betaSandwich: Example Using the BetaHC Function

In this example, a multiple regression model is fitted using program quality ratings (QUALITY) as the regressand/outcome variable and number of published articles attributed to the program faculty members (NARTIC), percent of faculty members holding research grants (PCTGRT), and percentage of program graduates who received support (PCTSUPP) as regressor/predictor variables using a data set from 1982 ratings of 46 doctoral programs in psychology in the USA (National Research Council, 1982). Robust confidence intervals for the standardized regression coefficients are generated using the BetaHC() function from the betaSandwich package following Dudgeon (2017).¹

library(betaSandwich)

df <- betaSandwich::nas1982

Fit the regression model using the `lm()` function.

object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = df)

Estimate the standardized regression slopes and the corresponding robust sampling covariance matrix.

BetaHC(object, type = "hc3", alpha = 0.05)
#> Call:
#> BetaHC(object = object, type = "hc3", alpha = 0.05)
#> 
#> Standardized regression slopes with HC3 standard errors:
#>            est     se      t df      p   2.5%  97.5%
#> NARTIC  0.4951 0.0786 6.3025 42 0.0000 0.3366 0.6537
#> PCTGRT  0.3915 0.0818 4.7831 42 0.0000 0.2263 0.5567
#> PCTSUPP 0.2632 0.0855 3.0786 42 0.0037 0.0907 0.4358

Methods

out <- BetaHC(object, type = "hc3", alpha = 0.05)

summary

Summary of the results of BetaHC().

summary(out)
#> Call:
#> BetaHC(object = object, type = "hc3", alpha = 0.05)
#> 
#> Standardized regression slopes with HC3 standard errors:
#>            est     se      t df      p   2.5%  97.5%
#> NARTIC  0.4951 0.0786 6.3025 42 0.0000 0.3366 0.6537
#> PCTGRT  0.3915 0.0818 4.7831 42 0.0000 0.2263 0.5567
#> PCTSUPP 0.2632 0.0855 3.0786 42 0.0037 0.0907 0.4358

coef

Calculate the standardized regression slopes.

coef(out)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477

vcov

Calculate the robust sampling covariance matrix of the standardized regression slopes.

vcov(out)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.006172168 -0.003602529 -0.001943469
#> PCTGRT  -0.003602529  0.006699155 -0.002443584
#> PCTSUPP -0.001943469 -0.002443584  0.007311625

confint

Generate robust confidence intervals for standardized regression slopes.

confint(out, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.33659828 0.6536920
#> PCTGRT  0.22631203 0.5566654
#> PCTSUPP 0.09068548 0.4358099

References

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

National Research Council. (1982). An assessment of research-doctorate programs in the United States: Social and behavioral sciences. National Academies Press. https://doi.org/10.17226/9781

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, 1–4. https://doi.org/10.1080/00273171.2023.2201277

Ivan Jacob Agaloos Pesigan

Fit the regression model using the lm() function.