo simulation procedure that can generate complex survey data that includes stratification, unequal probabilities of inclusion, finite population sampling, and clustering to study the parameter estimates obtained from likelihood-based and weighted-least-squares-based procedures and standard errors obtained from a generalized sandwich variance estimator and a generalized Jackknife variance estimator for the following models: latent class analysis for binary and ordered polytomous outcomes; factor analysis for binary, ordered polytomous, continuous, and combinations of categorical and continuous outcomes; and growth modeling for continuous outcomes; (2) develop and implement algorithms for a generalized sandwich variance (standard error) estimator for the models listed in 1; (3) develop and implement algorithms for a generalized Jackknife variance (standard error) estimator for the models listed in 1; (4) develop and implement algorithms for the generalized sandwich and Jackknife variance estimators for both likelihood-based and weighted-least-squares-based parameter estimation procedures that include sampling weights for the models listed in 1; and (5) develop and implement algorithms for generalized tests of model fit for both likelihood-based and weighted-least-squares-based parameter estimation procedures for the models listed in 1. [unreadable] [unreadable]