A Framework for Structural Equation Models in General Pedigrees

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.

[1]  S E Hodge,et al.  Inherent intractability of the ascertainment problem for pedigree data: a general likelihood framework. , 1995, American journal of human genetics.

[2]  Stan Lipovetsky,et al.  Generalized Latent Variable Modeling: Multilevel,Longitudinal, and Structural Equation Models , 2005, Technometrics.

[3]  Albert Satorra,et al.  Asymptotic robust inferences in the analysis of mean and covariance structures , 1992 .

[4]  K. Lange,et al.  Fishing for Pleiotropic QTLs in a Polygenic Sea , 2005, Annals of human genetics.

[5]  Karl G. Jöreskog,et al.  Lisrel 8: User's Reference Guide , 1997 .

[6]  B. Muthén,et al.  Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes , 1997 .

[7]  D. Boomsma,et al.  A Comparison of Power to Detect a QTL in Sib-Pair Data Using Multivariate Phenotypes, Mean Phenotypes, and Factor Scores , 1998, Behavior genetics.

[8]  B. Muthén.  BEYOND SEM: GENERAL LATENT VARIABLE MODELING , 2002 .

[9]  R. Elston,et al.  A general model for the genetic analysis of pedigree data. , 1971, Human heredity.

[10]  Daniel Gianola,et al.  Quantitative Genetic Models for Describing Simultaneous and Recursive Relationships Between Phenotypes This article is dedicated to Arthur B. Chapman, teacher and mentor of numerous animal breeding students and disciple and friend of Sewall Wright. , 2004, Genetics.

[11]  Tom Burr,et al.  Causation, Prediction, and Search , 2003, Technometrics.

[12]  Raphael Mrode,et al.  Linear models for the prediction of animal breeding values , 1996 .

[13]  C. Stein,et al.  Mendelian randomization in family data , 2009, BMC proceedings.

[14]  David A. Jaeger,et al.  Problems with Instrumental Variables Estimation when the Correlation between the Instruments and the Endogenous Explanatory Variable is Weak , 1995 .

[15]  D. A. Kenny,et al.  Correlation and Causation , 1937, Wilmott.

[16]  M. Province,et al.  Testing causal hypotheses in multivariate linkage analysis of quantitative traits: General formulation and application to sibpair data , 1998, Genetic epidemiology.

[17]  Yeunjoo E. Song,et al.  Defining genetic determinants of the Metabolic Syndrome in the Framingham Heart Study using association and structural equation modeling methods , 2009, BMC proceedings.

[18]  R. Wette,et al.  Multifactorial analysis of family data ascertained through truncation: a comparative evaluation of two methods of statistical inference. , 1988, American journal of human genetics.

[19]  B. Muthén.  A general structural equation model with dichotomous, ordered categorical, and continuous latent variable indicators , 1984 .

[20]  M. Neale,et al.  An integrated phenomic approach to multivariate allelic association , 2010, European Journal of Human Genetics.

[21]  A. Thapar,et al.  Methodology for Genetic Studies of Twins and Families , 1993 .

[22]  M C Neale,et al.  Multivariate multipoint linkage analysis of quantitative trait loci , 1996, Behavior genetics.

[23]  R. L. Quaas,et al.  Multiple Trait Evaluation Using Relatives' Records , 1976 .

[24]  Nicholas T. Longford,et al.  Factor analysis for clustered observations , 1992 .

[25]  Harvey Goldstein,et al.  Balanced versus unbalanced designs for linear structural relations in two‐level data , 1989 .

[26]  K. Yuan,et al.  5. Three Likelihood-Based Methods for Mean and Covariance Structure Analysis with Nonnormal Missing Data , 2000 .

[27]  E. J. van den Oord.  Framework for identifying quantitative trait loci in association studies using structural equation modeling , 2000, Genetic epidemiology.

[28]  D. A. Kenny,et al.  Correlation and Causation. , 1982 .

[29]  Keith Shockley,et al.  Structural Model Analysis of Multiple Quantitative Traits , 2006, PLoS genetics.

[30]  P. Bentler,et al.  Comparative fit indexes in structural models. , 1990, Psychological bulletin.

[31]  A. Tomarken,et al.  Structural equation modeling: strengths, limitations, and misconceptions. , 2005, Annual review of clinical psychology.

[32]  P. Bentler,et al.  Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives , 1999 .

[33]  J. S. Long,et al.  Testing Structural Equation Models , 1993 .

[34]  D I Boomsma,et al.  Combined Linkage and Association Tests in Mx , 2004, Behavior genetics.

[35]  R. Elston,et al.  Calculating Asymptotic Significance Levels of the Constrained Likelihood Ratio Test with Application to Multivariate Genetic Linkage Analysis , 2009, Statistical applications in genetics and molecular biology.

[36]  Guilherme J M Rosa,et al.  Searching for Recursive Causal Structures in Multivariate Quantitative Genetics Mixed Models , 2010, Genetics.

[37]  J. Pearl.  Causality: Models, Reasoning and Inference , 2000 .

[38]  Bill Shipley,et al.  Cause and Correlation in Biology: A User''s Guide to Path Analysis , 2016 .

[39]  K. Jöreskog.  A general approach to confirmatory maximum likelihood factor analysis , 1969 .

[40]  David M. Evans,et al.  Multivariate QTL linkage analysis suggests a QTL for platelet count on chromosome 19q , 2004, European Journal of Human Genetics.

[41]  B. Yandell,et al.  Inferring Causal Phenotype Networks From Segregating Populations , 2008, Genetics.

[42]  Bengt O. Muthén,et al.  BEYOND SEM: GENERAL LATENT VARIABLE MODELING , 2002 .