├── inst
    ├── lib
    │   └── python
    │   │   ├── __init__.py
    │   │   └── make_utils.py
    ├── test
    │   ├── output
    │   │   └── monte_carlo.log
    │   └── code
    │   │   ├── make_test.py
    │   │   └── monte_carlo.R
    └── make.py
├── .gitignore
├── LICENSE
├── .Rbuildignore
├── NAMESPACE
├── suptCriticalValue.Rproj
├── DESCRIPTION
├── LICENSE.md
├── man
    └── suptCriticalValue.Rd
├── R
    └── suptCriticalValue.R
├── README.Rmd
└── README.md


/inst/lib/python/__init__.py:
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1 | 


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/.gitignore:
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1 | .Rproj.user/
2 | .DS_Store


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/LICENSE:
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1 | YEAR: 2023
2 | COPYRIGHT HOLDER: suptCriticalValue authors
3 | 


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/.Rbuildignore:
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1 | ^.*\.Rproj$
2 | ^\.Rproj\.user$
3 | ^LICENSE\.md$
4 | ^README\.Rmd$
5 | 


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/NAMESPACE:
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1 | # Generated by roxygen2: do not edit by hand
2 | 
3 | export(suptCriticalValue)
4 | 


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/inst/test/output/monte_carlo.log:
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1 | [1] "POINTWISE COVERAGE WITH SINGLE REGRESSOR:"
2 | [1] 0.9544
3 | [1] "SIMULTANEOUS SUP-T COVERAG WITH SINGLE REGRESSOR:"
4 | [1] 0.9496
5 | [1] "POINTWISE COVERAGE WITH MULTIPLE REGRESSORS:"
6 | [1] 0.8484
7 | [1] "SIMULTANEOUS SUP-T COVERAG WITH MULTIPLE REGRESSORS:"
8 | [1] 0.9604
9 | 


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/inst/test/code/make_test.py:
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 1 | import os, sys, subprocess, shutil
 2 | 
 3 | python_lib_path = '../../lib/python/'
 4 | shutil.copytree(python_lib_path, './python_lib/')
 5 | from python_lib.make_utils import * 
 6 | 
 7 | clear_dirs(['../output/'])
 8 | 
 9 | run_rbatch(program = 'monte_carlo.R')
10 | 
11 | shutil.rmtree('python_lib')


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/suptCriticalValue.Rproj:
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 1 | Version: 1.0
 2 | 
 3 | RestoreWorkspace: Default
 4 | SaveWorkspace: Default
 5 | AlwaysSaveHistory: Default
 6 | 
 7 | EnableCodeIndexing: Yes
 8 | UseSpacesForTab: Yes
 9 | NumSpacesForTab: 2
10 | Encoding: UTF-8
11 | 
12 | RnwWeave: Sweave
13 | LaTeX: pdfLaTeX
14 | 
15 | AutoAppendNewline: Yes
16 | StripTrailingWhitespace: Yes
17 | 
18 | BuildType: Package
19 | PackageUseDevtools: Yes
20 | PackageInstallArgs: --no-multiarch --with-keep.source
21 | 


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/inst/make.py:
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 1 | import os, sys, subprocess, shutil
 2 | 
 3 | python_lib_path = './lib/python/'
 4 | shutil.copytree(python_lib_path, './python_lib/')
 5 | from python_lib.make_utils import * 
 6 | 
 7 | root = os.getcwd()
 8 | 
 9 | # UNIT TESTS 
10 | os.chdir('./test/code/')
11 | run_python(program = 'make_test.py')
12 | os.chdir(root)
13 | 
14 | # EXAMPLE 
15 | os.chdir('./example/code/')
16 | run_python(program = 'make_example.py')
17 | os.chdir(root)
18 | 
19 | shutil.rmtree('python_lib')
20 | raw_input('\n Press <Enter> to exit')


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/DESCRIPTION:
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 1 | Package: suptCriticalValue
 2 | Type: Package
 3 | Title: Computes critical values underlying simultaneous sup-t confidence bands
 4 | Version: 0.1.0
 5 | Authors@R: c(person("Ryan", "Kessler", email = "ryan.edmund.kessler@gmail.com", role = c("aut","cre")))
 6 | Description: This package computes the critical values underlying the simultaneous sup-t confidence bands proposed in Montiel Olea and Plagborg-Møller (2019) <https://doi.org/10.1002/jae.2656>.
 7 | Encoding: UTF-8
 8 | LazyData: true
 9 | Imports:
10 |     MASS
11 | Depends:
12 |     R (>= 3.0)
13 | RoxygenNote: 7.2.3.9000
14 | License: MIT + file LICENSE
15 | 


