| vif {car} | R Documentation |
Calculates variance-inflation and generalized variance-inflation factors (VIFs and GVIFs) for linear, generalized linear, and other regression models.
vif(mod, ...)
## Default S3 method:
vif(mod, ...)
## S3 method for class 'lm'
vif(mod, type=c("terms", "marginal", "high-order"), ...)
## S3 method for class 'merMod'
vif(mod, ...)
## S3 method for class 'polr'
vif(mod, ...)
## S3 method for class 'svyolr'
vif(mod, ...)
mod |
for the default method, an object that responds to
|
type |
for unweighted |
... |
not used. |
If all terms in an unweighted linear model have 1 df, then the usual variance-inflation factors are calculated.
If any terms in an unweighted linear model have more than 1 df, then generalized variance-inflation factors (Fox and Monette, 1992) are calculated. These are interpretable as the inflation in size of the confidence ellipse or ellipsoid for the coefficients of the term in comparison with what would be obtained for orthogonal data.
The generalized VIFs
are invariant with respect to the coding of the terms in the model (as long as
the subspace of the columns of the model matrix pertaining to each term is
invariant). To adjust for the dimension of the confidence ellipsoid, the function
also prints GVIF^{1/(2\times df)} where df is the degrees of freedom
associated with the term.
Through a further generalization, the implementation here is applicable as well to other sorts of models, in particular weighted linear models, generalized linear models, and mixed-effects models.
Three methods of computing GVIFs are provided for unweighted linear models:
Setting type="terms" (the default) behaves like the default method, and computes the GIF for each term in the model, ignoring relations of marginality among the terms in models with interactions.
Setting type="marginal" focuses in turn on each term in the model but ignores terms that are higher-order relatives of the focal term; e.g., in the model with formula y ~ a*b + c, the the GVIF for the main effect a ignores the interaction a:b to which a is marginal.
Setting type="high-order" computes a GVIF for each high-order term in the model, absorbing the lower-order relatives of the term (i.e., terms that are marginal to the focal term); thus, in the model with formula y ~ a*b + c, GVIFs are computed for a:b and c, and the former includes the terms a, b, and a:b (and is labelled a*b).
Specific methods are provided for ordinal regression model objects produced by polr in the MASS package and svyolr in the survey package, which are "intercept-less"; VIFs or GVIFs for linear and similar regression models without intercepts are generally not sensible.
A vector of VIFs, or a matrix containing one row for each term, and
columns for the GVIF, df, and GVIF^{1/(2\times df)}, the last
of which is intended to be comparable across terms of different dimension.
John Fox jfox@mcmaster.ca and Henric Nilsson
Fox, J. and Monette, G. (1992) Generalized collinearity diagnostics. JASA, 87, 178–183.
Fox, J. (2016) Applied Regression Analysis and Generalized Linear Models, Third Edition. Sage.
Fox, J. and Weisberg, S. (2018) An R Companion to Applied Regression, Third Edition, Sage.
vif(lm(prestige ~ income + education, data=Duncan))
vif(lm(prestige ~ income + education + type, data=Duncan))
vif(lm(prestige ~ (income + education)*type, data=Duncan),
type="high-order")
vif(lm(prestige ~ (income + education)*type, data=Duncan),
type="marginal")