Standard Errors of Standardized Estimates of Regression Coefficients (Textbook)

Standard Errors of Standardized Estimates of Regression Coefficients (Textbook)

.sehatslopeshatprimetb(
  slopeshat = NULL,
  sehatslopeshat = NULL,
  slopeshatprime = NULL,
  X,
  y
)

Arguments

slopeshat	Numeric vector of length p or p by 1 matrix. \(p \times 1\) column vector of estimated regression slopes \(\left( \boldsymbol{\hat{\beta}}_{2, 3, \cdots, k} = \left\{ \hat{\beta}_2, \hat{\beta}_3, \cdots, \hat{\beta}_k \right\}^{T} \right)\) .
sehatslopeshat	Numeric vector of length p or p by 1 matrix. \(p \times 1\) column vector of estimated standard errors of estimates of regression slopes \(\left( \mathbf{\widehat{se}}_{\boldsymbol{\hat{\beta}}_{2, 3, \cdots, k}^{\prime}} = \left\{ \mathrm{\hat{se}}_{\hat{\beta}_{2}^{\prime}}, \mathrm{\hat{se}}_{\hat{\beta}_{3}^{\prime}}, \cdots, \mathrm{\hat{se}}_{\hat{\beta}_{k}^{\prime}} \right\}^{T} \right)\) .
slopeshatprime	Numeric vector of length p or p by 1 matrix. \(p \times 1\) column vector of estimated standardized regression slopes \(\left( \boldsymbol{\hat{\beta}}_{2, 3, \cdots, k} = \left\{ \hat{\beta}_2, \hat{\beta}_3, \cdots, \hat{\beta}_k \right\}^{T} \right)\) .
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.

Details

$$ \mathbf{\widehat{se}}_{\boldsymbol{\hat{\beta}}_{2, \cdots, k}^{\prime}} = \mathbf{\widehat{se}}_{\boldsymbol{\hat{\beta}}_{2, \cdots, k}} \frac{\boldsymbol{\hat{\beta}}_{2, \cdots, k}^{\prime}}{\boldsymbol{\hat{\beta}}_{2, \cdots, k}} $$ According to Yuan and Chan (2011), this standard error is biased.

References

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

See also

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

Author

Ivan Jacob Agaloos Pesigan