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/LICENSE.md:
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 1 | # MIT License
 2 | 
 3 | Copyright (c) 2023 suptCriticalValue authors
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


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/inst/lib/python/make_utils.py:
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 1 | import os, sys, subprocess, shutil
 2 | 
 3 | LOG_DIR_DEFAULT = '../output/'
 4 | 
 5 | def run_python(program, log_dir = './'):
 6 | 
 7 |     cmd = 'python {0}'.format(program)
 8 | 
 9 |     print('\nExecuting: {0}'.format(cmd))
10 |     subprocess.call(cmd, shell = True) 
11 | 
12 | def run_stata(program, log_dir = LOG_DIR_DEFAULT):
13 |     
14 |     log_file = program.replace('.do', '.log') 
15 |     cmd      = 'stata-se -b {0}'.format(program)
16 | 
17 |     print('\n Executing: {0}'.format(cmd))
18 | 
19 |     subprocess.call(cmd, shell = True) 
20 |     os.rename(log_file, log_dir + log_file) 
21 | 
22 | def run_rbatch(program, log_dir = LOG_DIR_DEFAULT):
23 |     
24 |     log_file = program.replace('.R', '.log') 
25 |     cmd      = 'Rscript --no-save --no-restore --verbose {0} > {1}'.format(program, log_file)
26 | 
27 |     print('\n Executing: {0}'.format(cmd))
28 | 
29 |     subprocess.call(cmd, shell = True) 
30 |     os.rename(log_file, log_dir + log_file) 
31 | 
32 | def clear_dirs(dir_list):
33 | 
34 |     for dir in dir_list:
35 |         if os.path.exists(dir):
36 |             shutil.rmtree(dir)
37 |         os.mkdir(dir)
38 | 
39 | 


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/man/suptCriticalValue.Rd:
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 1 | % Generated by roxygen2: do not edit by hand
 2 | % Please edit documentation in R/suptCriticalValue.R
 3 | \name{suptCriticalValue}
 4 | \alias{suptCriticalValue}
 5 | \title{Create sup t critical value}
 6 | \usage{
 7 | suptCriticalValue(vcov_matrix, num_sim = 1000, conf_level = 0.95, seed = NULL)
 8 | }
 9 | \arguments{
10 | \item{vcov_matrix}{Variance-covariance matrix}
11 | 
12 | \item{num_sim}{Number of bootstrap simulations. Default is 1000.}
13 | 
14 | \item{conf_level}{Confidence level. Default is 0.95.}
15 | 
16 | \item{seed}{Random seed if provided. Default is NULL.}
17 | }
18 | \value{
19 | Numeric. Sup t critical value. Multiple by the standard error to get the confidence interval length.
20 | }
21 | \description{
22 | Create sup t critical value
23 | }
24 | \examples{
25 | library(MASS)
26 | data(Cars93, package = "MASS")
27 | conf_level  <- 0.95
28 | model       <- lm(Price ~ Weight + Wheelbase + Cylinders, data=Cars93)
29 | 
30 | beta        <- matrix(coef(model))
31 | vcov_matrix <- vcov(model)
32 | std_error   <- sqrt(diag(vcov_matrix))
33 | 
34 | pw_crit     <- qt(1 - ((1 - conf_level) / 2), model$df.residual) 
35 | supt_crit   <- suptCriticalValue(vcov_matrix = vcov_matrix)
36 | 
37 | pw_ci_lb    <- beta - pw_crit * std_error 
38 | pw_ci_ub    <- beta + pw_crit * std_error 
39 | supt_ci_lb  <- beta - supt_crit * std_error 
40 | supt_ci_ub  <- beta + supt_crit * std_error 
41 | 
42 | print("POINTWISE 95 PERCENT CONFIDENCE INTERVAL: ")
43 | print(paste0(
44 |   "[", pw_ci_lb, ", ", pw_ci_ub, "]"
45 | ))
46 | 
47 | print("SIMULTANEOUS SUP-T 95 PERCENT CONFIDENCE INTERVAL: ")
48 | print(paste0(
49 |   "[", supt_ci_lb, ", ", supt_ci_ub, "]"
50 | ))
51 | 
52 | }
53 | 


