A new robust model selection method in GLM with application to ecological data

Sakate, D. M.; Kashid, D. N.

doi:10.1186/s40068-016-0060-7

Cited by 4 publications

(7 citation statements)

References 28 publications

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“…To select a single optimal model from reduced model space, either from

A_{r}

A_{r}^{k}

, an information criterion can be used. For example, in our empirical work we use the Robust Deviance Based Criterion (RDBC) by Sakate & Kashid (2016) and select an optimal model through

\hat{α} = min_{α \in {scriptA}_{r}^{k}} RDBC false(α false) = min_{α \in {scriptA}_{r}^{k}} false[λ_{α} + C (n, p_{α}) false],

where the penalty term is chosen to be C ( n , p α )= p α ( log ( n )+1). Again we stress that the particular choice of criterion is not the focus of this article and in practice other choices may be preferred and may enjoy better performance depending on particular aspects of the data analysed.…”

Section: Robstab: a Robust And Fast Feature Stability Frameworkmentioning

confidence: 99%

“…We also note that the above criterion relies on the penalty term C ( n , p α ). We utilise the penalty term suggested by Sakate & Kashid (2016) and attempting to improve said measure is beyond the scope of this paper.…”

Section: Robstab: a Robust And Fast Feature Stability Frameworkmentioning

confidence: 99%

“…In all simulation settings: The design matrix,

X \in {double-struckR}^{n \times p}

is sampled from a N(0,Σ) distribution and held fixed across all simulation repeats. The response vector

Y \in {double-struckR}^{n}

is then generated by first estimating the probabilities of each observation,

π_{i} = g^{- 1} false(x_{i}^{⊤} bold-italicβ false)

. We consider Poisson GLMs with log‐links and calculate expected values

π_{i} = \log^{- 1} false(x_{i}^{⊤} bold-italicβ false)

to then generate the response vector Y by randomly drawing elements from a Pois( π i ) distribution. We introduce outliers into the data by altering the underlying response probabilities as further described below. We repeat each simulation 100 times and in each run we evaluate the performance of RobStab and compare it to a range of different methods. • Exhaustive search when p ≤15: We consider exhaustive searches using AIC (Akaike 1973), BIC (Schwarz 1978) and RDBC (Sakate & Kashid 2016). Exhaustive search is limited to p ≤15 because of current restrictions in the bestglm package (Mcleod et al .…”

Section: Simulationsmentioning

confidence: 99%

“…Recently, more classical methods of GLM variable selection have been brought into the robust space, however this literature is relatively scattered and sparse. Notable contributions to the robust selection of GLMs include the following: Müller & Welsh (2009) proposes an exhaustive but computationally slow k ‐out‐of‐ n stratified bias‐adjusted bootstrap model selection method; Guo, Yang & Lv (2017) uses smooth‐threshold estimating equations and a bounded exponential score function to deal with a diverging number of parameters; robust penalised estimators are used in Avella‐Medina & Ronchetti (2018) and Wang & Wang (2014) to deal with high‐dimensional GLMs; Sakate & Kashid (2016) introduces the idea of a robust deviance based criterion which builds on the work of Cantoni & Ronchetti (2001). There is a need for robust methods that can perform fast exhaustive searches.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Robust subtractive stability measures for fast and exhaustive feature importance ranking and selection in generalised linear models

Smith

Guennewig

Müller

2022

Aus NZ J of Statistics

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We introduce the relatively new concept of subtractive lack-of-fit measures in the context of robust regression, in particular in generalised linear models. We devise a fast and robust feature selection framework for regression that empirically enjoys better performance than other selection methods while remaining computationally feasible when fully exhaustive methods are not. Our method builds on the concepts of model stability, subtractive lack-of-fit measures and repeated model identification. We demonstrate how the multiple implementations add value in a robust regression type context, in particular through utilizing a combination of robust regression coefficient and scale estimates. Through resampling, we construct a robust stability matrix, which contains multiple measures of feature importance for each variable. By constructing this stability matrix and using it to rank features based on importance, we are able to reduce the candidate model space and then perform an exhaustive search on the remaining models. We also introduce two different visualisations to better convey information held within the stability matrix; a subtractive Mosaic Probability Plot and a subtractive Variable Inclusion Plot. We demonstrate how these graphics allow for a better understanding of how variable importance changes under small alterations to the underlying data. Our framework is made available in R through the RobStabR package.

