Global predictor collinearity diagnostics

Computes one global condition number, VIFs and the predictor correlation matrix, using all training observations with equal weights. No model fit is needed. The RcppArmadillo core stores an n-by-p centered design and p-by-p matrices, never an n-by-n spatial matrix.

Usage

gwr_global_collinearity(object, threshold_cn = 30, threshold_vif = 10, ...)

Arguments

object

A finite numeric predictor matrix/data frame without an intercept, or a `gwrs_fit` retaining its design matrix.

threshold_cn, threshold_vif

Positive flag thresholds, matching [gwr_local_collinearity()].

...

Unused.

Value

A `gwrs_global_collinearity` object including `condition_number`, `vif`, `correlation`, `eigenvalues`, `rank` and `constant_columns`.

Details

Predictors are centered and scaled by their root mean square deviations. The condition number is the square root of the largest/smallest eigenvalue ratio of the correlation matrix; the intercept is excluded. This equals the singular-value condition number of the standardized design. VIFs are the diagonal of the inverse correlation matrix. Eigenvalues at or below `max(1, largest eigenvalue) * 1e-10` are numerically rank deficient. Rank-deficient designs return infinite CN and VIFs. Constant columns make the correlation matrix undefined: CN/VIF are infinite, correlation and eigenvalues are missing, and rank is unavailable. No observations or predictors are silently removed. Threshold flags are diagnostics, not tests.

References

Wheeler, D. and Tiefelsdorf, M. (2005). Multicollinearity and correlation among local regression coefficients in geographically weighted regression. Journal of Geographical Systems, 7, 161-187. doi:10.1007/s10109-005-0155-6 .

Examples

global <- gwr_global_collinearity(datasets::mtcars[, c("wt", "hp", "disp")])
global
global$correlation