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/R/suptCriticalValue.R:
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 1 | #' Create sup t critical value
 2 | #'
 3 | #' @param vcov_matrix Variance-covariance matrix
 4 | #' @param num_sim Number of bootstrap simulations. Default is 1000.
 5 | #' @param conf_level Confidence level. Default is 0.95.
 6 | #' @param seed Random seed if provided. Default is NULL.
 7 | #'
 8 | #' @return Numeric. Sup t critical value. Multiple by the standard error to get the confidence interval length.
 9 | #' 
10 | #' @examples 
11 | #' library(MASS)
12 | #' data(Cars93, package = "MASS")
13 | #' conf_level  <- 0.95
14 | #' model       <- lm(Price ~ Weight + Wheelbase + Cylinders, data=Cars93)
15 | #' 
16 | #' beta        <- matrix(coef(model))
17 | #' vcov_matrix <- vcov(model)
18 | #' std_error   <- sqrt(diag(vcov_matrix))
19 | #' 
20 | #' pw_crit     <- qt(1 - ((1 - conf_level) / 2), model$df.residual) 
21 | #' supt_crit   <- suptCriticalValue(vcov_matrix = vcov_matrix)
22 | #' 
23 | #' pw_ci_lb    <- beta - pw_crit * std_error 
24 | #' pw_ci_ub    <- beta + pw_crit * std_error 
25 | #' supt_ci_lb  <- beta - supt_crit * std_error 
26 | #' supt_ci_ub  <- beta + supt_crit * std_error 
27 | #' 
28 | #' print("POINTWISE 95 PERCENT CONFIDENCE INTERVAL: ")
29 | #' print(paste0(
30 | #'   "[", pw_ci_lb, ", ", pw_ci_ub, "]"
31 | #' ))
32 | #' 
33 | #' print("SIMULTANEOUS SUP-T 95 PERCENT CONFIDENCE INTERVAL: ")
34 | #' print(paste0(
35 | #'   "[", supt_ci_lb, ", ", supt_ci_ub, "]"
36 | #' ))
37 | #' 
38 | #' @export
39 | suptCriticalValue <- function(vcov_matrix, num_sim = 1000, conf_level = 0.95, seed = NULL) {
40 |   if (!is.null(seed)) { 
41 |     if (exists(".Random.seed")) {
42 |       seed_before_call <- .Random.seed
43 |       on.exit({
44 |         .Random.seed <<- seed_before_call
45 |       })
46 |     }
47 |     set.seed(seed)
48 |   }
49 |   
50 |   if (conf_level <= 0 | conf_level >= 1) {
51 |     stop("Confidence level must live in (0, 1)")
52 |   }
53 | 
54 |   std_errors <- t(sqrt(diag(vcov_matrix)))
55 |   draws <- MASS::mvrnorm(n = num_sim, mu = rep(0, nrow(vcov_matrix)), Sigma = vcov_matrix)
56 | 
57 |   t <- apply(draws, 1, FUN = function(x) max(abs(x / std_errors)))
58 |   critical_value <- as.numeric(stats::quantile(t, probs = conf_level))
59 | 
60 |   return(critical_value)
61 | }
62 | 


