Practical variable selection for generalized additive models

Marra, Giampiero; Wood, Simon N.

doi:10.1016/j.csda.2011.02.004

Cited by 629 publications

(493 citation statements)

References 32 publications

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“…Variable selection was done in three steps. In the first step, double penalty selection was performed on the smooth terms [22]. In the second step, AIC backwards selection was done for the parametric terms.…”

Section: Statistical Si-modelmentioning

confidence: 99%

Possibilities and Limitations of Spatially Explicit Site Index Modelling for Spruce Based on National Forest Inventory Data and Digital Maps of Soil and Climate in Bavaria (SE Germany)

Brandl

Falk

Klemmt

et al. 2014

Forests

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Combining national forest inventory (NFI) data with digital site maps of high resolution enables spatially explicit predictions of site productivity. The aim of this study is to explore the possibilities and limitations of this database to analyze the environmental dependency of height-growth of Norway spruce and to predict site index (SI) on a scale that is relevant for local forest management. The study region is the German federal state of Bavaria. The exploratory methods comprise significance tests and hypervolume-analysis. SI is modeled with a Generalized Additive Model (GAM). In a second step the residuals are modeled using Boosted Regression Trees (BRT). The interaction between temperature regime and water supply strongly determined height growth. At sites with very similar temperature regime and water supply, greater heights were reached if the depth gradient of base saturation was favorable. Statistical model criteria (Double Penalty Selection, AIC) preferred composite variables for water supply OPEN ACCESSForests 2014, 5 2627 and the supply of basic cations. The ability to predict SI on a local scale was limited due to the difficulty to integrate soil variables into the model.

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Section: Statistical Si-modelmentioning

confidence: 99%

Possibilities and Limitations of Spatially Explicit Site Index Modelling for Spruce Based on National Forest Inventory Data and Digital Maps of Soil and Climate in Bavaria (SE Germany)

Brandl

Falk

Klemmt

et al. 2014

Forests

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“…This approach achieves model selection without involving inference of the estimates. Marra and Wood (2011) present an extensive discussion about the variable selection for the penalized regression splines and provide guidance regarding its implementation for mgcv users.…”

Section: Mixed Effects Model Framework Of Penalized Regression Splinementioning

confidence: 99%

“…Here, we cannot discriminate between the linear and the insignificant effects because the linear term is in the penalty null space, which means that the minimum value for the EDF is 1 for both the linear and insignificant effects. We employ a shrinkage method (Marra and Wood, 2011) as variable selection and it allows the discrimination. For variable selection we replace zero values in the penalty matrix S l in Eq.…”

Section: Mixed Effects Model Framework Of Penalized Regression Splinementioning

confidence: 99%

Trends in stratospheric ozone profiles using functional mixed models

2013

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Abstract. This paper is devoted to the modeling of altitudedependent patterns of ozone variations over time. Umkehr ozone profiles (quarter of Umkehr layer) from 1978 to 2011 are investigated at two locations: Boulder (USA) and Arosa (Switzerland). The study consists of two statistical stages. First we approximate ozone profiles employing an appropriate basis. To capture primary modes of ozone variations without losing essential information, a functional principal component analysis is performed. It penalizes roughness of the function and smooths excessive variations in the shape of the ozone profiles. As a result, data-driven basis functions (empirical basis functions) are obtained. The coefficients (principal component scores) corresponding to the empirical basis functions represent dominant temporal evolution in the shape of ozone profiles. We use those time series coefficients in the second statistical step to reveal the important sources of the patterns and variations in the profiles. We estimate the effects of covariates -month, year (trend), quasibiennial oscillation, the solar cycle, the Arctic oscillation, the El Niño/Southern Oscillation cycle and the Eliassen-Palm flux -on the principal component scores of ozone profiles using additive mixed effects models. The effects are represented as smooth functions and the smooth functions are estimated by penalized regression splines. We also impose a heteroscedastic error structure that reflects the observed seasonality in the errors. The more complex error structure enables us to provide more accurate estimates of influences and trends, together with enhanced uncertainty quantification. Also, we are able to capture fine variations in the time evolution of the profiles, such as the semi-annual oscillation. We conclude by showing the trends by altitude over Boulder and Arosa, as well as for total column ozone. There are great variations in the trends across altitudes, which highlights the benefits of modeling ozone profiles.

