mctest: An R Package for Detection of Collinearity among Regressors

Abstract

It is common for linear regression models to be plagued with the problem of multicollinearity when two or more regressors are highly correlated. This problem results in unstable estimates of regression coefficients and causes some serious problems in validation and interpretation of the model. Different diagnostic measures are used to detect multicollinearity among regressors. Many statistical software and R packages provide few diagnostic measures for the judgment of multicollinearity. Most widely used diagnostic measures in these software are: coefficient of determination (R 2), variance inflation factor/tolerance limit (VIF/TOL), eigenvalues, condition number (CN) and condition index (CI) etc. In this manuscript, we present an R package, mctest, that computes popular and widely used multicollinearity diagnostic measures. The package also indicates which regressors may be the reason of collinearity among regressors. Brief introduction of collinearity Consider the conventional multiple linear regression equation y = Xβ + u, where y is an n × 1 vector of observation on response variable, X is known design matrix of order n × p, β is an p × 1 vector of unknown parameters and u is an n × 1 vector of random errors with mean zero and variance σ 2 I n , where I n is an identity matrix of order n. One of the important assumptions of the classical linear regression model is that there is no exact collinearity among the regressors otherwise, the issue is referred to as multicollinearity. Generally, the problem of multicollinearity may also refer to have not only exact linear relationship but also high correlations among some or all regressors of a regression model under study. Strictly speaking, multicollinearity is usually refers to the existence of more than one exact linear relationship among regressors, while collinearity refers to the existence of a single linear relationship among regressors. However, in general, the term multicollinearity may be referred to both the cases. Data collection method, constraints on the fitted regression model, model specification error, overdefined model, some common trend in time series data and naturally correlated data may be some potential sources of multicollinearity.

The relationship between socioeconomic status and white matter microstructure in pre‐reading children: A longitudinal investigation

“…Multicollinearity among the variables in the regression models was evaluated using the variance inflation factor (VIF) and the Farrar–Glauber test (using the mctest package in R, Imdadullah, Aslam & Altaf ). Results indicated that although the predictors were moderately correlated (see Supporting Information Table S1), the VIF values for all variables ranged from 1.09 to 1.77, suggesting that multicollinearity is not an issue of concern for the regression models reported (O'brien, ).…”

“…Multicollinearity among the variables in the regression models was evaluated using the variance inflation factor (VIF) and the Farrar-Glauber test (using the mctest package in R, Imdadullah, Aslam & Altaf 2016).…”

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“…Finally, we use the subset of subjects which had a stroke, but no rich-club involvement, to demonstrate the specificity of the rich-club nodes with respect to outcome over a simple number of region count (Ntotal) affected by the acute lesion. All analyses were performed using the computing environment R [27][28][29] .…”

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“…We assayed for the potential presence of interactions among explanatory variables by generating coplots and tested for collinearity among explanatory variables (Zuur, Ieno, & Elphick, ). To do so, we visually inspected correlation matrices and calculated VIFs with the R package MCtest (Imdadullah, Aslam, & Altaf, ), with no evidence of significant collinearity among explanatory variables [all VIFs < 2 (Zuur et al, )].…”