This package contains R functions to create graphics of p-value functions, confidence distributions, confidence densities, or the Surprisal value (S-value) (Greenland 2019). An R-script to reproduce the plots in the publication is also available.
Download the file confidence_distributions.R to your computer. You can either source() the function in R or open it, select and run everything. After loading the function, it's ready for use.
To reproduce the plots from the publication, download the file paper_plots.R and run it after loading the main function contained in the file confidence_distributions.R (see above).
Alternatively, you can source the files directly from the GitHub repository using the devtools package:
library(devtools)
# Load function
source_url("https://raw.githubusercontent.com/DInfanger/pvalue_functions/master/confidence_distributions.R")
The function depends on the following R packages, which need to be installed beforehand:
Use the command install.packages(c("ggplot2", "scales", "zipfR")) in R to install those packages.
The newest version of ggplot2 (3.1.1) has a bug in sec_axis that will lead to the secondary y-axis being labelled wrongly.
It is therefore recommended that you install the developmental version of ggplot2 until the bug has been fixed. You can install the developmental version using the following command (after installing the devtools package): devtools::install_github("tidyverse/ggplot2")
There is only one function needed to create the plots: conf_dist(). The function has the following arguments:
estimate: Numerical vector containing the estimate(s).n: Numerical vector containing the sample size(s). Required for correlations, variances and proportions. Must be equal the number of estimates.df: Numerical vector containing the degrees of freedom. Required for statistics based on the t-distribution (e.g. linear regression) and t-tests. Must be equal the number of estimates.stderr: Numerical vector containing the standard error(s) of the estimate(s). Required for statistics based on the t-distribution (e.g. linear regression) and the normal distribution (e.g. logistic regression). Must be equal the number of estimate(s).tstat: Numerical vector containing the t-statistic(s). Required for t-tests (means and mean differences). Must be equal the number of estimates. type**: String indicating the type of the estimate. Must be one of the following: ttest, linreg, gammareg, general_t, logreg, poisreg, coxreg, general_z, pearson, spearman, kendall, var, prop.plot_type*: String indicating the type of plot. Must be one of the following: cdf (confidence distribution), pdf (confidence density), p_val (*p-value function), s_val (Surprisal).n_values (optional): Integer indicating the number of points that are used to generate the graphics. The higher this number, the higher the computation time and resolution.est_names (optional): String vector indicating the names of the estimate(s). Must be equal the number of estimates.conf_level (optional): Numerical vector indicating the confidence level(s). Bust be between 0 and 1.null_values (optional): Numerical vector indicating the null value(s) in the plottrans (optional): String indicating the transformation function that will be applied to the estimates and confidence curves. For example: “exp” for an exponential transformation of the log-odds in logistic regression. alternative**: String indicating if the confidence level(s) are two-sided or one-sided. Must be one of the following: two_sided, one_sided.log_yaxis: Logical. Indicating if a portion of the y-axis should be displayed on the logarithmic scale.cut_logyaxis: Numerical value indicating the threshold below which the y-axis will be displayed logarithmically. Must lie between 0 and 1.xlab (optional): String indicating the label of the x-axis.xlim (optional): Optional numerical vector of length 2 indicating the limits of the x-axis on the untransformed scale.together: Logical. Indicating if graphics for multiple estimates should be displayed together or on separate plots.plot_p_limit**: Numerical value indicating the lower limit of the y-axis. Must be greater than 0 for a logarithmic scale (i.e. log_yaxis = TRUE).estimate, df, tstat.estimate, df, stderr.estimate, stderr.estimate, n.The main function conf_dist() returns five objects in a list:
res_frame: A data frame containing the values used to construct the plot.conf_frame: A data frame containing the confidence intervals for the specified confidence levels for all estimates.counternull_frame: A data frame containing the counternull values for the specified null values (see Rosenthal & Rubin (1994) for more information about the counternull).point_est**: A data frame containing the point estimates for all estimates. The point estimates correspond to the mean, median or mode of the confidence density (see Xie & Singh (2013) for more information). Estimates are produced using numerical procedures: Increase the number of points n_values for higher numerical precision.plot: A ggplot2 plot object.
