Mixed-effects variance components models for biometric family analyses

Recent substantive research on biometric analyses of twin and family data has used both a biometric path analysis model (PAM) and a biometric variance components model (VCM). Methodological research on these same topics have suggested benefits of using linear structural equation model algorithms (SEMA) as well as mixed effect multilevel algorithms (MEMA). To better understand the potential similarities and differences among these approaches we first highlight the algebraic equivalence between the standard biometric PAM and the corresponding biometric VCM models for family data. Second, we demonstrate how several SEMA programs based on either the PAM or VCM approach produce equivalent estimates for all phenotypic and biometric parameters. Third, we show how the biometric VCM approach (but not the PAM approach) can be easily programmed using current MEMA programs (e.g., SAS PROC MIXED). We then expand the scope of these different approaches to include measured covariates, observed variable interactions and multiple relatives within each family. MEMA software is compared to SEMA software for programming complex models, including the flexibility of data input, treatment of missing data, inclusion of covariates, and ease of accommodating varying numbers of observations (per family or individual).