Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling

Verbyla, A. P.; Faveri, J. De; Wilkie, John; Lewis, Tom

doi:10.1007/s13253-018-0334-9

Cited by 12 publications

(22 citation statements)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Using the fact that in the one-dimensional case the variance-covariance for a P-spline with B = I n and q = n is proportional to + n , a natural tensor-product extension (Ruppert et al 2003, p. 240) in two dimensions is to fit variance terms for J s ⊗ + k , + s ⊗ J k and + s ⊗ + k , which are mutually orthogonal. For a similar decomposition into main effects and interaction effects see Verbyla et al (2018), Wood et al (2013) and Wood (2017, p. 233). We will have equivalence between LV, RW and P-splines when fitting fixed row and column effects.…”

Section: P-splinesmentioning

confidence: 99%

Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?

Boer

Piepho

Williams

2020

JABES

View full text Add to dashboard Cite

Nearest-neighbour methods based on first differences are an approach to spatial analysis of field trials with a long history, going back to the early work by Papadakis first published in 1937. These methods are closely related to a geostatistical model that assumes spatial covariance to be a linear function of distance. Recently, P-splines have been proposed as a flexible alternative to spatial analysis of field trials. On the surface, P-splines may appear like a completely new type of method, but closer scrutiny reveals intimate ties with earlier proposals based on first differences and the linear variance model. This paper studies these relations in detail, first focussing on one-dimensional spatial models and then extending to the two-dimensional case. Two yield trial datasets serve to illustrate the methods and their equivalence relations. Parsimonious linear variance and random walk models are suggested as a good point of departure for exploring possible improvements of model fit via the flexible P-spline framework.

show abstract

Section: P-splinesmentioning

confidence: 99%

Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?

Boer

Piepho

Williams

2020

JABES

View full text Add to dashboard Cite

show abstract

“…In the mixed model representation this leads to a fixed-effects component, representing an unpenalized part, and a random-effects component, representing the penalized part (Currie and Durbán, 2002;Wand and Omerod, 2008;Lee and Durbán, 2011). The resulting models are very similar to those proposed in Verbyla et al (2018) for smoothing using two covariates based on an integrated squared second derivative penalty used in cubic spline smoothing; but, as will be explained, there are slight differences in the way the unpenalized terms are handled. As our main impetus for this paper is to provide a P-spline framework that is conveniently implemented in a general REML-based mixed model package, we closely follow the philosophy set out in Wood et al (2013), primarily focussing on such penalties that have just a single parameter and upon conversion give rise to a variance-covariance matrix that is linear in the parameters.…”

Section: Introductionmentioning

confidence: 91%

“…For example, , the covariance structure would change, i.e., the model is not invariant to linear transformations with respect to c X , as is well known for random-coefficient models (Longford, 1993;Wolfinger, 1996). Also note that our suggestion here involves fitting a single penalty for both columns of c X , rather than two, as is commonly done (Wood et al, 2013;Verbyla et al, 2018). Fitting two separate penalties for X .…”

mentioning

confidence: 98%

Tensor P-Spline Smoothing for Spatial Analysis of Plant Breeding Trials

Piepho

Boer

2021

Preprint

View full text Add to dashboard Cite

Large agricultural field trials may display irregular spatial trends that cannot be fully captured by a purely randomization-based analysis. For this reason, paralleling the development of analysis-of-variance procedures for randomized field trials, there is a long history of spatial modelling for field trials, starting with the early work of Papadakis on nearest neighbour analysis, which can be cast in terms of first or second differences among neighbouring plot values. This kind of spatial modelling is amenable to a natural extension using P-splines, as has been demonstrated in recent publications in the field. Here, we consider the P-spline framework, focussing on model options that are easy to implement in linear mixed model packages. Two examples serve to illustrate and evaluate the methods. A key conclusion is that first differences are rather competitive with second differences. A further key observation is that second differences require special attention regarding the representation of the null space of the smooth terms for spatial interaction, and that an unstructured variance-covariance structure is required to ensure invariance to translation and rotation of eigenvectors associated with that null space. We develop a strategy that permits fitting this model with ease, but the approach is more demanding than that needed for fitting models using first differences. Hence, even though in other areas second differences are very commonly used in the application of P-splines, our main conclusion is that with field trials first differences have advantages for routine use.

show abstract

“…There are several approaches for spatiotemporal modelling of environmental data that could be used here. As we are using splines for modelling both the temporal and the spatial dimension, the most immediate option would be to use three-dimensional tensor spline smoothing (Wood, 2017;Verbyla et al, 2018;Pérez et al, 2020). However, most of these are rather more complex and computationally demanding and as such less suited for a seamless implementation for routine analysis.…”

Section: Limitations Of Processing In Stagesmentioning

confidence: 99%

Phenomics data processing: A plot-level model for repeated measurements to extract the timing of key stages and quantities at defined time points

Roth

Rodríguez‐Álvarez

Eeuwijk

et al. 2021

Preprint

View full text Add to dashboard Cite

Decision-making in breeding increasingly depends on the ability to capture and predict crop responses to changing environmental factors. Advances in crop modeling as well as high-throughput field phenotyping (HTFP) hold promise to provide such insights. Processing HTFP data is an interdisciplinary task that requires broad knowledge on experimental design, measurement techniques, feature extraction, dynamic trait modeling, and prediction of genotypic values using statistical models. To get an overview of sources of variations in HTFP, we develop a general plot-level model for repeated measurements. Based on this model, we propose a seamless stage-wise process that allows to carry on estimated means and variances from stage to stage and approximates the gold standard of a single-stage analysis. The process builds on the extraction of three intermediate trait categories; (1) timing of key stages, (2) quantities at defined time points or periods, and (3) dose-response curves. In a first stage, these intermediate traits are extracted from low-level traits' time series (e.g., canopy height) using P-splines and the quarter of maximum elongation rate method (QMER), as well as final height percentiles. In a second and third stage, extracted traits are further processed using a stage-wise linear mixed model analysis. Using a wheat canopy growth simulation to generate canopy height time series, we demonstrate the suitability of the stage-wise process for traits of the first two above-mentioned categories. Results indicate that, for the first stage, the P-spline/QMER method was more robust than the percentile method. In the subsequent two-stage linear mixed model processing, weighting the second and third stage with error variance estimates from the previous stages improved the root mean squared error. We conclude that processing phenomics data in stages represents a feasible approach if using appropriate weighting through all stages. P-splines in combination with the QMER method are suitable tools to extract timing of key stages and quantities at defined time points from HTFP data.

show abstract

Tensor Cubic Smoothing Splines in Designed Experiments Requiring Residual Modelling

Cited by 12 publications

References 35 publications

Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?

Linear Variance, P-splines and Neighbour Differences for Spatial Adjustment in Field Trials: How are they Related?

Tensor P-Spline Smoothing for Spatial Analysis of Plant Breeding Trials

Phenomics data processing: A plot-level model for repeated measurements to extract the timing of key stages and quantities at defined time points

Contact Info

Product

Resources

About