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 0.0771 20000 0.1836 0.2291 0.2719 0.5722 0.6260 0.6888
#> PCTGRT  0.3430 0.0734 20000 0.1112 0.1545 0.1943 0.4825 0.5330 0.5784
#> PCTSUPP 0.2385 0.0700 20000 0.0262 0.0673 0.1028 0.3783 0.4359 0.4887
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 0.2105 0.2707 0.5476 0.5922 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 0.3688 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 0.0863 20000  0.0551 0.1480 0.2241 0.5685 0.6203 0.6857
#> PCTGRT  0.3430 0.0821 20000  0.0456 0.1036 0.1630 0.4840 0.5430 0.6027
#> PCTSUPP 0.2385 0.0788 20000 -0.0418 0.0266 0.0792 0.3902 0.4456 0.5160

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   0.0059396222 -0.0012894115 -0.0008667068
#> PCTGRT  -0.0012894115  0.0053818999 -0.0006991077
#> PCTSUPP -0.0008667068 -0.0006991077  0.0048956256
vcov(adf)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0049939665  0.0002605552 -0.0003686549
#> PCTGRT   0.0002605552  0.0050259666 -0.0005947590
#> PCTSUPP -0.0003686549 -0.0005947590  0.0048520808
vcov(hc3)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0074450889  0.0006620586 -0.0001435567
#> PCTGRT   0.0006620586  0.0067474631 -0.0005242356
#> PCTSUPP -0.0001435567 -0.0005242356  0.0062043043

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.2719481 0.5721936
#> PCTGRT  0.1943133 0.4825255
#> PCTSUPP 0.1027590 0.3783105
confint(adf, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.27071131 0.5475904
#> PCTGRT  0.19156579 0.4687980
#> PCTSUPP 0.09507793 0.3688376
confint(hc3, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.22405462 0.5684939
#> PCTGRT  0.16300705 0.4840342
#> PCTSUPP 0.07924023 0.3902249

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