Estimate Standardized Regression Coefficients and the Corresponding Sampling Covariance Matrix Assuming Multivariate Normality

Estimate Standardized Regression Coefficients and the Corresponding Sampling Covariance Matrix Assuming Multivariate Normality

Usage

BetaN(object, alpha = c(0.05, 0.01, 0.001), std_y = TRUE, std_x = NULL)

Arguments

object

Object of class lm.

alpha

Numeric vector. Significance level \(\alpha\).

std_y

Logical. Standardize \(y\). With std_y = FALSE, \(y\) is left in its original units (\(b_j \sigma_{x_j}\)).

std_x

Character vector or NULL. Names of the regressors to standardize. NULL (default) standardizes all regressors; character(0) standardizes none (\(b_j / \sigma_y\)). Leaving a dummy variable out keeps its 0-1 contrast. The delta method accounts for the sampling variability of the standard deviations.

Value

Returns an object of class betasandwich which is a list with the following elements:

call

Function call.

args

Function arguments.

lm_process

Processed lm object.

gamma_n

Asymptotic covariance matrix of the sample covariance matrix assuming multivariate normality.

gamma_hc

Asymptotic covariance matrix HC correction.

gamma

Asymptotic covariance matrix of the sample covariance matrix.

acov

Asymptotic covariance matrix of the standardized slopes.

vcov

Sampling covariance matrix of the standardized slopes.

est

Vector of standardized slopes.

Details

Note that while the calculation in BetaN() is different from betaDelta::BetaDelta() with type = "mvn", the results are numerically equivalent. BetaN() assumes multivariate normality. BetaHC() is recommended in most situations.

References

Dudgeon, P. (2017). Some improvements in confidence intervals for standardized regression coefficients. Psychometrika, 82(4), 928–951. doi:10.1007/s11336-017-9563-z

Pesigan, I. J. A., Sun, R. W., & Cheung, S. F. (2023). betaDelta and betaSandwich: Confidence intervals for standardized regression coefficients in R. Multivariate Behavioral Research. doi:10.1080/00273171.2023.2201277

See also

Other Beta Sandwich Functions: BetaADF(), BetaHC(), DeltaRSqSandwich(), DiffBetaSandwich(), FSqSandwich(), PCorSandwich(), RSqSandwich(), SCorSandwich()

Author

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaN(object)
# Methods -------------------------------------------------------
print(std)
#> Call:
#> BetaN(object = object)
#> 
#> Standardized regression slopes with MVN standard errors:
#>            est     se      t df     p   0.05%   0.5%   2.5%  97.5%  99.5%
#> NARTIC  0.4951 0.0759 6.5272 42 0.000  0.2268 0.2905 0.3421 0.6482 0.6998
#> PCTGRT  0.3915 0.0770 5.0824 42 0.000  0.1190 0.1837 0.2360 0.5469 0.5993
#> PCTSUPP 0.2632 0.0747 3.5224 42 0.001 -0.0011 0.0616 0.1124 0.4141 0.4649
#>         99.95%
#> NARTIC  0.7635
#> PCTGRT  0.6640
#> PCTSUPP 0.5276
summary(std)
#> Call:
#> BetaN(object = object)
#> 
#> Standardized regression slopes with MVN standard errors:
#>            est     se      t df     p   0.05%   0.5%   2.5%  97.5%  99.5%
#> NARTIC  0.4951 0.0759 6.5272 42 0.000  0.2268 0.2905 0.3421 0.6482 0.6998
#> PCTGRT  0.3915 0.0770 5.0824 42 0.000  0.1190 0.1837 0.2360 0.5469 0.5993
#> PCTSUPP 0.2632 0.0747 3.5224 42 0.001 -0.0011 0.0616 0.1124 0.4141 0.4649
#>         99.95%
#> NARTIC  0.7635
#> PCTGRT  0.6640
#> PCTSUPP 0.5276
coef(std)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477 
vcov(std)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.005754524 -0.003360334 -0.002166127
#> PCTGRT  -0.003360334  0.005933462 -0.001769723
#> PCTSUPP -0.002166127 -0.001769723  0.005585256
confint(std, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.3420563 0.6482339
#> PCTGRT  0.2360380 0.5469395
#> PCTSUPP 0.1124272 0.4140682