Print Extreme Bounds Analysis Results

Description

hist.eba prints the results of extreme bounds analysis (EBA; performed by the eba function) and returns the printed object invisibly (via invisible(x)). The function prints out information about the distribution and significance of estimated regression coefficients, the results of Leamer's EBA, as well as those of Sala-i-Martin's EBA (both the normal and generic model).

Usage

## S3 method for class 'eba'
print(x, digits = 3, ...) 

Arguments

Output

print.eba prints the following information in its output:

• Call: the matched call (based on x$call).

• Confidence level: the confidence level for hypothesis testing (x$level).

• Number of combinations: the total number of doubtful variable combinations that contain at least one focus variable (x$ncomb).

• Regressions estimated: the number of regressions that were estimated in the course of EBA (x$nreg). When no random sampling of regression models was requested (i.e., when eba's argument draws is NULL), the number of combinations (above) will equal the number of regressions estimated.

• Number of regressions by variable: the number of regressions estimated, by variable (x$nreg.variable).

• Number of coefficients used by variable: the number of coefficients used in the extreme bounds analysis, by variable (x$ncoef.variable).

Beta coefficients:

• Coef (Wgt Mean): the weighted mean of the estimated regression coefficients. Individual regression models receive a weight specified by eba's argument weights.

• SE (Wgt Mean): the weighted mean of the standard errors on estimated regression coefficients. Individual regression models receive a weight specified by eba's argument weights.

• Min Coef and SE (Min Coef): the value of the lowest regression coefficient across the estimated models and the corresponding standard error.

• Max Coef and SE (Max Coef): the value of the highest regression coefficient across the estimated models and the corresponding standard error.

Distribution of beta coefficients:

• Pct(beta < mu): proportion of estimated regression coefficients whose value is less than mu.

• Pct(beta > mu): proportion of estimated regression coefficients whose value is greater than mu.

• Pct(significant != mu): proportion of regression models in which the estimated coefficient is statistically significantly different from mu.

• Pct(signif & beta < mu): proportion of estimated regression coefficients that are both statistically significantly different from and whose value is less than mu.

• Pct(signif & beta > mu): proportion of estimated regression coefficients that are both statistically significantly different from and whose value is greater than mu.

Leamer's Extreme Bounds Analysis (EBA):

• Lower Extreme Bound: Leamer's lower extreme bound at the specified confidence level.

• Upper Extreme Bound: Leamer's upper extreme bound at the specified confidence level.

• Robust/Fragile?: a character string indicating whether the variable is robust or fragile based on Leamer's extreme bounds analysis.

Sala-i-Martin's Extreme Bounds Analysis (EBA):

• N: CDF(beta <= 0): the value of the cumulative density function at CDF(mu) - i.e., the proportion of coefficients that are estimated to be lower or equal to mu - based on Sala-i-Martin's EBA that assumes that regression coefficients are normally distributed across the estimated models. Weights specified by eba's argument weights are applied.

• N: CDF(beta > 0): the proportion of coefficients that are estimated to be greater than mu, based on Sala-i-Martin's EBA that assumes that regression coefficients are normally distributed across the estimated models. Weights specified by eba's argument weights are applied.

• G: CDF(beta <= 0): the value of the cumulative density function at CDF(mu) based on Sala-i-Martin's EBA that does not assume any particular distribution of regression coefficients across the estimated models. Weights specified by eba's argument weights are applied.

• G: CDF(beta > 0): the proportion of coefficients that are estimated to be greater than mu, based on Sala-i-Martin's EBA that does not assume any particular distribution of regression coefficients across the estimated models. Weights specified by eba's argument weights are applied.

Note that all values of cumulative density functions for Sala-i-Martin's EBA are printed as percentages.

Please cite as:

Hlavac, Marek (2015). ExtremeBounds: Extreme Bounds Analysis in R.
R package version 0.1.5.1. http://CRAN.R-project.org/package=ExtremeBounds

Author(s)

Marek Hlavac < hlavac at fas.harvard.edu >
Harvard University, Political Economy and Government

See Also

eba, hist.eba

Examples

# perform Extreme Bounds Analysis

eba.results <- eba(formula = mpg ~ wt | hp + gear | cyl + disp + drat + qsec + vs + am + carb,
                   data = mtcars[1:10, ], k = 0:2)

# The same result can be achieved by running:
# eba.results <- eba(data = mtcars[1:10, ], y = "mpg", free = "wt",
#                    doubtful = c("cyl","disp","hp","drat","qsec","vs","am","gear","carb"),
#                    focus = c("hp","gear"), k = 0:2)

