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betaMC: Example Using the PCorMC Function

Ivan Jacob Agaloos Pesigan

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

Confidence intervals for squared partial correlation coefficients are generated using the PCorMC() 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")

Squared Partial Correlation Coefficients

Normal-Theory Approach 

mvn <- PCorMC(mvn)

Asymptotic distribution-free Approach 

adf <- PCorMC(adf)

Heteroskedasticity Consistent Approach (HC3) 

hc3 <- PCorMC(hc3)

Methods

summary

Summary of the results of PCorMC().

summary(mvn)
#> Call:
#> PCorMC(object = mvn)
#> 
#> Squared partial correlations
#> type = "mvn"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4874 0.1053 20000 0.1127 0.1807 0.2430 0.6514 0.7086 0.7763
#> PCTGRT  0.3757 0.1073 20000 0.0500 0.1001 0.1474 0.5618 0.6249 0.7069
#> PCTSUPP 0.2254 0.0993 20000 0.0057 0.0198 0.0468 0.4281 0.5062 0.5782
summary(adf)
#> Call:
#> PCorMC(object = adf)
#> 
#> Squared partial correlations
#> type = "adf"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4874 0.0997 20000 0.0381 0.1502 0.2411 0.6329 0.6893 0.7518
#> PCTGRT  0.3757 0.1004 20000 0.0334 0.0880 0.1460 0.5378 0.5936 0.6666
#> PCTSUPP 0.2254 0.1029 20000 0.0005 0.0094 0.0368 0.4335 0.5047 0.5897
summary(hc3)
#> Call:
#> PCorMC(object = hc3)
#> 
#> Squared partial correlations
#> type = "hc3"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4874 0.1182 20000 0.0110 0.0704 0.1815 0.6488 0.7051 0.7723
#> PCTGRT  0.3757 0.1155 20000 0.0108 0.0514 0.1052 0.5546 0.6194 0.6877
#> PCTSUPP 0.2254 0.1135 20000 0.0001 0.0036 0.0253 0.4562 0.5471 0.6347

coef

Return the vector of estimates.

coef(mvn)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4874382 0.3757383 0.2253739
coef(adf)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4874382 0.3757383 0.2253739
coef(hc3)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4874382 0.3757383 0.2253739

vcov

Return the sampling covariance matrix.

vcov(mvn)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC  0.0110932147 0.0006673043 0.0004004950
#> PCTGRT  0.0006673043 0.0115040181 0.0001156673
#> PCTSUPP 0.0004004950 0.0001156673 0.0098550210
vcov(adf)
#>              NARTIC       PCTGRT      PCTSUPP
#> NARTIC  0.009937808 0.0024649569 0.0020029526
#> PCTGRT  0.002464957 0.0100806855 0.0007876848
#> PCTSUPP 0.002002953 0.0007876848 0.0105864957
vcov(hc3)
#>              NARTIC       PCTGRT      PCTSUPP
#> NARTIC  0.013979885 0.0036328183 0.0028680953
#> PCTGRT  0.003632818 0.0133445630 0.0009319819
#> PCTSUPP 0.002868095 0.0009319819 0.0128842476

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.24300742 0.6514329
#> PCTGRT  0.14741339 0.5617781
#> PCTSUPP 0.04678045 0.4280831
confint(adf, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.24105542 0.6329125
#> PCTGRT  0.14596279 0.5377823
#> PCTSUPP 0.03683088 0.4334947
confint(hc3, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.18147876 0.6487877
#> PCTGRT  0.10524038 0.5546481
#> PCTSUPP 0.02534816 0.4561597

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