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“…To select a single optimal model from reduced model space, either from

A_{r}

A_{r}^{k}

, an information criterion can be used. For example, in our empirical work we use the Robust Deviance Based Criterion (RDBC) by Sakate & Kashid (2016) and select an optimal model through

\hat{α} = min_{α \in {scriptA}_{r}^{k}} RDBC false(α false) = min_{α \in {scriptA}_{r}^{k}} false[λ_{α} + C (n, p_{α}) false],

Section: Robstab: a Robust And Fast Feature Stability Frameworkmentioning

confidence: 99%

Section: Robstab: a Robust And Fast Feature Stability Frameworkmentioning

confidence: 99%

“…In all simulation settings: The design matrix,

X \in {double-struckR}^{n \times p}

is sampled from a N(0,Σ) distribution and held fixed across all simulation repeats. The response vector

Y \in {double-struckR}^{n}

is then generated by first estimating the probabilities of each observation,

π_{i} = g^{- 1} false(x_{i}^{⊤} bold-italicβ false)

. We consider Poisson GLMs with log‐links and calculate expected values

π_{i} = \log^{- 1} false(x_{i}^{⊤} bold-italicβ false)

Section: Simulationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robust subtractive stability measures for fast and exhaustive feature importance ranking and selection in generalised linear models

Smith

Guennewig

Müller

2022

Aus NZ J of Statistics

View full text Add to dashboard Cite

show abstract

“…Proper selection of SDM can significantly increase the efficiency of prediction. Selecting a specific model needs to provide justifiable criteria as it can affect the result (Sakate and Kashid 2016). However, in most cases, models are selected without providing significant justification.…”

Section: Challenges In the Combination Of Eo And Climate Datasetsmentioning

confidence: 99%

Integration of remote sensing and bioclimatic data for prediction of invasive species distribution in data-poor regions: a review on challenges and opportunities

2020

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Prediction and modeling using integrated datasets and expertise from various disciplines greatly improve the management of invasive species. So far several attempts have been made to predict, handle, and mitigate invasive alien species impacts using specific efforts from various disciplines. Yet, the most persuasive approach is to better control its invasion and subsequent expansion by making use of cross-disciplinary knowledge and principles. However, the information in this regard is limited and experts from several disciplines have sometimes difficulties understanding well each other. In this respect, the focus of this review was to overview challenges and opportunities in integrating bioclimatic, remote sensing variables, and species distribution models (SDM) for predicting invasive species in data-poor regions. Google Scholar search engine was used to collect relevant papers, published between 2005–2020 (15 years), using keywords such as SDM, remote sensing of invasive species, and contribution of remote sensing in SDM, bioclimatic variables, invasive species distribution in data-poor regions, and invasive species distribution in Ethiopia. Information on the sole contribution of remote sensing and bioclimatic datasets for SDM, major challenges, and opportunities for integration of both datasets are systematically collected, analyzed, and discussed in table and figure formats. Several major challenges such as quality of remotely sensed data and its poor interpretation, inappropriate methods, poor selection of variables, and models were identified. Besides, the availability of Earth Observation (EO) data with high spatial and temporal resolution and their capacity to cover large and inaccessible areas at a reasonable cost, as well as progress in remote sensing data integration techniques and analysis are among the opportunities. Also, the impacts of important sensor characteristics such as spatial and temporal resolution are crucial for future research prospects. Similarly important are studies analyzing the impacts of interannual variability of vegetation and land use patterns on invasive SDM. Urgently needed are clearly defined working principles for the selection of variables and the most appropriate SDM.

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Robust model selection using the out-of-bag bootstrap in linear regression

Rabbi

Khalil

Khan

et al. 2022

Sci Rep

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Outlying observations have a large influence on the linear model selection process. In this article, we present a novel approach to robust model selection in linear regression to accommodate the situations where outliers are present in the data. The model selection criterion is based on two components, the robust conditional expected prediction loss, and a robust goodness-of-fit with a penalty term. We estimate the conditional expected prediction loss by using the out-of-bag stratified bootstrap approach. In the presence of outliers, the stratified bootstrap ensures that we obtain bootstrap samples that are similar to the original sample data. Furthermore, to control the undue effect of outliers, we use the robust MM-estimator and a bounded loss function in the proposed criterion. Specifically, we observe that instead of minimizing the penalized loss function or the conditional expected prediction loss separately, it is better to minimize them simultaneously. The simulation and real-data based studies confirm the consistent and satisfactory behavior of our bootstrap model selection procedure in the presence of response outliers and covariate outliers.

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A new robust model selection method in GLM with application to ecological data

Cited by 4 publications

References 28 publications

Robust subtractive stability measures for fast and exhaustive feature importance ranking and selection in generalised linear models

Robust subtractive stability measures for fast and exhaustive feature importance ranking and selection in generalised linear models

Integration of remote sensing and bioclimatic data for prediction of invasive species distribution in data-poor regions: a review on challenges and opportunities

Robust model selection using the out-of-bag bootstrap in linear regression

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