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/README.Rmd:
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 1 | ---
 2 | output: github_document
 3 | ---
 4 | 
 5 | <!-- README.md is generated from README.Rmd. Please edit that file -->
 6 | 
 7 | ```{r, include = FALSE}
 8 | knitr::opts_chunk$set(
 9 |   collapse = TRUE,
10 |   comment = "#>",
11 |   fig.path = "man/figures/README-",
12 |   out.width = "100%"
13 | )
14 | ```
15 | 
16 | # Computing Simultaneous Confidence Bands in R
17 | 
18 | Simultaneous confidence bands are versatile tools for visualizing estimation uncertainty for parameter vectors ([Montiel Olea and Plagborg-Møller 2019](https://doi.org/10.1002/jae.2656)). 
19 | 
20 | This repository houses a [R](https://www.r-project.org/) package that computes the critical values underlying the simultaneous sup-t confidence bands proposed in [Montiel Olea and Plagborg-Møller (2019)](https://doi.org/10.1002/jae.2656). 
21 | 
22 | ## Installation
23 | 
24 | You can install the package from [GitHub](https://github.com/):
25 | 
26 | ``` r
27 | # install.packages("devtools")
28 | devtools::install_github("ryanedmundkessler/suptCriticalValue")
29 | ```
30 | 
31 | The following example shows how to calculate sup-t critical values and, in turn, construct sup-t confidence bands:
32 | 
33 | ```{r}
34 | library(suptCriticalValue)
35 | library(MASS)
36 | data(Cars93, package = "MASS")
37 | conf_level  <- 0.95
38 | model       <- lm(Price ~ Weight + Wheelbase + Cylinders, data=Cars93)
39 | 
40 | beta        <- matrix(coef(model))
41 | vcov_matrix <- vcov(model)
42 | std_error   <- sqrt(diag(vcov_matrix))
43 | 
44 | pw_crit     <- qt(1 - ((1 - conf_level) / 2), model$df.residual) 
45 | supt_crit   <- suptCriticalValue(vcov_matrix = vcov_matrix)
46 | 
47 | pw_ci_lb    <- beta - pw_crit * std_error 
48 | pw_ci_ub    <- beta + pw_crit * std_error 
49 | supt_ci_lb  <- beta - supt_crit * std_error 
50 | supt_ci_ub  <- beta + supt_crit * std_error 
51 | 
52 | print("POINTWISE 95 PERCENT CONFIDENCE INTERVAL: ")
53 | print(paste0(
54 |   "[", pw_ci_lb, ", ", pw_ci_ub, "]"
55 | ))
56 | 
57 | print("SIMULTANEOUS SUP-T 95 PERCENT CONFIDENCE INTERVAL: ")
58 | print(paste0(
59 |   "[", supt_ci_lb, ", ", supt_ci_ub, "]"
60 | ))
61 | ```
62 | 
63 | ## Unit Tests
64 | 
65 | [`monte_carlo.R`](./inst/test/code/monte_carlo.R) asserts that the resulting sup-t confidence bands have expected coverage under select data generating processes 
66 | 
67 | ## Author
68 | 
69 | Ryan Kessler
70 | <br>Email: ryan.edmund.kessler@gmail.com
71 | 
72 | ## License
73 | 
74 | This project is licensed under the MIT License. See the [LICENSE.md](LICENSE.md) file for details
75 | 
76 | ## References
77 | 
78 | Montiel Olea, José Luis and Mikkel Plagborg-Møller. 2019. Simultaneous Confidence Bands: Theory, Implementation, and an Application to SVARs. Journal of Applied Econometrics. https://doi.org/10.1002/jae.2656
79 | 


