Best Subset Selection for Eliminating Multicollinearity

Tamura, Ryuta; Kobayashi, Kurima; Takano, Yasunari; Miyashiro, Ryuhei; Nakata, Keiichi; Matsui, Tomomi

doi:10.15807/jorsj.60.321

Cited by 33 publications

(21 citation statements)

References 36 publications

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“…We will also consider modifying our heuristic algorithm to improve the accuracy of the tangent-plane-based approximation. Additionally, MIO approaches to eliminating multicollinearity have been studied in recent years [6], [24], [25], so such methods could be incorporated in our MILO formulation to reduce adverse effects of multicollinearity on the ordered logit model.…”

Section: Resultsmentioning

confidence: 99%

Feature Subset Selection for Ordered Logit Model via Tangent-Plane-Based Approximation

Naganuma

Takano

Miyashiro

2019

IEICE Trans. Inf. & Syst.

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This paper is concerned with a mixed-integer optimization (MIO) approach to selecting a subset of relevant features from among many candidates. For ordinal classification, a sequential logit model and an ordered logit model are often employed. For feature subset selection in the sequential logit model, Sato et al. [22] recently proposed a mixed-integer linear optimization (MILO) formulation. In their MILO formulation, a univariate nonlinear function contained in the sequential logit model was represented by a tangent-line-based approximation. We extend this MILO formulation toward the ordered logit model, which is more commonly used for ordinal classification than the sequential logit model is. Making use of tangent planes to approximate a bivariate nonlinear function involved in the ordered logit model, we derive an MILO formulation for feature subset selection in the ordered logit model. Our computational results verify that the proposed method is superior to the L1-regularized ordered logit model in terms of solution quality.

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Section: Resultsmentioning

confidence: 99%

Feature Subset Selection for Ordered Logit Model via Tangent-Plane-Based Approximation

Naganuma

Takano

Miyashiro

2019

IEICE Trans. Inf. & Syst.

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“…Variables with the strongest covariate relationship were removed from the dataset, strongest first, in an iterative stepwise process, whilst retaining the variables with the strongest univariate relationship with the response variable. To minimise this intercorrelation and prevent masking of trends whilst modelling, data were split into four sub-sets based on the stepwise reduction ( Zuur, Ieno & Elphick, 2010 ; Tamura et al, 2017 ). These four sub-sets were modelled separately to keep variables with strong covariate relationships apart (see Table 2 for the list of variables in each GLM).…”

Section: Methodsmentioning

confidence: 99%

Does bathymetry drive coastal whale shark (Rhincodon typus)aggregations?

Copping

Stewart

McClean

et al. 2018

PeerJ

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BackgroundThe whale shark (Rhincodon typus) is known to aggregate in a number of coastal locations globally, however what causes these aggregations to form where they do is largely unknown. This study examines whether bathymetry is an important driver of coastal aggregation locations for R. typus through bathymetry’s effect on primary productivity and prey availability. This is a global study taking into account all coastal areas within R. typus’ range.MethodsR. typus aggregation locations were identified through an extensive literature review. Global bathymetric data were compared at R. typus aggregation locations and a large random selection of non-aggregation areas. Generalised linear models were used to assess which bathymetric characteristic had the biggest influence on aggregation presence.ResultsAggregation sites were significantly shallower than non-aggregation sites and in closer proximity to deep water (the mesopelagic zone) by two orders of magnitude. Slope at aggregation sites was significantly steeper than non-aggregation sites. These three bathymetric variables were shown to have the biggest association with aggregation sites, with up to 88% of deviation explained by the GLMs.DiscussionThe three key bathymetric characteristics similar at the aggregation sites are known to induce upwelling events, increase primary productivity and consequently attract numerous other filter feeding species. The location of aggregation sites in these key areas can be attributed to this increased prey availability, thought to be the main reason R. typus aggregations occur, extensively outlined in the literature. The proximity of aggregations to shallow areas such as reefs could also be an important factor why whale sharks thermoregulate after deep dives to feed. These findings increase our understanding of whale shark behaviour and may help guide the identification and conservation of further aggregation sites.

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“…For many decades, this approach to regression model building has been extensively used in statistics and econometrics as an appropriate trade-off between time expenditures and model performance [101][102][103]. Nowadays, a stepwise regression model building commonly employs the best subsets approach (BSA) that allows evaluating all possible regression models for a given set of regressors in a timely-effective and accurate manner [104][105][106].…”

Section: Stagementioning

confidence: 99%

Capturing a Complexity of Nutritional, Environmental, and Economic Impacts on Selected Health Parameters in the Russian High North

Tianming

Erokhin

2020

Sustainability

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The rapid pace of economic exploration of the Arctic against the backdrop of progressing environmental change put a high priority on improving understanding of health impacts in the northern communities. Deficiencies in the capability to capture the complexity of health-influencing parameters along with a lack of observations in circumpolar territories present major challenges to establishing credible projections of disease incidence across varying northern environments. It is thus crucial to reveal the relative contributions of coacting factors to provide a basis for sustainable solutions in the sphere of public health. In order to better understand the adverse effects associated with public health, this study employed six-stage multiple regression analysis of incidence rates of fourteen diseases (International Classification of Diseases (ICD-11) codes most widespread in the Russian Arctic) against a set of environmental, nutritional, and economic variables. Variance inflationary factor and best-subsets regression methods were used to eliminate collinearity between the parameters of regression models. To address the diversity of health impacts across northern environments, territories of the Arctic zone of Russia were categorized as (1) industrial sites, (2) urban agglomerations, (3) rural inland, and (4) coastline territories. It was suggested that, in Type 1 territories, public health parameters were most negatively affected by air and water pollution, in Type 2 territories—by low-nutrient diets, in Type 3 and Type 4 territories—by economic factors. It was found that in the Western parts of the Russian Arctic, poor quality of running water along with low access to the quality-assured sources of water might increase the exposure to infectious and parasitic diseases and diseases of the circulatory, respiratory, and genitourinary systems. Low living standards across the Russian Arctic challenged the economic accessibility of adequate diets. In the cities, the nutritional transition to low-quality cheap market food correlated with a higher incidence of digestive system disorders, immune diseases, and neoplasms. In indigenous communities, the prevalence of low diversified diets based on traditional food correlated with the increase in the incidence rates of nutritional and metabolic diseases.

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Best Subset Selection for Eliminating Multicollinearity

Cited by 33 publications

References 36 publications

Feature Subset Selection for Ordered Logit Model via Tangent-Plane-Based Approximation

Feature Subset Selection for Ordered Logit Model via Tangent-Plane-Based Approximation

Does bathymetry drive coastal whale shark (Rhincodon typus)aggregations?

Capturing a Complexity of Nutritional, Environmental, and Economic Impacts on Selected Health Parameters in the Russian High North

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