Structural equation models (SEM) are a type of multi-trait model increasingly being used for inferring functional relationships between multiple outcomes using operational data from livestock production systems. These data often present a hierarchical architecture given by clustering of observations at multiple levels including animals, cohorts and farms. A hierarchical data architecture introduces correlation patterns that, if ignored, can have detrimental effects on parameter estimation and inference. Here, we evaluate the inferential implications of accounting for, or conversely, misspecifying data architecture in the context of SEM. Motivated by beef cattle feedlot data, we designed simulation scenarios consisting of multiple responses in a clustered architecture. Competing fitted SEMs differed in their model specification so that data architecture was explicitly accounted for (M1; true model) or misspecified due to disregarding either the cluster-level correlation between responses (M2) or the correlation between observations of a response within a cluster (M3), or ignored all together (M4). Model fit was increasingly impaired when data architecture was misspecified or ignored. Both accuracy and precision of estimation were also negatively affected when data architecture was disregarded. Our findings are further illustrated using data from feedlot operations from the US Great Plains. Standing statistical recommendations that call for proper model specification capturing relevant hierarchical levels in data structure extend to the multivariate context of structural equation modeling.
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Babcock, A. H., Renter, D., White, B., Dubnicka, S., and Scott, H. 2010. “Temporal Distributions of Respiratory Disease Events within Cohorts of Feedlot Cattle and Associations with Cattle Health and Performance Indices,” Preventive Veterinary Medicine, 97, 198–219.
Babot, D., Noguera, J. L., Alfonso, L., and Estany, J. 2003. “Fixed or Random Contemporary Groups in Genetic Evaluation for Litter Size in Pigs Using a Single Trait Repeatability Animal Model,” Journal of Animal Breeding and Genetics, 120(1), 12–22.
Bae, H., Monti, S., Montano, M., Steinberg, M. H., Perls, T. T., and Sebastiani, P. 2016. “Learning Bayesian Networks from Correlated Data,” Scientific Reports, 6, 25156, 1–14.
Bello, N. M., Steibel, J. P., and Tempelman, R. J. 2010. “Hierarchical Bayesian Modeling of Random and Residual Variance–covariance Matrices in Bivariate Mixed Effects Models,” Biometrical Journal, 52(3), 297–313.
Cernicchiaro, N., White, B. J., Renter, D. G., and Babcock, A. H. 2013. “Evaluation of Economic and Performance Outcomes Associated with the Number of Treatments after an Initial Diagnosis of Bovine Respiratory Disease in Commercial Feeder Cattle,” American Journal of Veterinary Research, 74(2), 300–309.
Cha, E., Sanderson, M., Renter, D., Jager, A.,Cernicchiaro, N., and Bello, N. M. 2017. “Implementing Structural Equation Models to Observational Data from Feedlot Production Systems,” Preventive Veterinary Medicine, 147, 163–171.
de los Campos, G., Gianola, D., Boettcher, P., and Moroni, P. 2006. “A Structural Equation Model for Describing Relationships between Somatic Cell Score and Milk Yield in Dairy Goats,” Journal of Animal Science, 84(11), 2934–2941.
Dohoo, I., Martin, W., and Stryhn, H. 2014. Veterinary Epidemiologic Research (2nd ed.), Canada: VER Inc.
Dohoo, I. R. 2008. “Quantitaive epidemiology: Progress and challenges,” Preventive Veterinary Medicine, 86(3), 260–269.
Duncan, O. D. 1966. “Path Analysis: Sociological Examples,” American Journal of Sociology, 72(1), 1–16.
Gbur, E. E., Stroup, W., McCarter, W., Kevin, S., Durham, S., Young, L. J., Christman, M., West, M., and Kramer, M. 2012. Analysis of Generalized Linear Mixed Models in the Agricultural and Natural Resources Sciences, Madison, WI, USA: American Society of Agronomy, Soil Science Society of America, Crop Science Society of America, Inc.
Gelman, A. 2006. “Prior Distributions for Variance Parameters in Hierarchical Models.” Bayesian Analysis, 1(3), 515–533.
Gianola, D., and Sorensen, D. 2004. “Quantitative Genetic Models for Describing Simultaneous and Recursive Relationships between Phenotypes,” Genetics, 167(3), 1407–1424.