--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
 1 | 
 2 | <!-- README.md is generated from README.Rmd. Please edit that file -->
 3 | 
 4 | # Computing Simultaneous Confidence Bands in R
 5 | 
 6 | Simultaneous confidence bands are versatile tools for visualizing
 7 | estimation uncertainty for parameter vectors ([Montiel Olea and
 8 | Plagborg-Møller 2019](https://doi.org/10.1002/jae.2656)).
 9 | 
10 | This repository houses a [R](https://www.r-project.org/) package that
11 | computes the critical values underlying the simultaneous sup-t
12 | confidence bands proposed in [Montiel Olea and Plagborg-Møller
13 | (2019)](https://doi.org/10.1002/jae.2656).
14 | 
15 | ## Installation
16 | 
17 | You can install the package from [GitHub](https://github.com/):
18 | 
19 | ``` r
20 | # install.packages("devtools")
21 | devtools::install_github("ryanedmundkessler/suptCriticalValue")
22 | ```
23 | 
24 | The following example shows how to calculate sup-t critical values and,
25 | in turn, construct sup-t confidence bands:
26 | 
27 | ``` r
28 | library(suptCriticalValue)
29 | library(MASS)
30 | data(Cars93, package = "MASS")
31 | conf_level  <- 0.95
32 | model       <- lm(Price ~ Weight + Wheelbase + Cylinders, data=Cars93)
33 | 
34 | beta        <- matrix(coef(model))
35 | vcov_matrix <- vcov(model)
36 | std_error   <- sqrt(diag(vcov_matrix))
37 | 
38 | pw_crit     <- qt(1 - ((1 - conf_level) / 2), model$df.residual) 
39 | supt_crit   <- suptCriticalValue(vcov_matrix = vcov_matrix)
40 | 
41 | pw_ci_lb    <- beta - pw_crit * std_error 
42 | pw_ci_ub    <- beta + pw_crit * std_error 
43 | supt_ci_lb  <- beta - supt_crit * std_error 
44 | supt_ci_ub  <- beta + supt_crit * std_error 
45 | 
46 | print("POINTWISE 95 PERCENT CONFIDENCE INTERVAL: ")
47 | #> [1] "POINTWISE 95 PERCENT CONFIDENCE INTERVAL: "
48 | print(paste0(
49 |   "[", pw_ci_lb, ", ", pw_ci_ub, "]"
50 | ))
51 | #> [1] "[-21.330171843335, 46.83621403265]"      
52 | #> [2] "[0.00251094532423298, 0.016128208267558]"
53 | #> [3] "[-0.690962683241204, 0.212504357845869]" 
54 | #> [4] "[-8.40398530927412, 9.84209118926257]"   
55 | #> [5] "[-11.7914298114545, 18.1682526011994]"   
56 | #> [6] "[-7.00047790888086, 15.8049479269484]"   
57 | #> [7] "[-1.15493094107966, 25.1081284937888]"   
58 | #> [8] "[-1.38976348129131, 32.8553708816936]"
59 | 
60 | print("SIMULTANEOUS SUP-T 95 PERCENT CONFIDENCE INTERVAL: ")
61 | #> [1] "SIMULTANEOUS SUP-T 95 PERCENT CONFIDENCE INTERVAL: "
62 | print(paste0(
63 |   "[", supt_ci_lb, ", ", supt_ci_ub, "]"
64 | ))
65 | #> [1] "[-33.2487461671825, 58.7547883564975]"     
66 | #> [2] "[0.000130030473141085, 0.0185091231186499]"
67 | #> [3] "[-0.848929677383055, 0.37047135198772]"    
68 | #> [4] "[-11.5942266000777, 13.0323324800662]"     
69 | #> [5] "[-17.0297404093453, 23.4065631990902]"     
70 | #> [6] "[-10.9879001451987, 19.7923701632663]"     
71 | #> [7] "[-5.74690426962871, 29.7001018223379]"     
72 | #> [8] "[-7.37736534532344, 38.8429727457257]"
73 | ```
74 | 
75 | ## Unit Tests
76 | 
77 | [`monte_carlo.R`](./inst/test/code/monte_carlo.R) asserts that the
78 | resulting sup-t confidence bands have expected coverage under select
79 | data generating processes
80 | 
81 | ## Author
82 | 
83 | Ryan Kessler <br>Email: <ryan.edmund.kessler@gmail.com>
84 | 
85 | ## License
86 | 
87 | This project is licensed under the MIT License. See the
88 | [LICENSE.md](LICENSE.md) file for details
89 | 
90 | ## References
91 | 
92 | Montiel Olea, José Luis and Mikkel Plagborg-Møller. 2019. Simultaneous
93 | Confidence Bands: Theory, Implementation, and an Application to SVARs.
94 | Journal of Applied Econometrics. <https://doi.org/10.1002/jae.2656>
95 | 


