Extended Linear Modeling with Splines

Huang, Jianhua Z.; Stone, Charles J.

doi:10.1007/978-0-387-21579-2_12

Cited by 7 publications

(7 citation statements)

References 24 publications

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“…Perhaps the largest change was the increased growth rate of chickens that resulted from selective breeding and improvements to diet. Havenstein et al (2003), for example, showed that compared to chickens from 1957 fed 1957-type diets, chickens from 2001 fed 2001-type diets, were approximately four times larger at various time points post hatch. In practice, the increased growth rate translated to decreased time to slaughter, shortened from an average of several months in 1960 to an average of about six weeks today.…”

Section: Discussionmentioning

confidence: 99%

“…Extended linear modeling is a generalization of a linear model that uses splines, or piece-wise polynomials, to model nonlinear relationships between model predictors and responses (Huang and Stone 2003). Extended linear modeling is more appropriate for this study than traditional linear modeling, because the effect of time on leukosis condemnation is expected to be nonlinear due to changes in farm practices, chicken life history, and pathogen virulence.…”

Section: Methodsmentioning

confidence: 99%

“…Extended linear modeling is more appropriate for this study than traditional linear modeling, because the effect of time on leukosis condemnation is expected to be nonlinear due to changes in farm practices, chicken life history, and pathogen virulence. Extended linear modeling, just like traditional linear modeling, can readily be used for hypothesis testing (Huang and Stone 2003). The drawback of extended linear modeling, however, is that effect sizes are often difficult to interpret, because they act on spline-transformed predictors, rather than on the measured predictors themselves.…”

Section: Methodsmentioning

confidence: 99%

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An observational study of the temporal and spatial patterns of Marek's-disease-associated leukosis condemnation of young chickens in the United States of America

Kennedy

Dunn

et al. 2015

Preventive Veterinary Medicine

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Marek’s disease, a disease primarily affecting immature chickens, is a worldwide problem that has on at least three occasions threatened the poultry industry in the United States. A rich dataset to study the epidemiology of this disease is available because the United States Department of Agriculture has required mandatory inspections of all commercially sold poultry of significant scale since the mid-20th century with over 99% of all chickens inspected. This dataset includes monthly totals aggregated by state since 1961 of the number of “young chickens” inspected and the number with “leukosis”, a condemnation category that is almost always associated with Marek’s disease in this category of birds. The objective of this study was to analyze temporal and spatial patterns in this condemnation data to gain insight into the ecology and epidemiology of the causative virus. We extracted visual patterns in the data using seasonal trend decomposition, and we tested for statistical significance using extended linear modeling techniques. The analysis confirmed previous findings that there are differences in leukosis condemnation rates between states, across years, and within years. The analysis also revealed several patterns not previously highlighted, including spatial and temporal autocorrelations in leukosis condemnation, changes to the amplitude of seasonality over time, and increasing within-year variation in condemnation rate over time. These patterns suggest that locally shared farm practices, virus transmission between farms, or viral persistence may be important to understanding the dynamics of the disease. We also discuss the plausibility of other potential explanations for these patterns.

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Section: Discussionmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

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An observational study of the temporal and spatial patterns of Marek's-disease-associated leukosis condemnation of young chickens in the United States of America

Kennedy

Dunn

et al. 2015

Preventive Veterinary Medicine

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“…The basis functions are smooth, often piecewise polynomials of degree d between the user-specified knots, with d − 1 continuous derivatives. The optimal convergence rate is attained; Huang and Stone (2002) provide a nice discussion of the trade-off between estimation error and approximation error in choosing the number SHAPE-RESTRICTED REGRESSION SPLINES 3 of knots. The set of linear combinations of the basis functions typically provides more than enough flexibility to fit a scatterplot; in fact, in the absense of shape restrictions, the flexibility for a rather small number of knots is so great that most of the regression spline literature concerns guarding against the over-fitting of data.…”

mentioning

confidence: 99%

Inference using shape-restricted regression splines

Meyer¹

2008

Ann. Appl. Stat.

164

171

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Regression splines are smooth, flexible, and parsimonious nonparametric function estimators. They are known to be sensitive to knot number and placement, but if assumptions such as monotonicity or convexity may be imposed on the regression function, the shape-restricted regression splines are robust to knot choices. Monotone regression splines were introduced by Ramsay [Statist. Sci. 3 (1998) 425--461], but were limited to quadratic and lower order. In this paper an algorithm for the cubic monotone case is proposed, and the method is extended to convex constraints and variants such as increasing-concave. The restricted versions have smaller squared error loss than the unrestricted splines, although they have the same convergence rates. The relatively small degrees of freedom of the model and the insensitivity of the fits to the knot choices allow for practical inference methods; the computational efficiency allows for back-fitting of additive models. Tests of constant versus increasing and linear versus convex regression function, when implemented with shape-restricted regression splines, have higher power than the standard version using ordinary shape-restricted regression.Comment: Published in at http://dx.doi.org/10.1214/08-AOAS167 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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“…Collection date was fit as two continuous factors, one the sine and one the cosine of 2π/365 times the calendar day that a sample was collected, to capture seasonal variation (28). Bird age was fit as a categorical factor using a spline with knots at cohort ages of 21, 42, 100, and 315 days (20,21). The spline was generated using the 'bs' function in the package "splines".…”

Section: Analysis Of the Cross-sectional Datamentioning

confidence: 99%