Abstract
We observe a group of pigs over a period of about 100 days. Using high frequency radio frequency identification, it is recorded when each pig is feeding, leading to very dense binary functional data for each pig and day. One aim of the data analysis is to find pig-specific feeding profiles showing us the typical feeding pattern of each pig. For modeling the data, we use a marginal functional logistic regression approach, allowing us to model the densely observed binary measurements by assuming an underlying smooth subject-specific profile. The method also allows to incorporate additional covariates such as temperature and humidity that may influence the pigs’ behavior. To account for correlation of measurements, we use robust standard errors and corresponding pointwise confidence intervals. Before analyzing the feeding behavior of pigs, the method employed is evaluated in simulation studies. As our approach is rather general, it may also be applied to other types of generalized functional data with similar characteristics as the pig data.
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References
Chen, H., Wang, Y., Paik, M. C., and Choi, H. A. (2013), A marginal approach to reduced-rank penalized spline smoothing with application to multilevel functional data, Journal of the American Statistical Association, 108, 1216–1229.
Crainiceanu, C. M., Staicu, A.-M., Ray, S., and Punjabi, N. (2012), Bootstrap-based inference on the difference in the means of two correlated functional processes, Statistics in Medicine, 31, 3223–3240.
Degras, D. A. (2011), Simultaneous confidence bands for nonparametric regression with functional data, Statistica Sinica, 21, 1735–1765.
Di, C.-Z., Crainiceanu, C., Caffo, B. S., and Punjabi, N. M. (2009) Multilevel functional principal components analysis, The Annals of Applied Statistics, 3, 458–488.
Fahrmeir, L., and Tutz, G. (2001), Multivariate Statistical Modelling Based on Generalized Linear Models, 2nd ed., Springer, New York.
Goldsmith, J., Bobb, J., Crainiceanu, C., Caffo, B., and Reich, D. (2011), Penalized functional regression, Journal of Computational and Graphical Statistics, 20, 830–851.
Goldsmith, J., Greven, S., and Crainiceanu, C. (2013), Corrected confidence bands for functional data using principal components, Biometrics, 69, 41–51.
Goldsmith, J., Zipunnikov, V., and Schrack, J. (2015), Generalized multilevel functional-on-scalar regression and principal components analysis, Biometrics, 71, 344–353.
Greven, S., Crainiceanu, C., Caffo, B., and Reich, D. (2010), Longitudinal functional principal components analysis, Electronic Journal of Statistics, 4, 1022–1054.
Hall, P., Müller, H.-G., and Yao, F. (2008), Modelling sparse generalized longitudinal observations with latent Gaussian processes, Journal of the Royal Statistical Society Series B (Statistical Methodology), 70, 703–723.
Hyun, Y., Ellis, M., McKeith, F. K., and Wilson, E. R. (1997), Feed intake pattern of group-housed growing-finishing pigs monitored using a computerized feed intake recording system, Journal of Animal Science, 75, 1443–1451.
Lee, Y. and Nelder, J. A. (2004), Conditional and marginal models: Another view, Statistical Science, 19, 219–238.
Leisch, F., Weingessel, A., and Hornik, K. (2012), bindata: Generation of Artificial Binary Data. R package version 0.9-19.
Liang, K. Y. and Zeger, S. L. (1986), Longitudinal data analysis using generalized linear models, Biometrika, 73, 13–22.
Marx, B. D. and Eilers, P. H. C. (1999), Generalized linear regression on sampled signals and curves: A p-spline approach, Technometrics, 41, 1–13.
Maselyne, J., Saeys, W., De Ketelaere, B., Mertens, K., Vangeyte, J., Hessel, E. F., Millet, S., and Van Nuffel, A. (2014), Validation of a High Frequency Radio Frequency Identification (HF RFID) system for registering feeding patterns of growing-finishing pigs, Computers and Electronics in Agriculture, 102, 10–18.
R Core Team (2014), R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing, Vienna, Austria.
Ramsay, J. and Silverman, B. (2005), Functional Data Analysis, Springer, New York.
Ruppert, D., Wand, M. P., and Carroll, R. J. (2003), Semiparametric Regression, Cambridge University Press, Cambridge.
Serban, N., Staicu, A.-M., and Carroll, R. J. (2013), Multilevel cross-dependent binary longitudinal data, Biometrics, 69, 903–913.
Tutz, G. and Gertheiss, J. (2010), Feature extraction in signal regression: A boosting technique for functional data regression, Journal of Computational and Graphical Statistics, 19, 154–174.
Usset, J., Staicu, A.-M., and Maity, A. (2013), Interaction models for functional regression. Preprint.
Wang, L., Li, H., and Huang, J. Z. (2008). Variable selection in nonparametric varying-coefficient models for analysis of repeated measurements, Journal of the American Statistical Association, 103, 1556–1569.
Wood, S. N. (2006). Generalized Additive Models: An Introduction with R, Chapman and Hall/CRC, London.
Young, R. J. and Lawrence, A. B. (1994), Feeding behaviour of pigs in groups monitored by a computerized feeding system, Animal Science, 58, 145–152.
Zeger, S. L. and Liang, K. Y. (1986). Longitudinal data analysis for discrete and continuous outcomes, Biometrics, 42, 121–130.
Acknowledgments
The results presented are generated in the framework of the ICT-AGRI era-net project PIGWISE “Optimizing performance and welfare of fattening pigs using HF RFID and synergistic control on individual level” (Call for transnational research projects 2010). The German contribution was funded by the German Federal Office for Agriculture and Food (BLE). Furthermore, we would like to thank two anonymous Reviewers for their helpful comments and constructive criticism which have led to a much improved manuscript.
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Gertheiss, J., Maier, V., Hessel, E.F. et al. Marginal Functional Regression Models for Analyzing the Feeding Behavior of Pigs. JABES 20, 353–370 (2015). https://doi.org/10.1007/s13253-015-0212-7
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DOI: https://doi.org/10.1007/s13253-015-0212-7