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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 0.1355 20000 -0.3799 -0.2534 -0.1678 0.3636 0.4346 0.5345
#> NARTIC-PCTSUPP 0.2319 0.1246 20000 -0.1961 -0.1027 -0.0190 0.4657 0.5407 0.6256
#> PCTGRT-PCTSUPP 0.1282 0.1221 20000 -0.2617 -0.1915 -0.1132 0.3660 0.4493 0.5222
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 0.1207 20000 -0.2849 -0.2066 -0.1348 0.3366 0.4053 0.4826
#> NARTIC-PCTSUPP 0.2319 0.1183 20000 -0.1761 -0.0821 -0.0077 0.4590 0.5321 0.6219
#> PCTGRT-PCTSUPP 0.1282 0.1212 20000 -0.2860 -0.1928 -0.1145 0.3616 0.4366 0.5067
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 0.1418 20000 -0.3656 -0.2617 -0.1736 0.3791 0.4652 0.5684
#> NARTIC-PCTSUPP 0.2319 0.1331 20000 -0.2243 -0.1275 -0.0378 0.4826 0.5576 0.6612
#> PCTGRT-PCTSUPP 0.1282 0.1372 20000 -0.3286 -0.2347 -0.1464 0.3871 0.4649 0.5444

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    0.018354660    0.009483257   -0.008871403
#> NARTIC-PCTSUPP   0.009483257    0.015525729    0.006042472
#> PCTGRT-PCTSUPP  -0.008871403    0.006042472    0.014913875
vcov(adf)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.014559232    0.006928914   -0.007630318
#> NARTIC-PCTSUPP   0.006928914    0.013983955    0.007055041
#> PCTGRT-PCTSUPP  -0.007630318    0.007055041    0.014685360
vcov(hc3)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.020097625    0.009489245   -0.010608380
#> NARTIC-PCTSUPP   0.009489245    0.017709672    0.008220427
#> PCTGRT-PCTSUPP  -0.010608380    0.008220427    0.018828807

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.16780803 0.3636429
#> NARTIC-PCTSUPP -0.01895561 0.4657480
#> PCTGRT-PCTSUPP -0.11322481 0.3659768
confint(adf, level = 0.95)
#>                       2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.134830802 0.3365734
#> NARTIC-PCTSUPP -0.007664018 0.4590029
#> PCTGRT-PCTSUPP -0.114513106 0.3615672
confint(hc3, level = 0.95)
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.17359895 0.3790514
#> NARTIC-PCTSUPP -0.03776915 0.4826152
#> PCTGRT-PCTSUPP -0.14637956 0.3870592

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