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betaMC

Ivan Jacob Agaloos Pesigan 2024-10-22

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 0.0758 20000 0.3402 0.6361
#> PCTGRT  0.3915 0.0767 20000 0.2368 0.5383
#> PCTSUPP 0.2632 0.0746 20000 0.1177 0.4094

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 0.0679 20000 0.3513 0.6170
#> PCTGRT  0.3915 0.0712 20000 0.2418 0.5228
#> PCTSUPP 0.2632 0.0769 20000 0.1071 0.4090

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 0.0800 20000 0.3227 0.6348
#> PCTGRT  0.3915 0.0826 20000 0.2192 0.5439
#> PCTSUPP 0.2632 0.0862 20000 0.0867 0.4267

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 0.0622 20000 0.6430 0.8876
#> adj 0.7906 0.0667 20000 0.6175 0.8796

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 0.0691 20000 0.0498 0.3231
#> PCTGRT  0.1177 0.0549 20000 0.0250 0.2392
#> PCTSUPP 0.0569 0.0378 20000 0.0056 0.1514

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 0.2231 0.5684
#> PCTGRT  0.3430 0.0834 20000 0.1581 0.4890
#> PCTSUPP 0.2385 0.0788 20000 0.0751 0.3891

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 0.1197 20000 0.1754 0.6491
#> PCTGRT  0.3757 0.1154 20000 0.1058 0.5558
#> PCTSUPP 0.2254 0.1134 20000 0.0234 0.4611

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 0.1428 20000 -0.1856 0.3771
#> NARTIC-PCTSUPP 0.2319 0.1336 20000 -0.0382 0.4868
#> PCTGRT-PCTSUPP 0.1282 0.1383 20000 -0.1483 0.3938

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