The overall goal for this Phase II proposal 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 general multivariate and multilevel latent variable models: linear, probit, and logistic regression; path analysis; exploratory and confirmatory factor analysis; latent class analysis; latent transition analysis; growth modeling for observed and latent variables; growth mixture modeling for observed and latent variables; multilevel linear, probit and logistic regression; multilevel structural equation models; discrete-time survival models with covariates; and combinations of these models. Without these software developments, researchers are forced to ignore the fact that their data were collected using a complex sampling design.
The specific aims are to develop and implement: (1) Pseudo maximum-likelihood (PML) and pseudo weighted least squares (PWLS) parameter and variance estimators for general multilevel and multivariate latent variable models for the following sampling designs: with replacement (WR), without replacement (WOR), and unequal probabilities of inclusion without replacement (UNEQWOR). Fully implement the Jackknife, BRR and bootstrap variance estimators for PML and PWLS. (2) Complex sample modeling capabilities using the PWLS estimator for two-level multivariate latent variable models and using the PML estimator for three-level multivariate latent variable models. (3) The PML and PWLS chi-square tests of model fit, the Wald test for multiple linear and non-linear parameter constraints, and the Pearson and the log-likelihood chi-square tests of model fit for contingency tables for general multilevel and multivariate latent variable models for the WR, WOR and UNEQWOR sampling designs. (4) Design-based and model-based simulation procedures that can generate complex survey data that include stratification, unequal probabilities of inclusion, finite population sampling, and clustering. (5) Additional complex sampling utilities such as Pfeffermann's test for informativeness of the sampling weights; univariate descriptive statistics such as the design effect, the multistage intraclass correlation, and the informative index for the weights; a bias-corrected estimator for structural equation models with continuous variables; a variance estimator for single PSU strata; weight trimming techniques; selection modeling techniques; and small area estimation. ? ? ?
