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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 0.0771 20000 0.1828 0.2286 0.2718 0.5720 0.6255 0.6888
#> PCTGRT  0.3430 0.0733 20000 0.1112 0.1551 0.1947 0.4823 0.5328 0.5784
#> PCTSUPP 0.2385 0.0700 20000 0.0262 0.0674 0.1030 0.3786 0.4365 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 0.0708 20000 0.1157 0.2112 0.2720 0.5496 0.5935 0.6477
#> PCTGRT  0.3430 0.0708 20000 0.0882 0.1499 0.1919 0.4673 0.5159 0.5807
#> PCTSUPP 0.2385 0.0696 20000 0.0032 0.0511 0.0955 0.3690 0.4160 0.4732
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 0.0865 20000  0.0487 0.1407 0.2215 0.5667 0.6168 0.6788
#> PCTGRT  0.3430 0.0831 20000  0.0483 0.1056 0.1604 0.4879 0.5407 0.6078
#> PCTSUPP 0.2385 0.0789 20000 -0.0346 0.0248 0.0775 0.3889 0.4467 0.5182

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   0.0059390404 -0.0012721726 -0.0008609524
#> PCTGRT  -0.0012721726  0.0053658116 -0.0006949645
#> PCTSUPP -0.0008609524 -0.0006949645  0.0048964555
vcov(adf)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0050107401  0.0002460707 -0.0004010920
#> PCTGRT   0.0002460707  0.0050101465 -0.0006346065
#> PCTSUPP -0.0004010920 -0.0006346065  0.0048373115
vcov(hc3)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0074841276  0.0008331550 -0.0001594435
#> PCTGRT   0.0008331550  0.0069004908 -0.0006089837
#> PCTSUPP -0.0001594435 -0.0006089837  0.0062239417

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.2718302 0.5719749
#> PCTGRT  0.1946928 0.4822687
#> PCTSUPP 0.1029988 0.3785698
confint(adf, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.27204612 0.5495748
#> PCTGRT  0.19192682 0.4672548
#> PCTSUPP 0.09553564 0.3690101
confint(hc3, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.22151770 0.5666839
#> PCTGRT  0.16039190 0.4879101
#> PCTSUPP 0.07746136 0.3889084

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