dot-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))

.sehatslopeshatprimedelta(
  slopeshat,
  sigma2hatepsilonhat,
  SigmaXhat,
  sigmayXhat,
  sigma2yhat,
  adjust = FALSE,
  n,
  X,
  y
)

`slopeshat`	Numeric vector of length `p` or `p` by `1` matrix. p \times 1 column vector of estimated regression slopes ≤ft( \boldsymbol{\hat{β}}_{2, 3, \cdots, k} = ≤ft\{ \hat{β}_2, \hat{β}_3, \cdots, \hat{β}_k \right\}^{T} \right) .
`sigma2hatepsilonhat`	Numeric. Estimate of error variance.
`SigmaXhat`	`p` by `p` numeric matrix. p \times p matrix of estimated variances and covariances between regressor variables X_2, X_3, \cdots, X_k ≤ft( \boldsymbol{\hat{Σ}}_{\mathbf{X}} \right).
`sigmayXhat`	Numeric vector of length `p` or `p` by `1` matrix. p \times 1 vector of estimated covariances between the regressand y variable and regressor variables X_2, X_3, \cdots, X_k ≤ft( \boldsymbol{\hat{σ}}_{\mathbf{y}, \mathbf{X}} = ≤ft\{ \hat{σ}_{y, X_2}, \hat{σ}_{y, X_3}, \cdots, \hat{σ}_{y, X_k} \right\}^{T} \right).
`sigma2yhat`	Numeric. Estimated variance of the regressand ≤ft( \hat{σ}_{y}^{2} \right)
`adjust`	Logical. Use n - 3 adjustment for small samples.
`n`	Integer. Sample size.
`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.

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(), .sehatslopeshatprimetb(), sehatbetahatbiased(), sehatbetahat(), sehatslopeshatprimedelta(), sehatslopeshatprimetb()

slopes <- c(-3.0748755, -1.5653133, 1.0959758, 1.3703010, 0.1666065)
SigmaXhat <- matrix(
  data = c(
    0.25018672, 0.00779108, -0.01626038, -0.04424864, -0.13217068,
    0.00779108, 0.12957466, 0.01061297, -0.08818286, -0.16427222,
    -0.016260378, 0.010612975, 0.133848763, 0.004083767, 0.658462191,
    -0.044248635, -0.088182856, 0.004083767, 7.917601877, -5.910469742,
    -0.1321707, -0.1642722, 0.6584622, -5.9104697, 136.0217584
  ),
  ncol = 5
)
sigma2hatepsilonhat <- 42.35584
sigma2yhat <- 62.35235
sigmayXhat <- c(-0.8819639, -0.3633559, 0.2953811, 10.1433433, 15.9481950)
n <- 1289
.sehatslopeshatprimedelta(
  slopes = slopes, sigma2hatepsilonhat = sigma2hatepsilonhat,
  SigmaXhat = SigmaXhat, sigma2yhat = sigma2yhat, sigmayXhat = sigmayXhat, n = n
)