#-----------------------------------------------------------------------------
# Sourcing function
#-----------------------------------------------------------------------------
#source("confidence_distributions.R")
#-----------------------------------------------------------------------------
# T-Test
#-----------------------------------------------------------------------------
with(sleep, mean(extra[group == 1])) - with(sleep, mean(extra[group == 2]))
#> [1] -1.58
t.test(extra ~ group, data = sleep, var.equal = FALSE)
#>
#> Welch Two Sample t-test
#>
#> data: extra by group
#> t = -1.8608, df = 17.776, p-value = 0.07939
#> alternative hypothesis: true difference in means is not equal to 0
#> 95 percent confidence interval:
#> -3.3654832 0.2054832
#> sample estimates:
#> mean in group 1 mean in group 2
#> 0.75 2.33
#-----------------------------------------------------------------------------
# Create p-value function
#-----------------------------------------------------------------------------
res <- conf_dist(
estimate = c(-1.58)
, df = c(17.77647)
, tstat = c(-1.860813)
, type = "ttest"
, plot_type = "p_val"
, n_values = 1e4L
# , est_names = c("")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(0)
, trans = "identity"
, alternative = "two_sided"
, log_yaxis = TRUE
, cut_logyaxis = 0.05
, xlab = "Mean difference (group 1 - group 2)"
, together = FALSE
, plot_p_limit = 1 - 0.999
)
#-----------------------------------------------------------------------------
# Model
#-----------------------------------------------------------------------------
mod <- lm(Infant.Mortality~Agriculture + Fertility + Examination, data = swiss)
summary(mod)
#>
#> Call:
#> lm(formula = Infant.Mortality ~ Agriculture + Fertility + Examination,
#> data = swiss)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -8.5375 -1.4021 -0.0066 1.7381 5.9150
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) 11.01896 4.47291 2.463 0.01784 *
#> Agriculture -0.02143 0.02394 -0.895 0.37569
#> Fertility 0.13115 0.04145 3.164 0.00285 **
#> Examination 0.04913 0.08351 0.588 0.55942
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 2.645 on 43 degrees of freedom
#> Multiple R-squared: 0.2291, Adjusted R-squared: 0.1753
#> F-statistic: 4.26 on 3 and 43 DF, p-value: 0.01014
#-----------------------------------------------------------------------------
# Create p-value function
#-----------------------------------------------------------------------------
res <- conf_dist(
estimate = c(-0.02143)
, df = c(43)
, stderr = (0.02394)
, type = "linreg"
, plot_type = "p_val"
, n_values = 1e4L
# , est_names = c("")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(0)
, trans = "identity"
, alternative = "two_sided"
, log_yaxis = TRUE
, cut_logyaxis = 0.05
, xlab = "Coefficient Agriculture"
, together = FALSE
, plot_p_limit = 1 - 0.999
)
res <- conf_dist(
estimate = c(-0.02143)
, df = c(43)
, stderr = (0.02394)
, type = "linreg"
, plot_type = "cdf"
, n_values = 1e4L
# , est_names = c("")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(0)
, trans = "identity"
, alternative = "two_sided"
# , log_yaxis = TRUE
# , cut_logyaxis = 0.05
, xlab = "Coefficient Agriculture"
, xlim = c(-0.12, 0.065)
, together = FALSE
# , plot_p_limit = 1 - 0.999
)
res <- conf_dist(
estimate = c(0.13115, 0.04913)
, df = c(43, 43)
, stderr = c(0.04145, 0.08351)
, type = "linreg"
, plot_type = "p_val"
, n_values = 1e4L
, est_names = c("Fertility", "Examination")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(0)
, trans = "identity"
, alternative = "two_sided"
, log_yaxis = TRUE
, cut_logyaxis = 0.05
, xlab = "Coefficients"
, together = TRUE
, plot_p_limit = 1 - 0.999
)
res <- conf_dist(
estimate = c(0.13115, 0.04913)
, df = c(43, 43)
, stderr = c(0.04145, 0.08351)
, type = "linreg"
, plot_type = "s_val"
, n_values = 1e4L
, est_names = c("Fertility", "Examination")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(0)
, trans = "identity"
, alternative = "two_sided"
# , log_yaxis = TRUE
# , cut_logyaxis = 0.05
, xlab = "Coefficients"
, together = TRUE
, plot_p_limit = 1 - 0.999
)
#-----------------------------------------------------------------------------
# Calculate Pearson's correlation coefficient
#-----------------------------------------------------------------------------
cor.test(swiss$Fertility, swiss$Agriculture, alternative = "two.sided", method = "pearson")
#>
#> Pearson's product-moment correlation
