Skip to contents

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 -0.1651 0.3647 0.4450 0.5439
#> NARTIC-PCTSUPP 0.2319 0.1251 20000 -0.2136 -0.0942 -0.0219 0.4701 0.5354 0.6025
#> PCTGRT-PCTSUPP 0.1282 0.1227 20000 -0.2852 -0.1901 -0.1155 0.3663 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 0.1214 20000 -0.3196 -0.2124 -0.1349 0.3384 0.4081 0.5024
#> NARTIC-PCTSUPP 0.2319 0.1183 20000 -0.1530 -0.0676 -0.0039 0.4560 0.5355 0.6304
#> PCTGRT-PCTSUPP 0.1282 0.1223 20000 -0.2746 -0.1931 -0.1166 0.3633 0.4418 0.5174
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 0.1425 20000 -0.3745 -0.2619 -0.1781 0.3811 0.4737 0.5792
#> NARTIC-PCTSUPP 0.2319 0.1327 20000 -0.2316 -0.1198 -0.0370 0.4800 0.5717 0.6545
#> PCTGRT-PCTSUPP 0.1282 0.1374 20000 -0.3573 -0.2464 -0.1519 0.3928 0.4746 0.5486

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    0.018415625    0.009501368   -0.008914258
#> NARTIC-PCTSUPP   0.009501368    0.015638911    0.006137543
#> PCTGRT-PCTSUPP  -0.008914258    0.006137543    0.015051801
vcov(adf)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT    0.014738725    0.006896875   -0.007841851
#> NARTIC-PCTSUPP   0.006896875    0.014004385    0.007107510
#> PCTGRT-PCTSUPP  -0.007841851    0.007107510    0.014949361
vcov(hc3)
#>                NARTIC-PCTGRT NARTIC-PCTSUPP PCTGRT-PCTSUPP
#> NARTIC-PCTGRT     0.02030562    0.009523790   -0.010781831
#> NARTIC-PCTSUPP    0.00952379    0.017609955    0.008086164
#> PCTGRT-PCTSUPP   -0.01078183    0.008086164    0.018867995

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.16512972 0.3647204
#> NARTIC-PCTSUPP -0.02193225 0.4701166
#> PCTGRT-PCTSUPP -0.11548008 0.3662706
confint(adf, level = 0.95)
#>                       2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.134903338 0.3383689
#> NARTIC-PCTSUPP -0.003920906 0.4559979
#> PCTGRT-PCTSUPP -0.116565175 0.3632955
confint(hc3, level = 0.95)
#>                      2.5 %    97.5 %
#> NARTIC-PCTGRT  -0.17807592 0.3810693
#> NARTIC-PCTSUPP -0.03696402 0.4799981
#> PCTGRT-PCTSUPP -0.15191434 0.3928330

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