std.coef: Standardized Coefficients

In misty: Miscellaneous Functions 'T. Yanagida'

Standardized Coefficients

Description

This function computes standardized coefficients for linear models estimated by using the lm() function.

Usage

std.coef(model, print = c("all", "stdx", "stdy", "stdyx"), digits = 3, p.digits = 4,
         write = NULL, check = TRUE, output = TRUE)

Arguments

model	a fitted model of class "lm".
print	a character vector indicating which results to show, i.e. "all", for all results, "stdx" for standardizing only the predictor, "stdy" for for standardizing only the criterion, and "stdyx" for for standardizing both the predictor and the criterion. Note that the default setting is depending on the level of measurement of the predictors, i.e., if all predictors are continuous, the default setting is print = "stdyx"; if all predictors are binary, the default setting is print = "stdy"; if predictors are continuous and binary, the default setting is print = c("stdy", "stdyx").
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 for writing the results into a Excel file naming a file with or without file extension '.xlsx', e.g., "Results.xlsx" or "Results".
check	logical: if TRUE, argument specification is checked.
output	logical: if TRUE, output is shown on the console.

Details

The slope \beta can be standardized with respect to only x, only y, or both y and x:

StdX(\beta_1) = \beta_1 SD(x)

StdX(\beta_1) standardizes with respect to x only and is interpreted as the change in y when x changes one standard deviation referred to as SD(x).

StdY(\beta_1) = \frac{\beta_1}{SD(x)}

StdY(\beta_1) standardizes with respect to y only and is interpreted as the change in y standard deviation units, referred to as SD(y), when x changes one unit.

StdYX(\beta_1) = \beta_1 \frac{SD(x)}{SD(y)}

StdYX(\beta_1) standardizes with respect to both y and x and is interpreted as the change in y standard deviation units when x changes one standard deviation.

Note that the StdYX(\beta_1) and the StdY(\beta_1) standardizations are not suitable for the slope of a binary predictor because a one standard deviation change in a binary variable is generally not of interest (Muthen, Muthen, & Asparouhov, 2016).

The standardization of the slope \beta_3 in a regression model with an interaction term uses the product of standard deviations SD(x_1)SD(x_2) rather than the standard deviation of the product SD(x_1 x_2) for the interaction variable x_1x_2 (see Wen, Marsh & Hau, 2010). Likewise, the standardization of the slope \beta_3 in a polynomial regression model with a quadratic term uses the product of standard deviations SD(x)SD(x) rather than the standard deviation of the product SD(x x) for the quadratic term x^2.

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 model
args	specification of function arguments
result	list with result tables, i.e., coef for the regression table including standardized coefficients and sd for the standard deviation of the outcome and predictor(s)

Author(s)

Takuya Yanagida [e-mail]

References

Muthen, B. O., Muthen, L. K., & Asparouhov, T. (2016). Regression and mediation analysis using Mplus. Muthen & Muthen.

Wen, Z., Marsh, H. W., & Hau, K.-T. (2010). Structural equation models of latent interactions: An appropriate standardized solution and its scale-free properties. Structural Equation Modeling: A Multidisciplinary Journal, 17, 1-22. https://doi.org/10.1080/10705510903438872

Examples

dat <- data.frame(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(0, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 1),
                  y = c(2, 7, 4, 4, 7, 8, 4, 2, 5, 1, 3, 8))

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

#...........
# Regression model with continuous predictors
mod.lm1 <- lm(y ~ x1 + x2, data = dat)
std.coef(mod.lm1)

# Print all standardized coefficients
std.coef(mod.lm1, print = "all")

#...........
# Regression model with dichotomous predictor
mod.lm2 <- lm(y ~ x3, data = dat)
std.coef(mod.lm2)

#...........
# Regression model with continuous and dichotomous predictors
mod.lm3 <- lm(y ~ x1 + x2 + x3, data = dat)
std.coef(mod.lm3)

#...........
# Regression model with continuous predictors and an interaction term
mod.lm4 <- lm(y ~ x1*x2, data = dat)

#...........
# Regression model with a quadratic term
mod.lm5 <- lm(y ~ x1 + I(x1^2), data = dat)
std.coef(mod.lm5)

misty documentation built on Nov. 15, 2023, 1:06 a.m.