betaMC

Ivan Jacob Agaloos Pesigan 2024-07-08

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:

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")

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.

library(betaMC)

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 0.0756 20000 0.3383 0.6338
#> PCTGRT  0.3915 0.0769 20000 0.2367 0.5373
#> PCTSUPP 0.2632 0.0744 20000 0.1203 0.4119

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 0.0678 20000 0.3523 0.6171
#> PCTGRT  0.3915 0.0708 20000 0.2434 0.5202
#> PCTSUPP 0.2632 0.0771 20000 0.1060 0.4067

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 0.3231 0.6352
#> PCTGRT  0.3915 0.0829 20000 0.2180 0.5425
#> PCTSUPP 0.2632 0.0852 20000 0.0901 0.4231

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 0.0621 20000 0.6436 0.8861
#> adj 0.7906 0.0666 20000 0.6181 0.8780

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 0.0686 20000 0.0492 0.3185
#> PCTGRT  0.1177 0.0552 20000 0.0251 0.2395
#> PCTSUPP 0.0569 0.0374 20000 0.0061 0.1468

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 0.0869 20000 0.2217 0.5644
#> PCTGRT  0.3430 0.0839 20000 0.1586 0.4894
#> PCTSUPP 0.2385 0.0782 20000 0.0776 0.3832

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 0.1194 20000 0.1768 0.6503
#> PCTGRT  0.3757 0.1158 20000 0.1029 0.5543
#> PCTSUPP 0.2254 0.1119 20000 0.0253 0.4525

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 0.1435 20000 -0.1824 0.3815
#> NARTIC-PCTSUPP 0.2319 0.1322 20000 -0.0394 0.4806
#> PCTGRT-PCTSUPP 0.1282 0.1373 20000 -0.1467 0.3899

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