Smoothing Parameter and Model Selection for General Smooth Models

Wood, Simon N.; Pya, Natalya; Säfken, Benjamin

doi:10.1080/01621459.2016.1180986

Cited by 1,017 publications

(920 citation statements)

References 40 publications

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“…8 Alternative models considered included 3 and 4-knot models and free knot models, specifically thin-plate splines and adaptive splines. 9,10 Final model selection was based on the Akaike Information Criteria (AIC). Results from our model identified 2 ranges of values of average annual hospital volume that corresponded to changes in the log hazard ratio (HR).…”

Section: Methodsmentioning

confidence: 99%

The Effect of Hospital Volume on Breast Cancer Mortality

et al. 2018

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Objective The aim of this study was to determine whether hospital volume was associated with mortality in breast cancer, and what thresholds of case volume impacted survival. Background Prior literature has demonstrated improved survival with treatment at high volume centers among less common cancers requiring technically complex surgery. Methods All adults (18 to 90 years) with stages 0–III unilateral breast cancer diagnosed from 2004 to 2012 were identified from the American College of Surgeons National Cancer Data Base (NCDB). A multivariable Cox proportional hazards model with restricted cubic splines was used to examine the association of annual hospital volume and overall survival, after adjusting for measured covariates. Intergroup comparisons of patient and treatment characteristics were conducted with X2 and analysis of variance (ANOVA). The log-rank test was used to test survival differences between groups. A multivariable Cox proportional hazards model was used to estimate hazard ratios (HRs) associated with each volume group. Results One million sixty-four thousand two hundred and fifty-one patients met inclusion criteria. The median age of the sample was 60 (interquartile range 50 to 70). Hospitals were categorized into 3 groups using restricted cubic spline analysis: low-volume (<148 cases/year), moderate-volume (148 to 298 cases/year), and high-volume (>298 cases/year). Treatment at high volume centers was associated with an 11% reduction in overall mortality for all patients (HR 0.89); those with stage 0–I, ER+/PR+ or ER+/PR− breast cancers derived the greatest benefit. Conclusions Treatment at high volume centers is associated with improved survival for breast cancer patients regardless of stage. High case volume could serve as a proxy for the institutional infrastructure required to deliver complex multidisciplinary breast cancer treatment.

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Section: Methodsmentioning

confidence: 99%

The Effect of Hospital Volume on Breast Cancer Mortality

et al. 2018

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“…This suggestion appears to be borne out by our comparative results, displayed in the lower subfigures of Figure 5, for two metrics of predictive performance: The new modified AIC implemented in mgcv, which adjusts the degrees of freedom to account for smoothing parameter uncertainty (Wood et al, 2016). …”

Section: Application: Signature Verificationmentioning

confidence: 80%

“…The new modified AIC implemented in mgcv, which adjusts the degrees of freedom to account for smoothing parameter uncertainty (Wood et al, 2016). …”

Section: Application: Signature Verificationmentioning

confidence: 99%

Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates

Reiß

Miller

et al. 2017

Journal of Computational and Graphical Statistics

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A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This paper introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model.

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“…We show in the results chapter that assuming a Gamma distribution leads to a sufficient variance stabilization in our case and in contrast to Lappi (1997) and Mehtätalo (2004Mehtätalo ( , 2005 we did not model the residual variance explicitly. However, the ongoing development of approaches like gam for location and scale (Wood et al 2016) will allow for a more flexible variance modelling in the future.…”

Section: Methodsmentioning

confidence: 99%

Longitudinal height-diameter curves for Norway spruce, Scots pine and silver birch in Norway based on shape constraint additive regression models

2018

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Background: Generalized height-diameter curves based on a re-parameterized version of the Korf function for Norway spruce (Picea abies (L.) Karst.), Scots pine (Pinus sylvestris L.) and silver birch (Betula pendula Roth) in Norway are presented. The Norwegian National Forest Inventory (NFI) is used as data base for estimating the model parameters. The derived models are developed to enable spatially explicit and site sensitive tree height imputation in forest inventories as well as future tree height predictions in growth and yield scenario simulations. Methods: Generalized additive mixed models (gamm) are employed to detect and quantify potentially non-linear effects of predictor variables. In doing so the quadratic mean diameter serves as longitudinal covariate since stand age, as measured in the NFI, shows only a weak correlation with a stands developmental status in Norwegian forests. Additionally the models can be locally calibrated by predicting random effects if measured height-diameter pairs are available. Based on the model selection of non-constraint models, shape constraint additive models (scam) were fit to incorporate expert knowledge and intrinsic relationships by enforcing certain effect patterns like monotonicity.Results: Model comparisons demonstrate that the shape constraints lead to only marginal differences in statistical characteristics but ensure reasonable model predictions. Under constant constraints the developed models predict increasing tree heights with decreasing altitude, increasing soil depth and increasing competition pressure of a tree. A two-dimensional spatially structured effect of UTM-coordinates accounts for the potential effects of large scale spatially correlated covariates, which were not at our disposal. The main result of modelling the spatially structured effect is lower tree height prediction for coastal sites and with increasing latitude. The quadratic mean diameter affects both the level and the slope of the height-diameter curve and both effects are positive. Conclusions: In this investigation it is assumed that model effects in additive modelling of height-diameter curves which are unfeasible and too wiggly from an expert point of view are a result of quantitatively or qualitatively limited data bases. However, this problem can be regarded not to be specific to our investigation but more general since growth and yield data that are balanced over the whole data range with respect to all combinations of predictor variables are exceptional cases. Hence, scam may provide methodological improvements in several applications by combining the flexibility of additive models with expert knowledge.

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Smoothing Parameter and Model Selection for General Smooth Models

Cited by 1,017 publications

References 40 publications

The Effect of Hospital Volume on Breast Cancer Mortality

The Effect of Hospital Volume on Breast Cancer Mortality

Penalized Nonparametric Scalar-on-Function Regression via Principal Coordinates

Longitudinal height-diameter curves for Norway spruce, Scots pine and silver birch in Norway based on shape constraint additive regression models

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