betaDelta: Confidence Intervals for Standardized Regression Coefficients

Ivan Jacob Agaloos Pesigan

Description

Generates confidence intervals for standardized regression coefficients using delta method standard errors for models fitted by lm() as described in Yuan and Chan (2011: http://doi.org/10.1007/s11336-011-9224-6) and Jones and Waller (2015: http://doi.org/10.1007/s11336-013-9380-y). The package can also be used to generate confidence intervals for differences of standardized regression coefficients and as a general approach to performing the delta method. A description of the package and code examples are presented in Pesigan, Sun, and Cheung (2023: https://doi.org/10.1080/00273171.2023.2201277).

Installation

You can install the CRAN release of betaDelta with:

install.packages("betaDelta")

You can install the development version of betaDelta from GitHub with:

if (!require("remotes")) install.packages("remotes")
remotes::install_github("jeksterslab/betaDelta")

Example

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). Confidence intervals for the standardized regression coefficients are generated using the BetaDelta() function from the betaDelta package following Yuan & Chan (2011) and Jones & Waller (2015).

library(betaDelta)

df <- betaDelta::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 sampling covariance matrix.

Multivariate Normal-Theory Approach

BetaDelta(object, type = "mvn", alpha = 0.05)

## Call:
## BetaDelta(object = object, type = "mvn", alpha = 0.05)
## 
## Standardized regression slopes with MVN standard errors:
##            est     se      t df     p   2.5%  97.5%
## NARTIC  0.4951 0.0759 6.5272 42 0.000 0.3421 0.6482
## PCTGRT  0.3915 0.0770 5.0824 42 0.000 0.2360 0.5469
## PCTSUPP 0.2632 0.0747 3.5224 42 0.001 0.1124 0.4141

Asymptotic Distribution-Free Approach

BetaDelta(object, type = "adf", alpha = 0.05)

## Call:
## BetaDelta(object = object, type = "adf", alpha = 0.05)
## 
## Standardized regression slopes with ADF standard errors:
##            est     se      t df      p   2.5%  97.5%
## NARTIC  0.4951 0.0674 7.3490 42 0.0000 0.3592 0.6311
## PCTGRT  0.3915 0.0710 5.5164 42 0.0000 0.2483 0.5347
## PCTSUPP 0.2632 0.0769 3.4231 42 0.0014 0.1081 0.4184

Other Features

The package can also be used to generate confidence intervals for differences of standardized regression coefficients using the DiffBetaDelta() function. It can also be used as a general approach to performing the delta method using the Delta() and DeltaGeneric() functions.

Citation

To cite betaDelta in publications, please use:

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. https://doi.org/10.1080/00273171.2023.2201277

Documentation

See GitHub Pages for package documentation.

Citation

To cite betaDelta in publications, please cite Pesigan et al. (2023).

References

Jones, J. A., & Waller, N. G. (2015). The normal-theory and asymptotic distribution-free (ADF) covariance matrix of standardized regression coefficients: Theoretical extensions and finite sample behavior. Psychometrika, 80(2), 365–378. https://doi.org/10.1007/s11336-013-9380-y

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, 58(6), 1183–1186. https://doi.org/10.1080/00273171.2023.2201277

Yuan, K.-H., & Chan, W. (2011). Biases and standard errors of standardized regression coefficients. Psychometrika, 76(4), 670–690. https://doi.org/10.1007/s11336-011-9224-6