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betaMC: Example Using the SCorMC Function

Ivan Jacob Agaloos Pesigan

Source: vignettes/example-s-cor-mc.Rmd
example-s-cor-mc.Rmd

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.

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 0.0773 20000 0.1757 0.2244 0.2699 0.5720 0.6225 0.6797
#> PCTGRT  0.3430 0.0744 20000 0.1116 0.1556 0.1934 0.4858 0.5424 0.6206
#> PCTSUPP 0.2385 0.0692 20000 0.0214 0.0598 0.1008 0.3724 0.4220 0.4871
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 0.0702 20000 0.1248 0.2175 0.2707 0.5461 0.5897 0.6409
#> PCTGRT  0.3430 0.0704 20000 0.0956 0.1488 0.1918 0.4702 0.5143 0.5699
#> PCTSUPP 0.2385 0.0703 20000 0.0013 0.0512 0.0924 0.3731 0.4212 0.4786
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 0.0872 20000  0.0433 0.1369 0.2235 0.5688 0.6192 0.6720
#> PCTGRT  0.3430 0.0830 20000  0.0401 0.0986 0.1583 0.4846 0.5388 0.6093
#> PCTSUPP 0.2385 0.0784 20000 -0.0199 0.0338 0.0784 0.3885 0.4440 0.5147

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   0.005968017 -0.0012519414 -0.0009054820
#> PCTGRT  -0.001251941  0.0055357707 -0.0007519029
#> PCTSUPP -0.000905482 -0.0007519029  0.0047828636
vcov(adf)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0049348275  0.0002556930 -0.0003926382
#> PCTGRT   0.0002556930  0.0049604267 -0.0006528814
#> PCTSUPP -0.0003926382 -0.0006528814  0.0049474322
vcov(hc3)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0076087026  0.0008684133 -0.0001089213
#> PCTGRT   0.0008684133  0.0068924894 -0.0006198172
#> PCTSUPP -0.0001089213 -0.0006198172  0.0061397950

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.2699467 0.5720038
#> PCTGRT  0.1933956 0.4858499
#> PCTSUPP 0.1007948 0.3723680
confint(adf, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.27071709 0.5460707
#> PCTGRT  0.19175402 0.4701798
#> PCTSUPP 0.09238786 0.3730507
confint(hc3, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.22347215 0.5687931
#> PCTGRT  0.15826925 0.4846184
#> PCTSUPP 0.07843045 0.3884719

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. https://doi.org/10.3758/s13428-023-02114-4