check.collin: 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)

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

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.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

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 $^{\frac{1}{2 d f}}$ 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.

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/

Examples

Run this code

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)

if (FALSE) {
# Load lme4, nlme, and glmmTMB package
libraries(lme4, nlme, glmmTMB)

#----------------------------------------------------------------------------
# Linear mixed-effects model

# Estimate linear mixed-effects model using lme4 package
mod.lmer <- 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 using nlme package
mod.lme <- 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 using glmmTMB package
mod.glmmTMB1 <- 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 using lme4 package
mod.glmer <- 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 using glmmTMB package
mod.glmmTMB2 <- 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")
}

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