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betaMC: Example Using the DiffBetaMC Function

Ivan Jacob Agaloos Pesigan

Source: vignettes/example-diff-beta-mc.Rmd
example-diff-beta-mc.Rmd

Confidence intervals for differences of standardized regression slopes are generated using the DiffBetaMC() 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")

Differences of Standardized Regression Slopes

Normal-Theory Approach 

mvn <- DiffBetaMC(mvn)

Asymptotic distribution-free Approach 

adf <- DiffBetaMC(adf)

Heteroskedasticity Consistent Approach (HC3) 

hc3 <- DiffBetaMC(hc3)

Methods

summary

Summary of the results of DiffBetaMC().

summary(mvn)
#> Call:
#> DiffBetaMC(object = mvn)
#> 
#> Differences of standardized regression slopes
#> type = "mvn"
#>                   est     se     R   0.05%    0.5%    2.5%  97.5%  99.5% 99.95%
#> NARTIC-PCTGRT  0.1037 0.1357 20000 -0.3469 -0.2507 -0.1652 0.3649 0.4450 0.5439
#> NARTIC-PCTSUPP 0.2319 0.1251 20000 -0.2136 -0.0942 -0.0219 0.4703 0.5357 0.6068
#> PCTGRT-PCTSUPP 0.1282 0.1227 20000 -0.2852 -0.1902 -0.1155 0.3659 0.4363 0.5280
summary(adf)
#> Call:
#> DiffBetaMC(object = adf)
#> 
#> Differences of standardized regression slopes
#> type = "adf"
#>                   est     se     R   0.05%    0.5%    2.5%  97.5%  99.5% 99.95%
#> NARTIC-PCTGRT  0.1037 0.1210 20000 -0.3039 -0.2089 -0.1364 0.3385 0.4034 0.4865
#> NARTIC-PCTSUPP 0.2319 0.1185 20000 -0.1493 -0.0720 -0.0038 0.4561 0.5370 0.6326
#> PCTGRT-PCTSUPP 0.1282 0.1220 20000 -0.2671 -0.1939 -0.1154 0.3636 0.4389 0.5356
summary(hc3)
#> Call:
#> DiffBetaMC(object = hc3)
#> 
#> Differences of standardized regression slopes
#> type = "hc3"
#>                   est     se     R   0.05%    0.5%    2.5%  97.5%  99.5% 99.95%
#> NARTIC-PCTGRT  0.1037 0.1435 20000 -0.3560 -0.2623 -0.1770 0.3839 0.4728 0.5558
#> NARTIC-PCTSUPP 0.2319 0.1322 20000 -0.2109 -0.1131 -0.0352 0.4794 0.5682 0.6552
#> PCTGRT-PCTSUPP 0.1282 0.1364 20000 -0.3257 -0.2256 -0.1470 0.3879 0.4653 0.5499

coef

Return the vector of estimates.

coef(mvn)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410
coef(adf)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410
coef(hc3)
#>  NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP 
#>      0.1036564      0.2318974      0.1282410

vcov

Return the sampling covariance matrix.

vcov(mvn)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.018423956    0.009506506   -0.008917450
#> NARTIC-PCTSUPP   0.009506506    0.015647252    0.006140746
#> PCTGRT-PCTSUPP  -0.008917450    0.006140746    0.015058197
vcov(adf)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.014645573    0.006896037   -0.007749536
#> NARTIC-PCTSUPP   0.006896037    0.014030954    0.007134917
#> PCTGRT-PCTSUPP  -0.007749536    0.007134917    0.014884453
vcov(hc3)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.020595223    0.009730846   -0.010864377
#> NARTIC-PCTSUPP   0.009730846    0.017474893    0.007744048
#> PCTGRT-PCTSUPP  -0.010864377    0.007744048    0.018608424

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>                      2.5 %   97.5 %
#> NARTIC-PCTGRT  -0.16520875 0.364853
#> NARTIC-PCTSUPP -0.02193225 0.470267
#> PCTGRT-PCTSUPP -0.11550774 0.365932
confint(adf, level = 0.95)
#>                       2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.136359460 0.3384644
#> NARTIC-PCTSUPP -0.003803225 0.4560676
#> PCTGRT-PCTSUPP -0.115396599 0.3635661
confint(hc3, level = 0.95)
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.17699199 0.3838620
#> NARTIC-PCTSUPP -0.03519803 0.4794462
#> PCTGRT-PCTSUPP -0.14699925 0.3879036

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