seBetaFixed {fungible}

Covariance Matrix and Standard Errors for Standardized Regression Coefficients for Fixed Predictors

Description

Computes Normal Theory Covariance Matrix and Standard Errors for Standardized Regression Coefficients for Fixed Predictors

Usage

seBetaFixed(
  X = NULL,
  y = NULL,
  cov.x = NULL,
  cov.xy = NULL,
  var.y = NULL,
  var.error = NULL,
  Nobs = NULL
)

Arguments

X

Matrix of predictor scores.

y

Vector of criterion scores.

cov.x

Covariance or correlation matrix of predictors.

cov.xy

Vector of covariances or correlations between predictors and criterion.

var.y

Criterion variance.

var.error

Optional argument to supply the error variance: var(y - yhat).

Nobs

Number of observations.

Value

cov.Beta

Normal theory covariance matrix of standardized regression coefficients for fixed predictors.

se.Beta

Standard errors for standardized regression coefficients for fixed predictors.

Author(s)

Jeff Jones and Niels Waller

References

Yuan, K. & Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76(4), 670-690.

See Also

seBeta

Examples

## We will generate some data and pretend that the Predictors are being held fixed

library(MASS)
R <- matrix(.5, 3, 3); diag(R) <- 1
Beta <- c(.2, .3, .4)

rm(list = ".Random.seed", envir = globalenv()); set.seed(123)
X <- mvrnorm(n = 200, mu = rep(0, 3), Sigma = R, empirical = TRUE)
y <- X %*% Beta + .64*scale(rnorm(200))

seBetaFixed(X, y)

# $covBeta
#              b1           b2           b3
# b1  0.003275127 -0.001235665 -0.001274303
# b2 -0.001235665  0.003037100 -0.001491736
# b3 -0.001274303 -0.001491736  0.002830157
# 
# $seBeta
#         b1         b2         b3 
# 0.05722872 0.05510989 0.05319922

## you can also supply covariances instead of raw data

seBetaFixed(cov.x = cov(X), cov.xy = cov(X, y), var.y = var(y), Nobs = 200)

# $covBeta
#              b1           b2           b3
# b1  0.003275127 -0.001235665 -0.001274303
# b2 -0.001235665  0.003037100 -0.001491736
# b3 -0.001274303 -0.001491736  0.002830157
# 
# $seBeta
#         b1         b2         b3 
# 0.05722872 0.05510989 0.05319922