sehatslopeshatprimedelta: Standard Errors of Standardized Estimates of Regression...
In jeksterslabds/jeksterslabRlinreg: Jekster's Lab Linear Regression Utilities

Description Usage Arguments Details Author(s) References See Also Examples

Standard Errors of Standardized Estimates of Regression Coefficients (Yuan and Chan (2011))

1	sehatslopeshatprimedelta(X, y, adjust = FALSE)

`X`	`n` by `k` numeric matrix. The data matrix \mathbf{X} (also known as design matrix, model matrix or regressor matrix) is an n \times k matrix of n observations of k regressors, which includes a regressor whose value is 1 for each observation on the first column.
`y`	Numeric vector of length `n` or `n` by `1` matrix. The vector \mathbf{y} is an n \times 1 vector of observations on the regressand variable.
`adjust`	Logical. Use n - 3 adjustment for small samples.

The pth estimated standard error is calculated using

\mathbf{\widehat{se}}_{\boldsymbol{\hat{β}}_{\text{p}}^{\prime}} = √{ \frac{\hat{σ}_{X_{p}}^{2} \hat{c}_{p} \hat{σ}_{\hat{\varepsilon}}^{2}}{n \hat{σ}_{y}^{2}} + \frac{\hat{β}_{p}^{2} ≤ft[ \hat{σ}_{X_{p}}^{2} ≤ft( \boldsymbol{\hat{β}}^{T} \boldsymbol{\hat{Σ}}_{X} \boldsymbol{\hat{β}} \right) - \hat{σ}_{X_{p}}^{2} \hat{σ}_{\hat{\varepsilon}}^{2} - \hat{σ}_{y, X_{p}}^{2} \right]}{n \hat{σ}_{y}^{4}} }

where

p = ≤ft\{2, 3, \cdots, k \right\}
\hat{σ}_{\hat{\varepsilon}}^{2} is the estimated residual variance
\boldsymbol{\hat{β}}_{2, 3, \cdots, k} = ≤ft\{ \hat{β}_{2}, \hat{β}_{3}, \cdots, \hat{β}_{k}\right\}^{T} is the p \times 1 column vector of estimated regression slopes
\hat{σ}_{y}^{2} is the variance of the regressand variable y
\boldsymbol{\hat{Σ}}_{\mathbf{X}} is the p \times p estimated covariance matrix of the regressor variables X_2, X_3, \cdots, X_k
\hat{σ}_{X_p}^{2} is the variance of the corresponding pth regressor variable.
\hat{σ}_{y, X_{p}}^{2} is the covariance of the regressand variable y and the regressor variables X_2, X_3, \cdots, X_k
c_p is the diagonal element that corresponds to the regressor variable in \boldsymbol{Σ}_{\mathbf{X}}^{-1}
n is the sample size

Ivan Jacob Agaloos Pesigan

Yuan, K., Chan, W. (2011). Biases and Standard Errors of Standardized Regression Coefficients. Psychometrika 76, 670-690. doi:10.1007/s11336-011-9224-6.

Other standard errors of estimates of regression coefficients functions: .sehatbetahatbiased(), .sehatbetahat(), .sehatslopeshatprimedelta(), .sehatslopeshatprimetb(), sehatbetahatbiased(), sehatbetahat(), sehatslopeshatprimetb()

# Simple regression------------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
X <- X[, c(1, ncol(X))]
y <- jeksterslabRdatarepo::wages.matrix[["y"]]
sehatslopeshatprimedelta(X = X, y = y)

# Multiple regression----------------------------------------------
X <- jeksterslabRdatarepo::wages.matrix[["X"]]
# age is removed
X <- X[, -ncol(X)]
sehatslopeshatprimedelta(X = X, y = y)