Estimate Standardized Regression Coefficients and the Corresponding Sampling Covariance Matrix Using the Asymptotic Distribution-Free Approach

Estimate Standardized Regression Coefficients and the Corresponding Sampling Covariance Matrix Using the Asymptotic Distribution-Free Approach

Usage

BetaADF(object, alpha = c(0.05, 0.01, 0.001))

Arguments

object

Object of class lm.

alpha

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

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 BetaADF() is different from betaDelta::BetaDelta() with type = "adf", the results are numerically equivalent. BetaADF() is appropriate when sample sizes are moderate to large (n > 250). BetaHC() is recommended in most situations.

References

Browne, M. W. (1984). Asymptotically distribution-free methods for the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology, 37(1), 62–83. doi:10.1111/j.2044-8317.1984.tb00789.x

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: BetaHC(), BetaN(), DiffBetaSandwich(), RSqBetaSandwich()

Author

Ivan Jacob Agaloos Pesigan

Examples

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = nas1982)
std <- BetaADF(object)
# Methods -------------------------------------------------------
print(std)
#> Call:
#> BetaADF(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 0.0674 7.3490 42 0.0000  0.2568 0.3134 0.3592 0.6311 0.6769
#> PCTGRT  0.3915 0.0710 5.5164 42 0.0000  0.1404 0.2000 0.2483 0.5347 0.5830
#> PCTSUPP 0.2632 0.0769 3.4231 42 0.0014 -0.0088 0.0558 0.1081 0.4184 0.4707
#>         99.95%
#> NARTIC  0.7335
#> PCTGRT  0.6426
#> PCTSUPP 0.5353
summary(std)
#> Call:
#> BetaADF(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 0.0674 7.3490 42 0.0000  0.2568 0.3134 0.3592 0.6311 0.6769
#> PCTGRT  0.3915 0.0710 5.5164 42 0.0000  0.1404 0.2000 0.2483 0.5347 0.5830
#> PCTSUPP 0.2632 0.0769 3.4231 42 0.0014 -0.0088 0.0558 0.1081 0.4184 0.4707
#>         99.95%
#> NARTIC  0.7335
#> PCTGRT  0.6426
#> PCTSUPP 0.5353
coef(std)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477 
vcov(std)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.004539472 -0.002552698 -0.001742698
#> PCTGRT  -0.002552698  0.005036538 -0.001906216
#> PCTSUPP -0.001742698 -0.001906216  0.005914088
confint(std, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.3591757 0.6311146
#> PCTGRT  0.2482683 0.5347091
#> PCTSUPP 0.1080509 0.4184444