std.coef: 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, 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 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)

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 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

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_1$$x_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 $x^2$.

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

Run this code

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

# Example 1: Regression model with continuous predictors
mod.lm1 <- lm(y ~ x1 + x2, data = dat)
std.coef(mod.lm1)

# Example 2: Print all standardized coefficients
std.coef(mod.lm1, print = "all")

# Example 3: Regression model with dichotomous predictor
mod.lm2 <- lm(y ~ x3, data = dat)
std.coef(mod.lm2)

# Example 4: Regression model with continuous and dichotomous predictors
mod.lm3 <- lm(y ~ x1 + x2 + x3, data = dat)
std.coef(mod.lm3)

# Example 5: Regression model with continuous predictors and an interaction term
mod.lm4 <- lm(y ~ x1*x2, data = dat)

# Example 6: Regression model with a quadratic term
mod.lm5 <- lm(y ~ x1 + I(x1^2), data = dat)
std.coef(mod.lm5)

#-------------------------------------------------------------------------------
# Example 7: Write Results into an Excel file

if (FALSE) {
mod.lm1 <- lm(y ~ x1 + x2, data = dat)

std.coef(mod.lm1, write = "Std_Coef.xlsx", output = FALSE)

result <- std.coef(mod.lm1, output = FALSE)
write.result(result, "Std_Coef.xlsx")
}

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