# print out results, rounded to 2 decimal places
print(eba.results, digits = 2)

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(ExtremeBounds)

Please cite as: 

 Hlavac, Marek (2015). ExtremeBounds: Extreme Bounds Analysis in R.
 R package version 0.1.5.1. http://CRAN.R-project.org/package=ExtremeBounds 

> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/ExtremeBounds/print.eba.Rd_%03d_medium.png", width=480, height=480)
> ### Name: print.eba
> ### Title: Print Extreme Bounds Analysis Results
> ### Aliases: print.eba
> ### Keywords: models regression nonlinear robust multivariate
> 
> ### ** Examples
> 
> # perform Extreme Bounds Analysis
> 
> eba.results <- eba(formula = mpg ~ wt | hp + gear | cyl + disp + drat + qsec + vs + am + carb,
+                    data = mtcars[1:10, ], k = 0:2)
ExtremeBounds: eba() performing analysis. Please wait.

Preparing variables (1/4): Done.

Generating combinations (2/4): Estimate all 66 combinations.

Estimating regressions (3/4):
1 / 66 (1.52%)
7 / 66 (10.61%)
14 / 66 (21.21%)
20 / 66 (30.3%)
27 / 66 (40.91%)
33 / 66 (50%)
40 / 66 (60.61%)
47 / 66 (71.21%)
53 / 66 (80.3%)
60 / 66 (90.91%)
66 / 66 (100%)

Calculating bounds (4/4): Done.
> 
> # The same result can be achieved by running:
> # eba.results <- eba(data = mtcars[1:10, ], y = "mpg", free = "wt",
> #                    doubtful = c("cyl","disp","hp","drat","qsec","vs","am","gear","carb"),
> #                    focus = c("hp","gear"), k = 0:2)
> 
> # print out results, rounded to 2 decimal places
> print(eba.results, digits = 2)

Call:
eba(formula = mpg ~ wt | hp + gear | cyl + disp + drat + qsec + 
    vs + am + carb, data = mtcars[1:10, ], k = 0:2)

Confidence level: 0.95
Number of combinations: 66
Regressions estimated: 66 (100% of combinations)

Number of regressions by variable:

(Intercept)          wt          hp        gear 
         66          66          37          37 

Number of coefficients used by variable:

(Intercept)          wt          hp        gear 
         66          66          37          37 

Beta coefficients:

              Type  Coef (Wgt Mean)  SE (Wgt Mean)  Min Coef  SE (Min Coef)
(Intercept)   free            26.74          10.99      0.75          12.18
wt            free            -2.59           2.34     -9.28           3.40
hp           focus            -0.04           0.02     -0.08           0.02
gear         focus             2.27           2.93     -7.49           4.80
             Max Coef  SE (Max Coef)
(Intercept)     55.88           9.05
wt               1.06           2.32
hp              -0.03           0.02
gear             8.09           4.99

Distribution of beta coefficients:

              Type  Pct(beta < 0)  Pct(beta > 0)  Pct(significant != 0)
(Intercept)   free           0.00         100.00                  65.15
wt            free          98.48           1.52                   7.58
hp           focus         100.00           0.00                  78.38
gear         focus          10.81          89.19                  10.81
             Pct(signif & beta < 0)  Pct(signif & beta > 0)
(Intercept)                    0.00                   65.15
wt                             7.58                    0.00
hp                            78.38                    0.00
gear                           0.00                   10.81

Leamer's Extreme Bounds Analysis (EBA):

              Type  Lower Extreme Bound  Upper Extreme Bound
(Intercept)   free               -37.27                80.73
wt            free               -18.69                 9.24
hp           focus                -0.11                 0.01
gear         focus               -20.97                25.42
             Robust/Fragile? (mu = 0)
(Intercept)                   fragile
wt                            fragile
hp                            fragile
gear                          fragile

Sala-i-Martin's Extreme Bounds Analysis (EBA):
- Normal model (N): beta coefficients assumed to be distributed normally across models
- Generic model (G): no assumption about the distribution of beta coefficients across models

              Type  N: CDF(beta <= 0)  N: CDF(beta > 0)  G: CDF(beta <= 0)
(Intercept)   free               1.34             98.66               6.40
wt            free              84.59             15.41              79.90
hp           focus              99.42              0.58              98.58
gear         focus              26.18             73.82              23.45
             G: CDF(beta > 0)
(Intercept)             93.60
wt                      20.10
hp                       1.42
gear                    76.55

> 
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> dev.off()
null device 
          1 
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