Abstract
Complex networks with causal relationships among variables are pervasive in biology. Their study, however, requires special modeling approaches. Structural equation models (SEM) allow the representation of causal mechanisms among phenotypic traits and inferring the magnitude of causal relationships. This information is important not only in understanding how variables relate to each other in a biological system, but also to predict how this system reacts under external interventions which are common in fields related to health and food production. Nevertheless, fitting a SEM requires defining a priori the causal structure among traits, which is the qualitative information that describes how traits are causally related to each other. Here, we present directions for the applications of SEM to investigate a system of phenotypic traits after searching for causal structures among them. The search may be performed under confounding effects exerted by genetic correlations.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Wright S (1921) Correlation and causation. J Agric Res 201:557–585
Haavelmo T (1943) The statistical implications of a system of simultaneous equations. Econometrica 11:12
Pearl J (2000) Causality: models, reasoning and inference. Cambridge University Press, Cambridge, UK
Gianola D, Sorensen D (2004) Quantitative genetic models for describing simultaneous and recursive relationships between phenotypes. Genetics 167:1407–1424
Varona L, Sorensen D, Thompson R (2007) Analysis of litter size and average litter weight in pigs using a recursive model. Genetics 177:1791–1799
Henderson CR, Quaas RL (1976) Multiple trait evaluation using relative records. J Anim Sci 43:1188–1197
Wu XL, Heringstad B, Gianola D (2010) Bayesian structural equation models for inferring relationships between phenotypes: a review of methodology, identifiability, and applications. J Anim Breed Genet 127:3–15
de los Campos G, Gianola D, Boettcher P, Moroni P (2006) A structural equation model for describing relationships between somatic cell score and milk yield in dairy goats. J Anim Sci 84:2934–2941
Heringstad B, Wu XL, Gianola D (2009) Inferring relationships between health and fertility in Norwegian Red cows using recursive models. J Dairy Sci 92:1778–1784
Maturana EL, Wu XL, Gianola D, Weigel KA, Rosa GJM (2009) Exploring biological relationships between calving traits in primiparous cattle with a Bayesian recursive model. Genetics 181:277–287
Ibanez-Escriche N, de Maturana EL, Noguera JL, Varona L (2010) An application of change-point recursive models to the relationship between litter size and number of stillborns in pigs. J Anim Sci 88:3493–3503
Jamrozik J, Schaeffer LR (2010) Recursive relationships between milk yield and somatic cell score of Canadian Holsteins from finite mixture random regression models. J Dairy Sci 93:5474–5486
Akaike H (1973) Information theory and an extension of the maximum likelihood principle. In: Petrov BN, Csaki F (eds) Second International symposium on information theory. Publishing House of the Hungarian Academy of Sciences, Budapest
Schwarz G (1978) Estimating dimension of a model. Ann Stat 6:461–464
Spiegelhalter DJ, Best NG, Carlin BR, van der Linde A (2002) Bayesian measures of model complexity and fit. J R Stat Soc Ser B-Stat Methodol 64:583–616
Spirtes P, Glymour C, Scheines R (2000) Causation, prediction and search, 2nd edn. MIT Press, Cambridge, MA
Verma T, Pearl J (1990) Equivalence and synthesis of causal models. Proceedings of the 6th conference on uncertainty in artificial intelligence 1990, Cambridge, MA
Valente BD, Rosa GJM, de los Campos G, Gianola D, Silva MA (2010) Searching for recursive causal structures in multivariate quantitative genetics mixed models. Genetics 185:633–644
Rosa GJM, Valente BD, de los Campos G, Wu XL, Gianola D, Silva MA (2011) Inferring causal phenotype networks using structural equation models. Genet Sel Evol 43:6
Yu JM, Pressoir G, Briggs WH, Bi IV, Yamasaki M, Doebley JF, McMullen MD, Gaut BS, Nielsen DM, Holland JB, Kresovich S, Buckler ES (2006) A unified mixed-model method for association mapping that accounts for multiple levels of relatedness. Nat Genet 38:203–208
Mrode RA, Thompson R (2005) Linear models for the prediction of animal breeding values, 2nd edn. Cabi Publishing-C a B Int, Wallingford
VanRaden PM (2008) Efficient methods to compute genomic predictions. J Dairy Sci 91:4414–4423
Gianola D, de los Campos G, Hill WG, Manfredi E, Fernando R (2009) Additive genetic variability and the Bayesian alphabet. Genetics 183:347–363
Forni S, Aguilar I, Misztal I (2011) Different genomic relationship matrices for single-step analysis using phenotypic, pedigree and genomic information. Genet Sel Evol 43
Gianola D, de los Campos G (2008) Inferring genetic values for quantitative traits non-parametrically. Genet Res 90:525–540
Gelman A, Carlin JB, Stern HS, Rubin DB (2004) Bayesian data analysis, 2nd edn. Chapman & Hall, New York, NY
Mrode MA (1996) Linear models for the prediction of animal breeding values. CAB International, Wallingford
Smith BJ (2008) Bayesian Output Analysis Program (BOA) for MCMC
Shipley B (2002) Cause and correlation in biology. Cambridge University Press, Cambridge
Gentry J, Long L, Gentleman R, Falcon S, Hahne F, Sarkar D, Hansen K (2012) Rgraphviz: provides plotting capabilities for R graph objects
Acknowledgments
The authors thank Gustavo de los Campos for his contribution on the development of the function gibbsREC. This work was supported by the Agriculture and Food Research Initiative Competitive Grant no. 2011-67015-30219 from the USDA National Institute of Food and Agriculture.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media, LLC
About this protocol
Cite this protocol
Valente, B.D., de Magalhães Rosa, G.J. (2013). Mixed Effects Structural Equation Models and Phenotypic Causal Networks. In: Gondro, C., van der Werf, J., Hayes, B. (eds) Genome-Wide Association Studies and Genomic Prediction. Methods in Molecular Biology, vol 1019. Humana Press, Totowa, NJ. https://doi.org/10.1007/978-1-62703-447-0_21
Download citation
DOI: https://doi.org/10.1007/978-1-62703-447-0_21
Published:
Publisher Name: Humana Press, Totowa, NJ
Print ISBN: 978-1-62703-446-3
Online ISBN: 978-1-62703-447-0
eBook Packages: Springer Protocols