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betaMC

Ivan Jacob Agaloos Pesigan 2025-10-19

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, 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.

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 0.0759 20000 0.3385 0.6349
#> PCTGRT  0.3915 0.0767 20000 0.2380 0.5390
#> PCTSUPP 0.2632 0.0745 20000 0.1211 0.4127

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 0.0677 20000 0.3509 0.6169
#> PCTGRT  0.3915 0.0708 20000 0.2438 0.5221
#> PCTSUPP 0.2632 0.0765 20000 0.1061 0.4084

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 0.0798 20000 0.3227 0.6352
#> PCTGRT  0.3915 0.0818 20000 0.2204 0.5398
#> PCTSUPP 0.2632 0.0855 20000 0.0900 0.4260

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 0.0620 20000 0.6447 0.8873
#> adj 0.7906 0.0665 20000 0.6193 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 0.0689 20000 0.0481 0.3206
#> PCTGRT  0.1177 0.0541 20000 0.0248 0.2351
#> PCTSUPP 0.0569 0.0375 20000 0.0063 0.1503

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 0.0871 20000 0.2193 0.5662
#> PCTGRT  0.3430 0.0827 20000 0.1576 0.4848
#> PCTSUPP 0.2385 0.0782 20000 0.0792 0.3877

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 0.1739 0.6469
#> PCTGRT  0.3757 0.1148 20000 0.1065 0.5500
#> PCTSUPP 0.2254 0.1128 20000 0.0267 0.4553

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 0.1421 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 0.3856

Documentation

See GitHub Pages for package documentation.

Citation

To cite betaMC in publications, please cite Pesigan & Cheung (2024).

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. (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