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/inst/test/code/monte_carlo.R:
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  1 | library(MASS)
  2 | library(suptCriticalValue)
  3 | set.seed(19240)
  4 | 
  5 | main <- function() {
  6 |     num_reps      <- 2500
  7 |     num_obs       <- 100000
  8 |     conf_level    <- 0.95
  9 |     cov_tolerance <- 0.02
 10 |     
 11 |     results       <- replicate(num_reps, coverage_simulation(num_obs = num_obs, multiple_regressors = FALSE,
 12 |                                                              conf_level = conf_level))
 13 |     pw_coverage   <- mean(unlist(results[1,]))
 14 |     supt_coverage <- mean(unlist(results[2,]))
 15 |     
 16 |     print("POINTWISE COVERAGE WITH SINGLE REGRESSOR:")
 17 |     print(pw_coverage)
 18 |     
 19 |     print("SIMULTANEOUS SUP-T COVERAG WITH SINGLE REGRESSOR:")
 20 |     print(supt_coverage)
 21 |     
 22 |     stopifnot(abs(pw_coverage - conf_level) <= cov_tolerance)
 23 |     stopifnot(abs(supt_coverage - conf_level) <= cov_tolerance)
 24 |     
 25 |     results       <- replicate(num_reps, coverage_simulation(num_obs = num_obs, multiple_regressors = TRUE,
 26 |                                                              conf_level = conf_level))
 27 |     pw_coverage   <- mean(unlist(results[1,]))
 28 |     supt_coverage <- mean(unlist(results[2,]))
 29 |     
 30 |     print("POINTWISE COVERAGE WITH MULTIPLE REGRESSORS:")
 31 |     print(pw_coverage)
 32 |     
 33 |     print("SIMULTANEOUS SUP-T COVERAG WITH MULTIPLE REGRESSORS:")
 34 |     print(supt_coverage)
 35 |     
 36 |     stopifnot(abs(pw_coverage - conf_level) > 3 * cov_tolerance)
 37 |     stopifnot(abs(supt_coverage - conf_level) <= cov_tolerance)
 38 | }
 39 | 
 40 | coverage_simulation <- function(num_obs, num_reps, multiple_regressors, conf_level = 0.95) {
 41 |     data     <- simulate_data(num_obs = num_obs, multiple_regressors = multiple_regressors)
 42 |     coverage <- determine_coverage(data, conf_level = conf_level, multiple_regressors = multiple_regressors)
 43 |     return(coverage)
 44 | }
 45 | 
 46 | simulate_data <- function(num_obs, multiple_regressors = TRUE) {
 47 |   
 48 |     num_obs <- num_obs
 49 |     if (multiple_regressors == TRUE) {
 50 |         vcov_matrix <- matrix(c(1, 0.2, 0.2, 
 51 |                                 0.2, 1, 0.2, 
 52 |                                 0.2, 0.2, 1), nrow = 3, ncol = 3, byrow = TRUE)     
 53 |     } else {
 54 |         vcov_matrix <- matrix(1)
 55 |     }
 56 | 
 57 |     true_beta <- rep(1, nrow(vcov_matrix))
 58 |     X         <- mvrnorm(n = num_obs, mu = rep(0, nrow(vcov_matrix)), Sigma = vcov_matrix)
 59 |     y         <- X %*% true_beta + rnorm(num_obs, 0, 10)
 60 |     data      <- as.data.frame(cbind(y, X))
 61 |     
 62 |     if (multiple_regressors == TRUE) {
 63 |         colnames(data) <- c("y", "x1", "x2", "x3")
 64 |     } else {
 65 |         colnames(data) <- c("y", "x1")
 66 |     }
 67 |     
 68 |     return(data)
 69 | }
 70 | 
 71 | determine_coverage <- function(data, multiple_regressors, conf_level = 0.95) {
 72 |   
 73 |     if (multiple_regressors == TRUE) {
 74 |         model <- lm(y ~ x1 + x2 + x3 - 1, data = data)
 75 |     } else {
 76 |         model <- lm(y ~ x1 - 1, data = data)
 77 |     }
 78 |     beta        <- matrix(coef(model))
 79 |     vcov_matrix <- vcov(model)
 80 |     std_error   <- sqrt(diag(vcov_matrix))
 81 |     true_beta   <- rep(1, nrow(vcov_matrix))
 82 |     
 83 |     pw_crit     <- qt(1 - ((1 - conf_level) / 2), model$df.residual) 
 84 |     supt_crit   <- suptCriticalValue(vcov_matrix = vcov_matrix)
 85 |     
 86 |     pw_cover    <- is_beta_covered(beta = beta, vcov_matrix = vcov_matrix, 
 87 |                                    true_beta = true_beta, critical_value = pw_crit)
 88 |     
 89 |     supt_cover  <- is_beta_covered(beta = beta, vcov_matrix = vcov_matrix, 
 90 |                                    true_beta = true_beta, critical_value = supt_crit)
 91 |     
 92 |     return_list <- list(pw_cover   = pw_cover,
 93 |                         supt_cover = supt_cover)
 94 |     
 95 |     return(return_list)
 96 | }
 97 | 
 98 | is_beta_covered <- function(beta, vcov_matrix, true_beta, critical_value) {
 99 |   
100 |     std_error   <- sqrt(diag(vcov_matrix))
101 |   
102 |     conf_lb     <- beta - critical_value * std_error 
103 |     conf_ub     <- beta + critical_value * std_error
104 |   
105 |     covered     <- (true_beta >= conf_lb) & (true_beta <= conf_ub)
106 |     all_covered <- min(covered)
107 |   
108 |     return(all_covered)
109 | }
110 | 
111 | main()
112 | 


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