betaMC: Example Using the SCorMC Function

Ivan Jacob Agaloos Pesigan

Confidence intervals for semipartial correlation coefficients are generated using the SCorMC() function from the betaMC package. In this example, we use the data set and the model used in betaMC: Example Using the BetaMC Function.

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")

Semipartial Correlation Coefficients

Normal-Theory Approach

mvn <- SCorMC(mvn)

Asymptotic distribution-free Approach

adf <- SCorMC(adf)

Heteroskedasticity Consistent Approach (HC3)

hc3 <- SCorMC(hc3)

Methods

summary

Summary of the results of SCorMC().

summary(mvn)
#> Call:
#> SCorMC(object = mvn)
#> 
#> Semipartial correlations
#> type = "mvn"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4312 0.0770 20000 0.1705 0.2285 0.2707 0.5723 0.6244 0.6898
#> PCTGRT  0.3430 0.0744 20000 0.1191 0.1573 0.1947 0.4857 0.5435 0.6031
#> PCTSUPP 0.2385 0.0701 20000 0.0265 0.0644 0.1013 0.3770 0.4287 0.4858
summary(adf)
#> Call:
#> SCorMC(object = adf)
#> 
#> Semipartial correlations
#> type = "adf"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4312 0.0707 20000 0.0893 0.2103 0.2706 0.5477 0.5924 0.6456
#> PCTGRT  0.3430 0.0709 20000 0.0766 0.1453 0.1916 0.4688 0.5152 0.5804
#> PCTSUPP 0.2385 0.0697 20000 0.0013 0.0502 0.0951 0.3689 0.4170 0.4716
summary(hc3)
#> Call:
#> SCorMC(object = hc3)
#> 
#> Semipartial correlations
#> type = "hc3"
#>            est     se     R   0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4312 0.0860 20000  0.0553 0.1454 0.2258 0.5654 0.6173 0.6797
#> PCTGRT  0.3430 0.0832 20000  0.0490 0.1077 0.1609 0.4885 0.5421 0.6048
#> PCTSUPP 0.2385 0.0789 20000 -0.0352 0.0247 0.0772 0.3897 0.4495 0.5207

coef

Return the vector of estimates.

coef(mvn)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4311525 0.3430075 0.2384789
coef(adf)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4311525 0.3430075 0.2384789
coef(hc3)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4311525 0.3430075 0.2384789

vcov

Return the sampling covariance matrix.

vcov(mvn)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0059272821 -0.0012167694 -0.0008616098
#> PCTGRT  -0.0012167694  0.0055337929 -0.0008326223
#> PCTSUPP -0.0008616098 -0.0008326223  0.0049179926
vcov(adf)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0049971396  0.0002631899 -0.0003698228
#> PCTGRT   0.0002631899  0.0050250993 -0.0005940763
#> PCTSUPP -0.0003698228 -0.0005940763  0.0048536905
vcov(hc3)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0073916866  0.0007281651 -0.0002022310
#> PCTGRT   0.0007281651  0.0069252053 -0.0005981009
#> PCTSUPP -0.0002022310 -0.0005981009  0.0062233130

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.2706736 0.5723131
#> PCTGRT  0.1947400 0.4857045
#> PCTSUPP 0.1012615 0.3770397
confint(adf, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.27063965 0.5476799
#> PCTGRT  0.19156579 0.4687909
#> PCTSUPP 0.09507792 0.3688795
confint(hc3, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.22582761 0.5653624
#> PCTGRT  0.16092780 0.4884945
#> PCTSUPP 0.07723053 0.3896925

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

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