check.collin {misty}

Collinearity Diagnostics

Description

This function computes tolerance, standard error inflation factor, variance inflation factor, eigenvalues, condition index, and variance proportions for linear, generalized linear, and mixed-effects models.

Usage

check.collin(model, print = c("all", "vif", "eigen"), digits = 3, p.digits = 3,
             write = NULL, append = TRUE, check = TRUE, output = TRUE)

Arguments

model

a fitted model of class "lm", "glm", "lmerMod", "lmerModLmerTest", "glmerMod", "lme", or "glmmTMB".

print

a character vector indicating which results to show, i.e. "all", for all results, "vif" for tolerance, std. error inflation factor, and variance inflation factor, or eigen for eigenvalue, condition index, and variance proportions.

digits

an integer value indicating the number of decimal places to be used for displaying results.

p.digits

an integer value indicating the number of decimal places to be used for displaying the p-value.

write

a character string naming a text file with file extension ".txt" (e.g., "Output.txt") for writing the output into a text file.

append

logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.

check

logical: if TRUE (default), argument specification is checked.

output

logical: if TRUE (default), output is shown on the console.

Details

Collinearity diagnostics can be conducted for objects returned from the lm() and glm() function, but also from objects returned from the lmer() and glmer() function from the lme4 package, lme() function from the nlme package, and the glmmTMB() function from the glmmTMB package.

The generalized variance inflation factor (Fox & Monette, 1992) is computed for terms with more than 1 df resulting from factors with more than two levels. The generalized VIF (GVIF) is 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. GVIF is invariant to the coding of the terms in the model. In order to adjust for the dimension of the confidence ellipsoid, GVIF^\frac{1}{2df} is computed. Note that the adjusted GVIF (aGVIF) is actually a generalized standard error inflation factor (GSIF). Thus, the aGIF needs to be squared before applying a common cutoff threshold for the VIF (e.g., VIF > 10). Note that the output of check.collin() function reports either the variance inflation factor or the squared generalized variance inflation factor in the column VIF, while the standard error inflation factor or the adjusted generalized variance inflation factor is reported in the column SIF.

Value

Returns an object of class misty.object, which is a list with following entries:

call

function call

type

type of analysis

model

model specified in the model argument

args

specification of function arguments

result

list with result tables, i.e., coef for the regression table including tolerance, std. error inflation factor and variance inflation factors, vif for the tolerance, std. error inflation factor, and variance inflation factor, and eigen for eigenvalue condition index, and variance proportion

Note

The computation of the VIF and the GVIF is based on the vif() function in the car package by John Fox, Sanford Weisberg and Brad Price (2020), and the computation of eigenvalues, condition index, and variance proportions is based on the ols_eigen_cindex() function in the olsrr package by Aravind Hebbali (2020).

Author(s)

Takuya Yanagida [e-mail]

References

Fox, J., & Monette, G. (1992). Generalized collinearity diagnostics. Journal of the American Statistical Association, 87, 178-183.

Fox, J., Weisberg, S., & Price, B. (2020). car: Companion to Applied Regression. R package version 3.0-8. https://cran.r-project.org/web/packages/car/

Hebbali, A. (2020). olsrr: Tools for building OLS regression models. R package version 0.5.3. https://cran.r-project.org/web/packages/olsrr/

See Also

check.outlier, lm

Examples

dat <- data.frame(group = c(1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4),
                  x1 = c(3, 2, 4, 9, 5, 3, 6, 4, 5, 6, 3, 5),
                  x2 = c(1, 4, 3, 1, 2, 4, 3, 5, 1, 7, 8, 7),
                  x3 = c(7, 3, 4, 2, 5, 6, 4, 2, 3, 5, 2, 8),
                  x4 = c("a", "b", "a", "c", "c", "c", "a", "b", "b", "c", "a", "c"),
                  y1 = c(2, 7, 4, 4, 7, 8, 4, 2, 5, 1, 3, 8),
                  y2 = c(0, 1, 0, 1, 1, 1, 0, 0, 0, 1, 0, 1),
                  stringsAsFactors = TRUE)

#-------------------------------------------------------------------------------
# Linear model

# Estimate linear model with continuous predictors
mod.lm1 <- lm(y1 ~ x1 + x2 + x3, data = dat)

# Example 1: Tolerance, std. error, and variance inflation factor
check.collin(mod.lm1)

# Example 2: Tolerance, std. error, and variance inflation factor
# Eigenvalue, Condition index, and variance proportions
check.collin(mod.lm1, print = "all")

# Estimate model with continuous and categorical predictors
mod.lm2 <- lm(y1 ~ x1 + x2 + x3 + x4, data = dat)

# Example 3: Tolerance, generalized std. error, and variance inflation factor
check.collin(mod.lm2)

#-------------------------------------------------------------------------------
# Generalized linear model

# Estimate logistic regression model with continuous predictors
mod.glm <- glm(y2 ~ x1 + x2 + x3, data = dat, family = "binomial")

# Example 4: Tolerance, std. error, and variance inflation factor
check.collin(mod.glm)

## Not run: 
#-------------------------------------------------------------------------------
# Linear mixed-effects model

# Estimate linear mixed-effects model with continuous predictors using lme4 package
mod.lmer <- lme4::lmer(y1 ~ x1 + x2 + x3 + (1|group), data = dat)

# Example 5: Tolerance, std. error, and variance inflation factor
check.collin(mod.lmer)

# Estimate linear mixed-effects model with continuous predictors using nlme package
mod.lme <- nlme::lme(y1 ~ x1 + x2 + x3, random = ~ 1 | group, data = dat)

# Example 6: Tolerance, std. error, and variance inflation factor
check.collin(mod.lme)

# Estimate linear mixed-effects model with continuous predictors using glmmTMB package
mod.glmmTMB1 <- glmmTMB::glmmTMB(y1 ~ x1 + x2 + x3 + (1|group), data = dat)

# Example 7: Tolerance, std. error, and variance inflation factor
check.collin(mod.glmmTMB1)

#-------------------------------------------------------------------------------
# Generalized linear mixed-effects model

# Estimate mixed-effects logistic regression model with continuous predictors using lme4 package
mod.glmer <- lme4::glmer(y2 ~ x1 + x2 + x3 + (1|group), data = dat, family = "binomial")

# Example 8: Tolerance, std. error, and variance inflation factor
check.collin(mod.glmer)

# Estimate mixed-effects logistic regression model with continuous predictors using glmmTMB package
mod.glmmTMB2 <- glmmTMB::glmmTMB(y2 ~ x1 + x2 + x3 + (1|group), data = dat, family = "binomial")

# Example 9: Tolerance, std. error, and variance inflation factor
check.collin(mod.glmmTMB2)

#----------------------------------------------------------------------------
# Write Results

# Example 10: Write results into a text file
check.collin(mod.lm1, write = "Diagnostics.txt")

## End(Not run)