Haavelmo, T. 1943. “The Statistical Implications of a System of Simultaneous Equations,” Econometrica, 11(1), 1–12.
Hay, K. E., Barnes, T. S., Morton, J. M., Clements, A. C. A., and Mahony, T. J. 2014. “Risk Factors for Bovine Respiratory Disease in Australian Feedlot Cattle: Use of a Causal Diagram-informed Approach to Estimate Effects of Animal Mixing and Movements before Feedlot Entry,” Preventive Veterinary Medicine, 117(1), 160–169.
Inoue, K., Valente, B. D., Shoji, N., Honda, T., Oyama, K., and Rosa, G. J. 2016. “Inferring Phenotypic Causal Structures among Meat Quality Traits and the Application of a Structural Equation Model in Japanese Black Cattle,” Journal of Animal Science, 94(10), 4133–4142.
Johnson, R. A., and Wichern, D. W. 2007. Applied Multivariate Statistical Analysis (6th ed), Upper Saddle River, New Jersey: Pearson Prentice Hall.
Joreskog, K.G. 1973. A General Method for Estimating a Linear Structural Equation System, Edited by A. S. Goldberger and O. D. Duncan, Equation Models in the Social Sciences, New York: Senimar Press.
Konig, S., Wu, X. L., Gianola, D., Heringstad, B., and Simianer, H. 2008. “Exploration of Relationships between Claw Disorders and Milk Yield in Holstein Cows via Recursive Linear and Threshold Models,” Journal of Dairy Science, 91(1), 395–406.
Lauritzen, S. L. 1996. Graphical models. Oxford, UK: Oxford University Press.
Littell, R. C., Milliken G. A., Stroup W., Russell, D. W., and Schabenberger, O. 2006. SAS for Mixed Models (2nd ed.), Cary, NC: SAS Institute Inc.
Lopez de Maturana, E., Wu, X. L., Gianola, D., Weigel, K. A. and Rosa, G. J. 2009. “Exploring biological relationships between calving traits in primiparous cattle with a Bayesian recursive model,” Genetics, 181(1), 277–87.
Milliken, G. A., and Johnson, D. E. 2009. Analysis of Messy Data - Volume 1: Designed Experiments (2nd ed.), Boca Raton, Florida, USA: Chapman and Hall/CRC Press.
Pearl, J. 2009. Causality: Models, Reasoning, and Inference (2nd ed.), Cambridge University Press.
Peñagaricano, F., Valente, B. D., Steibel, J. P., Bates, R. O., Ernst, C. W., Khatib, H., and Rosa, G. J. 2015. “Searching for Causal Networks Involving Latent Variables in Complex Traits: Application to Growth, Carcass, and Meat Quality Traits in Pig,” Journal of Animal Science, 93(10), 4617–4623.
Plummer, M., Best, N., Cowles, K., and Vines, K. 2006. “CODA: Convergence Diagnosis and Output Analysis for MCMC,” R News, 6, 7–11.
Raftery, A. and Lewis, S. 1992. “How many iterations in the Gibbs sampler,” In Bayesian Statistics 4, 763–773, Oxford University Press.
Robinson, G. K. 1991. “That BLUP is a Good Thing: The Estimation of Random Effects,” Statistics Science, 6(1), 15–32.
Rosa, G. J., and Valente, B. D. 2013. “BREEDING AND GENETICS SYMPOSIUM: Inferring causal effects from observational data in livestock.” Journal of Animal Science, 91(2), 553–564.
Rosa, G. J., Valente, B. D., de los Campos, G., Wu, X. L., Gianola, D., and Silva, M. A. 2011. “Inferring Causal Phenotype Networks Using Structural Equation Models,” Genetics Selection Evolution, 43, 6–18.
R Development Core Team. 2017. R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.
Sanderson, M., Dargatz, D. A., and Wagner, B. A. 2008. “Risk Factors for Initial Respiratory Disease in United States’ Feedlots based on Producer-collected Daily Morbidity Counts,” Canadian Veterianary Journal, 49(4), 373–378.
Shipley, B. 2002. Cause and Correlation in Biology: A User’s Guide to Path Analysis, Structural Equations and Causal Inference, Cambridge University Press.
