Mini-models – Local Regression Models for the Function Approximation Learning

2012 ◽  
pp. 160-167 ◽  
Author(s):  
Marcin Pluciński
Keyword(s):  
Function Approximation ◽  
Regression Models ◽  
Local Regression

scholarly journals Exploring spatial nonstationary environmental effects on Yellow Perch distribution in Lake Erie

PeerJ ◽  
2019 ◽  
Vol 7 ◽  
pp. e7350
Author(s):  
Changdong Liu ◽  
Junchao Liu ◽  
Yan Jiao ◽  
Yanli Tang ◽  
Kevin B. Reid
Keyword(s):  
Environmental Effects ◽  
Geographically Weighted Regression ◽  
Regression Models ◽  
Yellow Perch ◽  
Lake Erie ◽  
Regression Coefficients ◽  
Weighted Regression ◽  
Local Regression ◽  
Spatially Varying ◽  
Spatial Locations

Background Global regression models under an implicit assumption of spatial stationarity were commonly applied to estimate the environmental effects on aquatic species distribution. However, the relationships between species distribution and environmental variables may change among spatial locations, especially at large spatial scales with complicated habitat. Local regression models are appropriate supplementary tools to explore species-environment relationships at finer scales. Method We applied geographically weighted regression (GWR) models on Yellow Perch in Lake Erie to estimate spatially-varying environmental effects on the presence probabilities of this species. Outputs from GWR were compared with those from generalized additive models (GAMs) in exploring the Yellow Perch distribution. Local regression coefficients from the GWR were mapped to visualize spatially-varying species-environment relationships. K-means cluster analyses based on the t-values of GWR local regression coefficients were used to characterize the distinct zones of ecological relationships. Results Geographically weighted regression resulted in a significant improvement over the GAM in goodness-of-fit and accuracy of model prediction. Results from the GWR revealed the magnitude and direction of environmental effects on Yellow Perch distribution changed among spatial locations. Consistent species-environment relationships were found in the west and east basins for adults. The different kinds of species-environment relationships found in the central management unit (MU) implied the variation of relationships at a scale finer than the MU. Conclusions This study draws attention to the importance of accounting for spatial nonstationarity in exploring species-environment relationships. The GWR results can provide support for identification of unique stocks and potential refinement of the current jurisdictional MU structure toward more ecologically relevant MUs for the sustainable management of Yellow Perch in Lake Erie.

scholarly journals Mobile Proximal Sensing with Visible and Near Infrared Spectroscopy for Digital Soil Mapping

Soil Systems ◽  
2020 ◽  
Vol 4 (3) ◽  
pp. 40
Author(s):  
Masakazu Kodaira ◽  
Sakae Shibusawa
Keyword(s):  
Soil Properties ◽  
Regression Models ◽  
Near Infrared ◽  
Soil Property ◽  
Coefficient Of Determination ◽  
Clay Loam ◽  
Soil Maps ◽  
Local Regression ◽  
Predicted Values ◽  
Digital Soil Maps

The objective of this study was to estimate multiple soil property local regression models, confirm the accuracy of the predicted values using visible near-infrared subsurface diffuse reflectance spectra collected by a mobile proximal soil sensor, and show that digital soil maps predicted by multiple soil property local regression models are able to visualize empirical knowledge of the grower. The parent materials in the experimental fields were light clay, clay loam, and sandy clay loam. The study was conducted in Saitama Prefecture, Japan. To develop local regression models for the 30 chemical and 4 physical properties, a total of 231 samples were collected; to evaluate accuracy of prediction, 65 samples were collected. The local regression models were developed using 2nd derivative pretreatment by the Savitzky–Golay algorithm and partial least squares regression. The local regression models were evaluated using the coefficient of determination (R2), residual prediction deviation (RPD), range error ratio (RER), and the ratio of prediction error to interquartile range (RPIQ). The R2 accuracy of the 34 local regression models was 0.81 or higher. In the predicted values for 65 unknown samples, the local regression models could ‘distinguish between high and low’ for 3 of the 34 soil properties, but were ‘not useful’ as absolute quantitative values for the other 31 soil properties. However, it was confirmed that the predicted values followed the transition in measured values, and thus that the developed 34 regression models could be used for generating digital soil maps based on relative quantitative values. The grower changed the ridge direction in the field from east–west to north–south just looking at the digital soil maps.

Local Regression Models

2017 ◽  
pp. 309-376 ◽  
Author(s):  
William S. Cleveland ◽  
Eric Grosse ◽  
William M. Shyu
Keyword(s):  
Regression Models ◽  
Local Regression

scholarly journals Exploring spatial nonstationary environmental effects on species distribution: a case study of Yellow Perch in Lake Erie

2019 ◽  
Author(s):  
Changdong Liu ◽  
Junchao Liu ◽  
Yan Jiao ◽  
Yanli Tang
Keyword(s):  
Species Distribution ◽  
Environmental Effects ◽  
Regression Models ◽  
Yellow Perch ◽  
Lake Erie ◽  
Management Unit ◽  
Regression Coefficients ◽  
Local Regression ◽  
Global Regression ◽  
Spatially Varying

Background: Global regression models under an implicit assumption of spatial stationarity were commonly applied to estimate the environmental effects on aquatic species distribution. However, the relationships between species distribution and environmental variables may change among spatial locations, especially at large spatial scales with complicated habitat. Local regression models are appropriate supplementary tools to explore species-environment relationships at finer scales. Method: We applied geographically weighted regression (GWR) models on Yellow Perch in Lake Erie to estimate spatially-varying environmental effects on the presence probabilities of this species. Outputs from GWR were compared with those from generalized additive models (GAMs) in exploring the Yellow Perch distribution. Local regression coefficients from the GWR were mapped to visualize spatially-varying species-environment relationships. K-means cluster analyses based on the t-values of GWR local regression coefficients were used to characterize the distinct zones of ecological relationships. Results: GWR resulted in a significant improvement over the GAM in goodness-of-fit and accuracy of model prediction. Results from the GWR revealed the magnitude and direction of environmental effects on Yellow Perch distribution changed among spatial location. Consistent species-environment relationships were found in the east basin for juveniles and in the west and east basins for adults. The different kinds of species-environment relationships found in the central management unit implied the variation of relationships at a scale finer than the management unit. Conclusions: This study draws attention to the importance of accounting for spatial nonstationarity in exploring species-environment relationships. The superiority of GWR over the GAM highlights the limitations of using one global regression model to explore species-environment relationships at a large spatial scale and provides insights for managing Yellow Perch at finer scales.

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