Extending Hierarchical Generalized Transformation Models to Complex Survey Data

Thomas M. Menino Convention & Exhibition Center 

Bradley (2022) introduced hierarchical generalized transformation (HGT) models for joint Bayesian analysis of multiple response types by a two-step composite sampler exploiting Diaconis-Ylvisaker (DY) conjugacy. However, HGT assumes simple random sampling, precluding application to complex surveys like the National Survey of Children's Health (NSCH; Ghandour et al., 2018). This study extends HGT using pseudo-likelihood weighting (Pfeffermann, 1993) raising each observation's likelihood to the power of its survey weight. We prove DY conjugacy is preserved across all three data models- the weighted posteriors retain the same DY form, with weights rescaling sufficient statistics (alpha_j + Z_ij becomes alpha_j + w_i*Z_ij; kappa_j + c_j becomes kappa_j + w_i*c). Thus, preserving computational efficiency, Bradley's Algorithm 1 requires only minimal modification. This study applies survey-weighted HGT to NSCH data, jointly modeling child screen time (continuous), sleep problems (ordinal), and anxiety (binary), and demonstrate that ignoring survey design yields biased estimates and invalid inference.

complex surveys

hierarchical transformation models

Diaconis-Ylvisaker conjugacy

pseudo-likelihood

Bayesian inference

survey weights 

Survey Research Methods Section