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betaMC: Example Using the BetaMC Function

Ivan Jacob Agaloos Pesigan

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

In this example, a multiple regression model is fitted using program quality ratings (QUALITY) as the regressand/outcome variable and number of published articles attributed to the program faculty members (NARTIC), percent of faculty members holding research grants (PCTGRT), and percentage of program graduates who received support (PCTSUPP) as regressor/predictor variables using a data set from 1982 ratings of 46 doctoral programs in psychology in the USA (National Research Council, 1982). Confidence intervals for the standardized regression coefficients are generated using the BetaMC() function from the betaMC package.

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")

Standardized Regression Slopes

Normal-Theory Approach 

mvn <- BetaMC(mvn)

Asymptotic distribution-free Approach 

adf <- BetaMC(adf)

Heteroskedasticity Consistent Approach (HC3) 

hc3 <- BetaMC(hc3)

Methods

summary

Summary of the results of BetaMC().

summary(mvn)
#> Call:
#> BetaMC(object = mvn)
#> 
#> Standardized regression slopes
#> type = "mvn"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4951 0.0762 20000 0.2324 0.2920 0.3391 0.6377 0.6796 0.7263
#> PCTGRT  0.3915 0.0773 20000 0.1424 0.1922 0.2371 0.5393 0.5919 0.6462
#> PCTSUPP 0.2632 0.0747 20000 0.0274 0.0758 0.1181 0.4077 0.4615 0.5244
summary(adf)
#> Call:
#> BetaMC(object = adf)
#> 
#> Standardized regression slopes
#> type = "adf"
#>            est     se     R  0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4951 0.0678 20000 0.2591 0.3088 0.3494 0.6152 0.6559 0.6942
#> PCTGRT  0.3915 0.0711 20000 0.1449 0.1955 0.2413 0.5215 0.5625 0.6120
#> PCTSUPP 0.2632 0.0767 20000 0.0134 0.0582 0.1079 0.4080 0.4490 0.4999
summary(hc3)
#> Call:
#> BetaMC(object = hc3)
#> 
#> Standardized regression slopes
#> type = "hc3"
#>            est     se     R   0.05%   0.5%   2.5%  97.5%  99.5% 99.95%
#> NARTIC  0.4951 0.0794 20000  0.2178 0.2690 0.3228 0.6339 0.6745 0.7254
#> PCTGRT  0.3915 0.0824 20000  0.0960 0.1575 0.2169 0.5406 0.5856 0.6371
#> PCTSUPP 0.2632 0.0856 20000 -0.0318 0.0278 0.0889 0.4283 0.4782 0.5403

coef

Return the vector of estimates.

coef(mvn)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477
coef(adf)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477
coef(hc3)
#>    NARTIC    PCTGRT   PCTSUPP 
#> 0.4951451 0.3914887 0.2632477

vcov

Return the sampling covariance matrix.

vcov(mvn)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.005811264 -0.003377116 -0.002133562
#> PCTGRT  -0.003377116  0.005977965 -0.001726979
#> PCTSUPP -0.002133562 -0.001726979  0.005577850
vcov(adf)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.004600246 -0.002562396 -0.001689232
#> PCTGRT  -0.002562396  0.005051016 -0.001860037
#> PCTSUPP -0.001689232 -0.001860037  0.005887343
vcov(hc3)
#>               NARTIC       PCTGRT      PCTSUPP
#> NARTIC   0.006311116 -0.003622202 -0.001964332
#> PCTGRT  -0.003622202  0.006797582 -0.002339048
#> PCTSUPP -0.001964332 -0.002339048  0.007325528

confint

Return confidence intervals.

confint(mvn, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.3391226 0.6377052
#> PCTGRT  0.2370561 0.5393107
#> PCTSUPP 0.1180515 0.4077326
confint(adf, level = 0.95)
#>             2.5 %    97.5 %
#> NARTIC  0.3493922 0.6151987
#> PCTGRT  0.2413328 0.5215218
#> PCTSUPP 0.1078522 0.4079892
confint(hc3, level = 0.95)
#>              2.5 %    97.5 %
#> NARTIC  0.32277942 0.6338670
#> PCTGRT  0.21693842 0.5406124
#> PCTSUPP 0.08894597 0.4283310

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
National Research Council. (1982). An assessment of research-doctorate programs in the United States: Social and behavioral sciences. National Academies Press. https://doi.org/10.17226/9781