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Linear Splines (linear + spline)

Distribution by Scientific Domains

Medical Sciences	71%

Selected Abstracts

Bayesian regression with multivariate linear splines

JOURNAL OF THE ROYAL STATISTICAL SOCIETY: SERIES B (STATISTICAL METHODOLOGY), Issue 1 2001
C. C. Holmes
We present a Bayesian analysis of a piecewise linear model constructed by using basis functions which generalizes the univariate linear spline to higher dimensions. Prior distributions are adopted on both the number and the locations of the splines, which leads to a model averaging approach to prediction with predictive distributions that take into account model uncertainty. Conditioning on the data produces a Bayes local linear model with distributions on both predictions and local linear parameters. The method is spatially adaptive and covariate selection is achieved by using splines of lower dimension than the data. [source]

Selection of locations of knots for linear splines in random regression test-day models

JOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 2 2010
J. Jamrozik
Summary Using spline functions (segmented polynomials) in regression models requires the knowledge of the location of the knots. Knots are the points at which independent linear segments are connected. Optimal positions of knots for linear splines of different orders were determined in this study for different scenarios, using existing estimates of covariance functions and an optimization algorithm. The traits considered were test-day milk, fat and protein yields, and somatic cell score (SCS) in the first three lactations of Canadian Holsteins. Two ranges of days in milk (from 5 to 305 and from 5 to 365) were taken into account. In addition, four different populations of Holstein cows, from Australia, Canada, Italy and New Zealand, were examined with respect to first lactation (305 days) milk only. The estimates of genetic and permanent environmental covariance functions were based on single- and multiple-trait test-day models, with Legendre polynomials of order 4 as random regressions. A differential evolution algorithm was applied to find the best location of knots for splines of orders 4 to 7 and the criterion for optimization was the goodness-of-fit of the spline covariance function. Results indicated that the optimal position of knots for linear splines differed between genetic and permanent environmental effects, as well as between traits and lactations. Different populations also exhibited different patterns of optimal knot locations. With linear splines, different positions of knots should therefore be used for different effects and traits in random regression test-day models when analysing milk production traits. [source]

Properties of random regression models using linear splines

JOURNAL OF ANIMAL BREEDING AND GENETICS, Issue 2 2006
I. Misztal
Summary Properties of random regression models using linear splines (RRMS) were evaluated with respect to scale of parameters, numerical properties, changes in variances and strategies to select the number and positions of knots. Parameters in RRMS are similar to those in multiple trait models with traits corresponding to points at knots. RRMS have good numerical properties because of generally superior numerical properties of splines compared with polynomials and sparser system of equations. These models also contain artefacts in terms of depression of variances and predictions in the middle of intervals between the knots, and inflation of predictions close to knots; the artefacts become smaller as correlations corresponding to adjacent knots increase. The artefacts can be greatly reduced by a simple modification to covariables. With the modification, the accuracy of RRMS increases only marginally if the correlations between the adjacent knots are ,0.6. In practical analyses the knots for each effect in RRMS can be selected so that: (i) they cover the entire trajectory; (ii) changes in variances in intervals between the knots are approximately linear; and (iii) the correlations between the adjacent knots are at least 0.6. RRMS allow for simple and numerically stable implementations of genetic evaluations with artefacts present but transparent and easily controlled. [source]

Bayesian regression with multivariate linear splines

The Cinderella of public health news: physical activity coverage in Australian newspapers, 1986-2006

AUSTRALIAN AND NEW ZEALAND JOURNAL OF PUBLIC HEALTH, Issue 2 2009
Josephine Chau
Abstract Objective: This research examined trends in physical activity reporting by Australian newspapers, and described these trends compared to coverage of obesity and tobacco. Method: The Factiva database was searched for articles published in major Australian metropolitan newspapers (1986-2006) that mentioned physical activity, obesity or tobacco smoking. Standardised frequencies compared the three health issues, and trends in reporting were estimated by using standard multiple regression models to fit linear splines with fixed knots at years 1991, 1996 and 2001 to the standardised data. Results: Physical activity received the least coverage 1986-2006, appearing in 4,988 articles, compared with 15,410 and 63,738 articles for obesity and tobacco respectively. Between 1996 and 2000, there were significant increases in the rate of coverage of physical activity (,=0.21; p<0.01), obesity (,=0.13; p<0.01) and tobacco (,=0.24; p<0.0001). From 2001 to 2006 the rate of physical activity coverage was relatively steady, while the obesity coverage rate increased dramatically (,=0.34; p<0.0001), and tobacco coverage rate slowed (,=-0.33; p<0.0001). Conclusions: This study demonstrates that physical activity reporting in the media has increased, but received less attention than obesity and tobacco. Implications: Physical activity advocates face the challenge of highlighting the newsworthiness of physical activity and raising the issue higher on the public agenda. [source]