Collinearity refers to the non independence of predictor variables, usually in a regression-type analysis. It is a common feature of any descriptive ecological data set and can be a problem for parameter estimation because it inflates the variance of regression parameters and hence potentially leads to the wrong identification of relevant predictors in a statistical model. Collinearity is a severe problem when a model is trained on data from one region or time, and predicted to another with a different or unknown structure of collinearity. To demonstrate the reach of the problem of collinearity in ecology, we show how relationships among predictors differ between biomes, change over spatial scales and through time. Across disciplines, different approaches to addressing collinearity problems have been developed, ranging from clustering of predictors, threshold-based pre-selection, through latent variable methods, to shrinkage and regularisation. Using simulated data with five predictor-response relationships of increasing complexity and eight levels of collinearity we compared ways to address collinearity with standard multiple regression and machine-learning approaches. We assessed the performance of each approach by testing its impact on prediction to new data. In the extreme, we tested whether the methods were able to identify the true underlying relationship in a training dataset with strong collinearity by evaluating its performance on a test dataset without any collinearity. We found that methods specifically designed for collinearity, such as latent variable methods and tree based models, did not outperform the traditional GLM and threshold-based pre-selection. Our results highlight the value of GLM in combination with penalised methods (particularly ridge) and threshold-based pre-selection when omitted variables are considered in the final interpretation. However, all approaches tested yielded degraded predictions under change in collinearity structure and the ‘folk lore’-thresholds of correlation coefficients between predictor variables of |r| >0.7 was an appropriate indicator for when collinearity begins to severely distort model estimation and subsequent prediction. The use of ecological understanding of the system in pre-analysis variable selection and the choice of the least sensitive statistical approaches reduce the problems of collinearity, but cannot ultimately solve them.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1600-0587.2012.07348.x

Collinearity: a review of methods to deal with it and a simulation study evaluating their performance

1. Introduction and Overview. 2. Detecting Influential Observations and Outliers. 3. Detecting and Assessing Collinearity. 4. Applications and Remedies. 5. Research Issues and Directions for Extensions. Bibliography. Author Index. Subject Index.

Regression Diagnostics: Identifying Influential Data and Sources of Collinearity

sdm is an object-oriented, reproducible and extensible, platform for species distribution modelling. It uses individual species and community-based approaches, enabling ensembles of models to be fitted and evaluated, to project species potential distributions in space and time. It provides a standardized and unified structure for handling species distributions data and modelling techniques, and supports markedly different modelling approaches, including correlative, process-based (mechanistic), agent-based, and cellular automata. The object-oriented design of software is such that scientists can modify existing methods, extend the framework by developing new methods or modelling procedures, and share them to be reproduced by other scientists. sdm can handle spatial and temporal data for single or multiple species and uses high performance computing solutions to speed up modelling and simulations. The framework is implemented in R, providing a flexible and easy-to-use GUI interface.

https://onlinelibrary.wiley.com/doi/pdf/10.1111/ecog.01881

sdm: a reproducible and extensible R platform for species distribution modelling

Feature selection becomes prominent, especially in the data sets with many variables and features. It will eliminate unimportant variables and improve the accuracy as well as the performance of classification. Random Forest has emerged as a quite useful algorithm that can handle the feature selection issue even with a higher number of variables. In this paper, we use three popular datasets with a higher number of variables (Bank Marketing, Car Evaluation Database, Human Activity Recognition Using Smartphones) to conduct the experiment. There are four main reasons why feature selection is essential. First, to simplify the model by reducing the number of parameters, next to decrease the training time, to reduce overfilling by enhancing generalization, and to avoid the curse of dimensionality. Besides, we evaluate and compare each accuracy and performance of the classification model, such as Random Forest (RF), Support Vector Machines (SVM), K-Nearest Neighbors (KNN), and Linear Discriminant Analysis (LDA). The highest accuracy of the model is the best classifier. Practically, this paper adopts Random Forest to select the important feature in classification. Our experiments clearly show the comparative study of the RF algorithm from different perspectives. Furthermore, we compare the result of the dataset with and without essential features selection by RF methods varImp(), Boruta, and Recursive Feature Elimination (RFE) to get the best percentage accuracy and kappa. Experimental results demonstrate that Random Forest achieves a better performance in all experiment groups.

/pdf/selecting-critical-features-for-data-classification-based-on-vlfz2eyf1v.pdf

Selecting critical features for data classification based on machine learning methods

Three flawed practices associated with model averaging coefficients for predictor variables in regression models commonly occur when making multimodel inferences in analyses of ecological data. Model-averaged regression coefficients based on Akaike information criterion (AIC) weights have been recommended for addressing model uncertainty but they are not valid, interpretable estimates of partial effects for individual predictors when there is multicollinearity among the predictor variables. Multicollinearity implies that the scaling of units in the denominators of the regression coefficients may change across models such that neither the parameters nor their estimates have common scales, therefore averaging them makes no sense. The associated sums of AIC model weights recommended to assess relative importance of individual predictors are really a measure of relative importance of models, with little information about contributions by individual predictors compared to other measures of relative importance based on effects size or variance reduction. Sometimes the model-averaged regression coefficients for predictor variables are incorrectly used to make model-averaged predictions of the response variable when the models are not linear in the parameters. I demonstrate the issues with the first two practices using the college grade point average example extensively analyzed by Burnham and Anderson. I show how partial standard deviations of the predictor variables can be used to detect changing scales of their estimates with multicollinearity. Standardizing estimates based on partial standard deviations for their variables can be used to make the scaling of the estimates commensurate across models, a necessary but not sufficient condition for model averaging of the estimates to be sensible. A unimodal distribution of estimates and valid interpretation of individual parameters are additional requisite conditions. The standardized estimates or equivalently the t statistics on unstandardized estimates also can be used to provide more informative measures of relative importance than sums of AIC weights. Finally, I illustrate how seriously compromised statistical interpretations and predictions can be for all three of these flawed practices by critiquing their use in a recent species distribution modeling technique developed for predicting Greater Sage-Grouse (Centrocercus urophasianus) distribution in Colorado, USA. These model averaging issues are common in other ecological literature and ought to be discontinued if we are to make effective scientific contributions to ecological knowledge and conservation of natural resources.

Model averaging and muddled multimodel inferences

Determining the importance of independent variables is of practical relevance to ecologists and managers concerned with allocating limited resources to the management of natural systems. Although techniques that identify explanatory variables having the largest influence on the response variable are needed to design management actions effectively, the use of various indices to evaluate variable importance is poorly understood. Using Monte Carlo simulations, we compared six different indices commonly used to evaluate variable importance; zero-order correlations, partial correlations, semipartial correlations, standardized regression coefficients, Akaike weights, and independent effects. We simulated four scenarios to evaluate the indices under progressively more complex circumstances that included correlation between explanatory variables, as well as a spurious variable that was correlated with other explanatory variables, but not with the dependent variable. No index performed perfectly under all circumstances, but partial correlations and Akaike weights performed poorly in all cases. Zero-order correlations was the only measure that detected the presence of a spurious variable, whereas only independent effects assigned overlap areas correctly once the spurious variable was removed. We therefore recommend using zero-order correlations to eliminate predictor variables with correlations near zero, followed by the use of independent effects to assign overlap areas and rank variable importance.

/pdf/methods-to-quantify-variable-importance-implications-for-the-2snomnhfe1.pdf

Methods to quantify variable importance: implications for the analysis of noisy ecological data.

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Methods to quantify variable importance: implications for the analysis of noisy ecological data.