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betaMC: Example Using the DeltaRSqMC Function

Ivan Jacob Agaloos Pesigan

Source: vignettes/example-delta-r-sq-mc.Rmd
example-delta-r-sq-mc.Rmd

Confidence intervals for improvement in R-squared are generated using the DeltaRSqMC() 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")

Improvement in R-squared

Normal-Theory Approach 

mvn <- DeltaRSqMC(mvn)

Asymptotic distribution-free Approach 

adf <- DeltaRSqMC(adf)

Heteroskedasticity Consistent Approach (HC3) 

hc3 <- DeltaRSqMC(hc3)

Methods

summary

Summary of the results of DeltaRSqMC().

summary(mvn)
#> Call:
#> DeltaRSqMC(object = mvn)
#> 
#> Improvement in R-squared
#> type = "mvn"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.1859 0.0663 20000 0.0324 0.0510 0.0726 0.3282 0.3908 0.4682
#> PCTGRT  0.1177 0.0511 20000 0.0141 0.0244 0.0382 0.2365 0.2914 0.3703
#> PCTSUPP 0.0569 0.0338 20000 0.0007 0.0049 0.0103 0.1403 0.1786 0.2342
summary(adf)
#> Call:
#> DeltaRSqMC(object = adf)
#> 
#> Improvement in R-squared
#> type = "adf"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.1859 0.0582 20000 0.0077 0.0450 0.0745 0.3032 0.3512 0.4044
#> PCTGRT  0.1177 0.0470 20000 0.0057 0.0219 0.0368 0.2198 0.2638 0.3255
#> PCTSUPP 0.0569 0.0330 20000 0.0001 0.0028 0.0094 0.1354 0.1748 0.2182
summary(hc3)
#> Call:
#> DeltaRSqMC(object = hc3)
#> 
#> Improvement in R-squared
#> type = "hc3"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.1859 0.0691 20000 0.0024 0.0185 0.0517 0.3245 0.3791 0.4458
#> PCTGRT  0.1177 0.0546 20000 0.0016 0.0109 0.0254 0.2334 0.2951 0.3749
#> PCTSUPP 0.0569 0.0372 20000 0.0000 0.0010 0.0064 0.1483 0.1923 0.2512

coef

Return the vector of estimates.

coef(mvn)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.1858925 0.1176542 0.0568722
coef(adf)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.1858925 0.1176542 0.0568722
coef(hc3)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.1858925 0.1176542 0.0568722

vcov

Return the sampling covariance matrix.

vcov(mvn)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   0.0043927066 -0.0007420947 -0.0003420446
#> PCTGRT  -0.0007420947  0.0026064133 -0.0002431884
#> PCTSUPP -0.0003420446 -0.0002431884  0.0011422639
vcov(adf)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   3.391031e-03  4.874407e-05 -0.0001580216
#> PCTGRT   4.874407e-05  2.207210e-03 -0.0002018811
#> PCTSUPP -1.580216e-04 -2.018811e-04  0.0010870440
vcov(hc3)
#>                NARTIC        PCTGRT       PCTSUPP
#> NARTIC   4.770940e-03  0.0001563451 -4.443315e-05
#> PCTGRT   1.563451e-04  0.0029767221 -1.524671e-04
#> PCTSUPP -4.443315e-05 -0.0001524671  1.381807e-03

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.07256185 0.3281640
#> PCTGRT  0.03821714 0.2365150
#> PCTSUPP 0.01031463 0.1402773
confint(adf, level = 0.95)
#>               2.5 %    97.5 %
#> NARTIC  0.074519672 0.3031958
#> PCTGRT  0.036764139 0.2197601
#> PCTSUPP 0.009403787 0.1353896
confint(hc3, level = 0.95)
#>               2.5 %    97.5 %
#> NARTIC  0.051720568 0.3244929
#> PCTGRT  0.025360626 0.2333554
#> PCTSUPP 0.006386026 0.1483131

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