Sorensen, D., Andersen, S., Gianola, D., and Korsgaard., I. 1995. “Bayesian-inference in Threshold Models Using Gibbs Sampling, Genetics Selection Evolution, 27(3), 229–249.
Sorensen, D., and Gianola, D. 2002. Likelihood, Bayesian, and MCMC Methods in Quantitative Genetics, New York, Springer-Verlag.
Spiegelhalter, D. J., Best, N. G., Carlin, B. P., and Van Der Linde, A. 2002. “Bayesian Measures of Model Complexity and Fit,” Journal of the Royal Statistical Society: Series B (Statistical Methodology), 64(4), 583–639.
Stroup, W. W. 2013. Generalized Linear Mixed Models, Boca Raton, Florida, CRC Press Taylor & Francis Group.
Tempelman, R. J. 2009. “Invited Review: Assessing Experimental Designs for Research Conducted on Commercial Dairies,” Journal of Dairy Science, 92(1), 1–15.
Valente, B. D., Morota, G., Peñagaricano, F., Gianola, D., Weigel, K., and Rosa, G. J. 2015. “The Causal Meaning of Genomic Predictors and How It Affects Construction and Comparison of Genome-Enabled Selection Models,” Genetics, 200(2), 483–494
Valente, B. D., Rosa, G. J., de los Campos, G., Gianola, D., and Silva, M. A. 2010. “Searching for Recursive Causal Structures in Multivariate Quantitative Genetics Mixed Models,” Genetics, 185(2), 633–644.
Valente, B. D., Rosa G. J., Silva, M. A., Teixeira, R. B., and Torres, R. A. 2011. “Searching for Phenotypic Causal Networks Involving Complex Traits: an Application to European Quail,” Genetics Selection Evolution, 43, 37–48.
Valente, B. D., and Rosa, G. J. 2013. “Mixed Effects Structural Equation Models and Phenotypic Causal Networks.” In Genome-Wide Association Studies and Genomic Prediction, edited by Cedric Gondro, et al., 449–464. Totowa, NJ: Humana Press.
Varona, L., and Sorensen, D. 2014. “Joint Analysis of Binomial and Continuous Traits with a Recursive Model: A Case Study Using Mortality and Litter Size of Pigs,” Genetics, 196(3), 643–651.
Verma, T., and Pearl, J. 1991. “A Theory of Inferred Causation,” In Allen, J. A., Fike, R. snd Sandwall, E. (editors), Principles of Knowledge Representation and Reasoning: Proceedings of the Second International Conference, 441–452, Morgan Kaufmann, San Mateo.
Visscher, P. M., and Goddard, M. E. 1993. “Fixed and Random Contemporary Groups,” Journal of Dairy Science, 76(5), 1444–1454.
Wright, S. 1934. “The Method of Path Coefficients,” The Annals of Mathematical Statistics, 5(3), 161–215.
Wu, X. L., Heringstad, B., Chang, Y. M., de Los Campos, G., and Gianola, D. 2007. “Inferring Relationships between Somatic Cell Score and Milk Yield Using Simultaneous and Recursive models,” Journal of Dairy Science, 90(7), 3508–3521.
Wittum, T. E., Woollen, N. E., Perino, L. J., and Littledike, E. T. 1996. “Relationships among Treatment for Respiratory Tract Disease, Pulmonary Lesions Evident at Slaughter, and Rate of Weight Gain in Feedlot Cattle,” Journal of the American Veterinary Medical Association, 209(4), 814–8.
Yates, F. 1940. “The Recovery of Inter-block Information in Balanced Incomplete Block Designs,” Annals of Eugenics, 10(1), 317–325.
This project was partially funded by the United States Department of Agriculture National Institute of Food and Agriculture Award # 2015-67015-23079. Computing for this project was partially performed on the Beocat Research Cluster at Kansas State University, which is funded in part by NSF Grants CNS-1006860, EPS-1006860 and EPS-0919443.
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Chitakasempornkul, K., Sanderson, M.W., Cha, E. et al. Accounting for Data Architecture on Structural Equation Modeling of Feedlot Cattle Performance. JABES 23, 529–549 (2018). https://doi.org/10.1007/s13253-018-0336-7
- Hierarchical modeling
- Multilevel correlation
- Structural equation models
- Beef cattle