MuMIn (version 1.47.5)

std.coef: Standardized model coefficients

Description

Standardize model coefficients by Standard Deviation or Partial Standard Deviation.

Usage

std.coef(x, partial.sd, ...)
partial.sd(x)
# Deprecated:
beta.weights(model)

Value

A matrix with at least two columns for the standardized coefficient estimate and its standard error. Optionally, the third column holds degrees of freedom associated with the coefficients.

Arguments

x, model

a fitted model object.

partial.sd

logical, if set to TRUE, model coefficients are multiplied by partial SD, otherwise they are multiplied by the ratio of the standard deviations of the independent variable and dependent variable.

...

additional arguments passed to coefTable, e.g. dispersion.

Author

Kamil Bartoń. Variance inflation factors calculation is based on function vif from package car written by Henric Nilsson and John Fox.

Details

Standardizing model coefficients has the same effect as centring and scaling the input variables. “Classical” standardized coefficients are calculated as \(\beta^{*}_i = \beta_i\frac{s_{X_{i}}}{s_{y}} \) , where \(\beta\) is the unstandardized coefficient, \(s_{X_{i}}\) is the standard deviation of associated dependent variable \(X_i\) and \(s_{y}\) is SD of the response variable.

If variables are intercorrelated, the standard deviation of \(X_i\) used in computing the standardized coefficients \(\beta_i^{*}\) should be replaced by the partial standard deviation of \(X_i\) which is adjusted for the multiple correlation of \(X_i\) with the other \(X\) variables included in the regression equation. The partial standard deviation is calculated as \(s_{X_{i}}^{*}=s_{X_{i}} VIF(X_i)^{-0.5} (\frac{n-1}{n-p} )^{0.5} \), where VIF is the variance inflation factor, n is the number of observations and p, the number of predictors in the model. The coefficient is then transformed as \(\beta^{*}_i = \beta_i s_{X_{i}}^{*} \).

References

Cade, B.S. 2015 Model averaging and muddled multimodel inferences. Ecology 96, 2370-2382.

Afifi, A., May, S., Clark, V.A. 2011 Practical Multivariate Analysis, Fifth Edition. CRC Press.

Bring, J. 1994 How to standardize regression coefficients. The American Statistician 48, 209--213.

See Also

partial.sd can be used with stdize.

coef or coeffs and coefTable for unstandardized coefficients.

Examples

# Fit model to original data:
fm  <- lm(y ~ x1 + x2 + x3 + x4, data = GPA)

# Partial SD for the default formula:   y ~ x1 + x2 + x3 + x4
psd <- partial.sd(lm(data = GPA))[-1] # remove first element for intercept

# Standardize data:
zGPA <- stdize(GPA, scale = c(NA, psd), center = TRUE)
# Note: first element of 'scale' is set to NA to ignore the first column 'y'

# Coefficients of a model fitted to standardized data:
zapsmall(coefTable(stdizeFit(fm, newdata = zGPA)))
# Standardized coefficients of a model fitted to original data:
zapsmall(std.coef(fm, partial = TRUE))


# Standardizing nonlinear models:
fam <- Gamma("inverse")
fmg <- glm(log(y) ~ x1 + x2 + x3 + x4, data = GPA, family = fam)

psdg <- partial.sd(fmg)
zGPA <- stdize(GPA, scale = c(NA, psdg[-1]), center = FALSE)
fmgz <- glm(log(y) ~ z.x1 + z.x2 + z.x3 + z.x4, zGPA, family = fam)

# Coefficients using standardized data:
coef(fmgz) # (intercept is unchanged because the variables haven't been
           #  centred)
# Standardized coefficients:
coef(fmg) * psdg