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“…For selecting environmental variables for each GAM, we used a shrinkage approach (Roberts et al, 2016;Mannocci et al, 2017). In addition to the shrinkage approach, we applied an extra penalty to each environmental covariate as the smoothing parameter approached zero, which allowed its removal when the smoothing parameter was equal to zero (Marra and Wood, 2011;Drexler and Ainsworth, 2013;Grüss et al, 2014). Once a GAM was fitted, if an environmental covariate p-value had a p > 0.05, it was removed and the model was refitted (Koubbi et al, 2006;Weber and McClatchie, 2010;Grüss et al, 2014Grüss et al, , 2016dGrüss et al, , 2017aChagaris et al, 2015).…”

Section: Surface Salinity Unitless Terrain Ruggedness Index Unitlessmentioning

confidence: 99%

Producing Distribution Maps for a Spatially-Explicit Ecosystem Model Using Large Monitoring and Environmental Databases and a Combination of Interpolation and Extrapolation

et al. 2018

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To be able to simulate spatial patterns of predator-prey interactions, many spatially-explicit ecosystem modeling platforms, including Atlantis, need to be provided with distribution maps defining the annual or seasonal spatial distributions of functional groups and life stages. We developed a methodology combining extrapolation and interpolation of the predictions made by statistical habitat models to produce distribution maps for the fish and invertebrates represented in the Atlantis model of the Gulf of Mexico (GOM) Large Marine Ecosystem (LME) ("Atlantis-GOM"). This methodology consists of: (1) compiling a large monitoring database, gathering all the fisheries-independent and fisheries-dependent data collected in the northern (U.S.) GOM since 2000; (2) compiling a large environmental database, storing all the environmental parameters known to influence the spatial distribution patterns of fish and invertebrates of the GOM; (3) fitting binomial generalized additive models (GAMs) to the large monitoring and environmental databases, and geostatistical binomial generalized linear mixed models (GLMMs) to the large monitoring database; and (4) employing GAM predictions to infer spatial distributions in the southern GOM, and GLMM predictions to infer spatial distributions in the U.S. GOM. Thus, our methodology allows for reasonable extrapolation in the southern GOM based on a large amount of monitoring and environmental data, and for interpolation in the U.S. GOM accurately reflecting the probability of encountering fish and invertebrates in that region. We used an iterative cross-validation procedure to validate GAMs. When a GAM did not pass the validation test, we employed a GAM for a related functional group/life stage to generate distribution maps for the southern GOM. In addition, no geostatistical GLMMs were fit for the functional groups and life stages whose depth, longitudinal and latitudinal ranges within the U.S. GOM are not entirely covered by the data from the large monitoring database; for those, only GAM predictions were employed to obtain distribution maps for Atlantis-GOM. Pearson residuals were Grüss et al.Maps for an Ecosystem Model computed to validate geostatistical binomial GLMMs. Ultimately, 53 annual maps and 64 seasonal maps (for 32 different functional groups/life stages) were produced for Atlantis-GOM. Our methodology could serve other world's regions characterized by a large surface area, particularly LMEs bordered by several countries.

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Practical variable selection for generalized additive models

Cited by 629 publications

References 32 publications

Possibilities and Limitations of Spatially Explicit Site Index Modelling for Spruce Based on National Forest Inventory Data and Digital Maps of Soil and Climate in Bavaria (SE Germany)

Possibilities and Limitations of Spatially Explicit Site Index Modelling for Spruce Based on National Forest Inventory Data and Digital Maps of Soil and Climate in Bavaria (SE Germany)

Trends in stratospheric ozone profiles using functional mixed models

Producing Distribution Maps for a Spatially-Explicit Ecosystem Model Using Large Monitoring and Environmental Databases and a Combination of Interpolation and Extrapolation

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