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betaMC

Ivan Jacob Agaloos Pesigan 2025-07-22

Description

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, 2023: 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.

Installation

You can install the CRAN release of betaMC with:

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

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

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 BetaMC() function from the betaMC package.

df <- betaMC::nas1982

Regression

Fit the regression model using the lm() function.

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

Monte Carlo Sampling Distribution of Parameters

Normal-Theory Approach 

mvn <- MC(object, type = "mvn")

Asymptotic distribution-free Approach 

adf <- MC(object, type = "adf")

Heteroskedasticity Consistent Approach (HC3) 

hc3 <- MC(object, type = "hc3")

Standardized Regression Slopes

Normal-Theory Approach 

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 0.0760 20000 0.3385 0.6366
#> PCTGRT  0.3915 0.0766 20000 0.2366 0.5372
#> PCTSUPP 0.2632 0.0749 20000 0.1178 0.4113

Asymptotic distribution-free Approach 

BetaMC(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 0.0683 20000 0.3502 0.6175
#> PCTGRT  0.3915 0.0719 20000 0.2403 0.5214
#> PCTSUPP 0.2632 0.0767 20000 0.1061 0.4063

Heteroskedasticity Consistent Approach (HC3) 

BetaMC(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 0.0790 20000 0.3259 0.6338
#> PCTGRT  0.3915 0.0822 20000 0.2192 0.5415
#> PCTSUPP 0.2632 0.0856 20000 0.0894 0.4230

Other Effect Sizes

The 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.

Multiple Correlation Coefficients (R-squared and adjusted R-squared) 

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 0.0614 20000 0.6477 0.8873
#> adj 0.7906 0.0658 20000 0.6225 0.8793

Improvement in R-squared 

DeltaRSqMC(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 0.0683 20000 0.0503 0.3177
#> PCTGRT  0.1177 0.0548 20000 0.0254 0.2386
#> PCTSUPP 0.0569 0.0374 20000 0.0060 0.1490

Semipartial Correlation Coefficients 

SCorMC(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 0.0861 20000 0.2242 0.5637
#> PCTGRT  0.3430 0.0832 20000 0.1592 0.4885
#> PCTSUPP 0.2385 0.0783 20000 0.0774 0.3860

Squared Partial Correlation Coefficients 

PCorMC(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 0.1804 0.6503
#> PCTGRT  0.3757 0.1157 20000 0.1076 0.5546
#> PCTSUPP 0.2254 0.1127 20000 0.0255 0.4559

Differences of Standardized Regression Coefficients 

DiffBetaMC(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 0.1417 20000 -0.1752 0.3756
#> NARTIC-PCTSUPP 0.2319 0.1322 20000 -0.0351 0.4816
#> PCTGRT-PCTSUPP 0.1282 0.1371 20000 -0.1480 0.3915

Documentation

See GitHub Pages for package documentation.

Citation

To cite betaMC in publications, please cite Pesigan & Cheung (2023).

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., & Cheung, S. F. (2023). 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