A Framework for Structural Equation Models in General Pedigrees

Abstract

Background/Aims: Structural Equation Modeling (SEM) is an analysis approach that accounts for both the causal relationships between variables and the errors associated with the measurement of these variables. In this paper, a framework for implementing structural equation models (SEMs) in family data is proposed. Methods: This framework includes both a latent measurement model and a structural model with covariates. It allows for a wide variety of models, including latent growth curve models. Environmental, polygenic and other genetic variance components can be included in the SEM. Kronecker notation makes it easy to separate the SEM process from a familial correlation model. A limited information method of model fitting is discussed. We show how missing data and ascertainment may be handled. We give several examples of how the framework may be used. Results: A simulation study shows that our method is computationally feasible, and has good statistical properties. Conclusion: Our framework may be used to build and compare causal models using family data without any genetic marker data. It also allows for a nearly endless array of genetic association and/or linkage tests. A preliminary Matlab program is available, and we are currently implementing a more complete and user-friendly R package.

The household contact study design for genetic epidemiological studies of infectious diseases

“…We have also identified novel chromosomal regions linked to a unique resistance phenotype (Stein et al, 2008); we are uniquely able to clinically and epidemiologically characterize this phenotype because of our solid study design. Our future plans will incorporate structural equation modeling (SEM to multivariately analyze the influences of host genetics, immunology, and environment on clinical outcome; this shall be done using a SEM approach that jointly models familial relationship and covariance among variables (Morris et al, 2011). …”

strum: an R package for structural modeling of latent variables for general pedigrees

“…The statistical details of the framework implemented by strum are described by Morris et al [ 20 ], and creating the R package involved a considerable amount of additional innovative work. Briefly, our method uses Kronecker product notation to model the covariance among relatives as well as the covariance among measured variables (phenotypes, genes, covariates, etc.…”

“…Previously, we developed a robust and flexible framework for SEM in general pedigree data. It not only can handle both measurement and structural models, but it can also estimate polygenic variance effects, genetic linkage effects and association effects while correcting for ascertainment, which sets it apart from other SEM methods for genetics [ 20 ]. One of the primary conceptual innovations of this framework is that it enables the analyst to mentally separate the model of familial correlation from the causal/measurement model by the use of Kronecker notation.…”

An Accidental Genetic Epidemiologist

“…Back in Chapel Hill, I had a student who worked on this problem, synthesized the two approaches for large pedigrees, and developed the mixed major-gene and polygenic model to include assortative mating and several familial sources of environmental variation (9). Much later, we developed under the assumption of multivariate normality a structural equation model framework that could also include linkage and association (81). Because multivariate normality can be a strong assumption, we also developed a method of estimating all the possible familial correlations from pedigree data without this assumption and, on the basis of extensive simulation results, determined an algorithm that would produce accurate confidence intervals for the estimates (75).…”