Ivan Jacob Agaloos Pesigan 2025-10-19
Generates Monte Carlo confidence intervals for standardized regression
coefficients (beta) and other effect sizes, including multiple
correlation, semipartial correlations, improvement in R-squared, squared
partial correlations, and differences in standardized regression
coefficients, for models fitted by lm(). betaMC combines ideas from
Monte Carlo confidence intervals for the indirect effect (Pesigan and
Cheung, 2024: http://doi.org/10.3758/s13428-023-02114-4) and the
sampling covariance matrix of regression coefficients (Dudgeon, 2017:
http://doi.org/10.1007/s11336-017-9563-z) to generate confidence
intervals effect sizes in regression.
You can install the CRAN release of betaMC with:
install.packages("betaMC")You can install the development version of betaMC from
GitHub with:
if (!require("remotes")) install.packages("remotes")
remotes::install_github("jeksterslab/betaMC")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 BetaMC() function from
the betaMC package.
library(betaMC)df <- betaMC::nas1982Fit the regression model using the lm() function.
object <- lm(QUALITY ~ NARTIC + PCTGRT + PCTSUPP, data = df)mvn <- MC(object, type = "mvn")adf <- MC(object, type = "adf")hc3 <- MC(object, type = "hc3")BetaMC(mvn, alpha = 0.05)
#> Call:
#> BetaMC(object = mvn, alpha = 0.05)
#>
#> Standardized regression slopes
#> type = "mvn"
#> est se R 2.5% 97.5%
#> NARTIC 0.4951 0.0759 20000 0.3385 0.6349
#> PCTGRT 0.3915 0.0767 20000 0.2380 0.5390
#> PCTSUPP 0.2632 0.0745 20000 0.1211 0.4127BetaMC(adf, alpha = 0.05)
#> Call:
#> BetaMC(object = adf, alpha = 0.05)
#>
#> Standardized regression slopes
#> type = "adf"
#> est se R 2.5% 97.5%
#> NARTIC 0.4951 0.0677 20000 0.3509 0.6169
#> PCTGRT 0.3915 0.0708 20000 0.2438 0.5221
#> PCTSUPP 0.2632 0.0765 20000 0.1061 0.4084BetaMC(hc3, alpha = 0.05)
#> Call:
#> BetaMC(object = hc3, alpha = 0.05)
#>
#> Standardized regression slopes
#> type = "hc3"
#> est se R 2.5% 97.5%
#> NARTIC 0.4951 0.0798 20000 0.3227 0.6352
#> PCTGRT 0.3915 0.0818 20000 0.2204 0.5398
#> PCTSUPP 0.2632 0.0855 20000 0.0900 0.4260The betaMC package also has functions to generate Monte Carlo
confidence intervals for other effect sizes such as RSqMC() for
multiple correlation coefficients (R-squared and adjusted R-squared),
DeltaRSqMC() for improvement in R-squared, SCorMC() for semipartial
correlation coefficients, PCorMC() for squared partial correlation
coefficients, and DiffBetaMC() for differences of standardized
regression coefficients.
RSqMC(hc3, alpha = 0.05)
#> Call:
#> RSqMC(object = hc3, alpha = 0.05)
#>
#> R-squared and adjusted R-squared
#> type = "hc3"
#> est se R 2.5% 97.5%
#> rsq 0.8045 0.0620 20000 0.6447 0.8873
#> adj 0.7906 0.0665 20000 0.6193 0.8793DeltaRSqMC(hc3, alpha = 0.05)
#> Call:
#> DeltaRSqMC(object = hc3, alpha = 0.05)
#>
#> Improvement in R-squared
#> type = "hc3"
#> est se R 2.5% 97.5%
#> NARTIC 0.1859 0.0689 20000 0.0481 0.3206
#> PCTGRT 0.1177 0.0541 20000 0.0248 0.2351
#> PCTSUPP 0.0569 0.0375 20000 0.0063 0.1503SCorMC(hc3, alpha = 0.05)
#> Call:
#> SCorMC(object = hc3, alpha = 0.05)
#>
#> Semipartial correlations
#> type = "hc3"
#> est se R 2.5% 97.5%
#> NARTIC 0.4312 0.0871 20000 0.2193 0.5662
#> PCTGRT 0.3430 0.0827 20000 0.1576 0.4848
#> PCTSUPP 0.2385 0.0782 20000 0.0792 0.3877PCorMC(hc3, alpha = 0.05)
#> Call:
#> PCorMC(object = hc3, alpha = 0.05)
#>
#> Squared partial correlations
#> type = "hc3"
#> est se R 2.5% 97.5%
#> NARTIC 0.4874 0.1192 20000 0.1739 0.6469
#> PCTGRT 0.3757 0.1148 20000 0.1065 0.5500
#> PCTSUPP 0.2254 0.1128 20000 0.0267 0.4553DiffBetaMC(hc3, alpha = 0.05)
#> Call:
#> DiffBetaMC(object = hc3, alpha = 0.05)
#>
#> Differences of standardized regression slopes
#> type = "hc3"
#> est se R 2.5% 97.5%
#> NARTIC-PCTGRT 0.1037 0.1421 20000 -0.1778 0.3778
#> NARTIC-PCTSUPP 0.2319 0.1333 20000 -0.0387 0.4841
#> PCTGRT-PCTSUPP 0.1282 0.1364 20000 -0.1447 0.3856See GitHub Pages for package documentation.
To cite betaMC in publications, please cite Pesigan & Cheung (2024).
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., & Cheung, S. F. (2024). Monte Carlo confidence intervals for the indirect effect with missing data. Behavior Research Methods, 56(3), 1678–1696. https://doi.org/10.3758/s13428-023-02114-4