#>
#> data: swiss$Fertility and swiss$Agriculture
#> t = 2.5316, df = 45, p-value = 0.01492
#> alternative hypothesis: true correlation is not equal to 0
#> 95 percent confidence interval:
#> 0.07334947 0.58130587
#> sample estimates:
#> cor
#> 0.3530792
#-----------------------------------------------------------------------------
# Create p-value function
#-----------------------------------------------------------------------------
res <- conf_dist(
estimate = c(0.3530792)
, n = 47
, type = "pearson"
, plot_type = "p_val"
, n_values = 1e4L
# , est_names = c("")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(0)
, trans = "identity"
, alternative = "one_sided"
, log_yaxis = TRUE
, cut_logyaxis = 0.05
, xlab = "Pearson correlation"
, together = TRUE
, plot_p_limit = 1 - 0.999
)
#-----------------------------------------------------------------------------
# Calculate logistic regression model using a dataset from UCLA
#-----------------------------------------------------------------------------
dat_tmp <- read.csv("https://stats.idre.ucla.edu/stat/data/binary.csv")
dat_tmp$rank <- factor(dat_tmp$rank)
logistic_mod <- glm(admit ~ gre + gpa + rank, data = dat_tmp, family = "binomial")
summary(logistic_mod)
#>
#> Call:
#> glm(formula = admit ~ gre + gpa + rank, family = "binomial",
#> data = dat_tmp)
#>
#> Deviance Residuals:
#> Min 1Q Median 3Q Max
#> -1.6268 -0.8662 -0.6388 1.1490 2.0790
#>
#> Coefficients:
#> Estimate Std. Error z value Pr(>|z|)
#> (Intercept) -3.989979 1.139951 -3.500 0.000465 ***
#> gre 0.002264 0.001094 2.070 0.038465 *
#> gpa 0.804038 0.331819 2.423 0.015388 *
#> rank2 -0.675443 0.316490 -2.134 0.032829 *
#> rank3 -1.340204 0.345306 -3.881 0.000104 ***
#> rank4 -1.551464 0.417832 -3.713 0.000205 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> (Dispersion parameter for binomial family taken to be 1)
#>
#> Null deviance: 499.98 on 399 degrees of freedom
#> Residual deviance: 458.52 on 394 degrees of freedom
#> AIC: 470.52
#>
#> Number of Fisher Scoring iterations: 4
rm(dat_tmp)
#-----------------------------------------------------------------------------
# Create p-value function
#-----------------------------------------------------------------------------
res <- conf_dist(
estimate = c(0.804037549)
, stderr = c(0.331819298)
, type = "logreg"
, plot_type = "p_val"
, n_values = 1e4L
, est_names = c("GPA")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(log(1))
, trans = "exp"
, alternative = "two_sided"
, log_yaxis = TRUE
, cut_logyaxis = 0.05
, xlab = "Odds Ratio (GPA)"
, xlim = log(c(0.4, 5))
, together = FALSE
, plot_p_limit = 1 - 0.999
)
res <- conf_dist(
estimate = c(0.44)
, n = c(50)
, type = "prop"
, plot_type = "p_val"
, n_values = 1e4L
# , est_names = c("")
, conf_level = c(0.95, 0.90, 0.80)
, null_values = c(0.5)
, trans = "identity"
, alternative = "two_sided"
, log_yaxis = TRUE
, cut_logyaxis = 0.05
, xlab = "Proportion"
# , xlim = log(c(0.95, 1.2))
, together = FALSE
, plot_p_limit = 1 - 0.999
)
Bender R, Berg G, Zeeb H. (2005): Tutorial: using confidence curves in medical research. Biom J. 47(2): 237-47.
Fraser D. A. S. (2019): The p-value function and statistical inference. The American Statistician, 73:sup1, 135-147.
Greenland S (2019): Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution with S-Values. The American Statistician, 73sup1, 106-114.
Poole C. (1987a): Beyond the confidence interval. Am J Public Health. 77(2): 195-9.
Poole C. (1987b) Confidence intervals exclude nothing. Am J Public Health. 77(4): 492-3.
Rosenthal R, Rubin DB. (1994): The counternull value of an effect size: A new statistic. Psychol Sci. 5(6): 329-34.
Schweder T, Hjort NL. (2016): Confidence, likelihood, probability: statistical inference with confidence distributions. New York, NY: Cambridge University Press.
Xie M, Singh K, Strawderman WE. (2011): Confidence Distributions and a Unifying Framework for Meta-Analysis. J Am Stat Assoc 106(493): 320-33. doi: 10.1198/jasa.2011.tm09803.
Xie Mg, Singh K. (2013): Confidence distribution, the frequentist distribution estimator of a parameter: A review. Internat Statist Rev. 81(1): 3-39.
#> R version 3.6.0 (2019-04-26)
#> Platform: x86_64-w64-mingw32/x64 (64-bit)
#> Running under: Windows 10 x64 (build 17134)
#>
#> Matrix products: default
#>
#> locale:
#> [1] LC_COLLATE=C LC_CTYPE=German_Switzerland.1252
#> [3] LC_MONETARY=German_Switzerland.1252 LC_NUMERIC=C
#> [5] LC_TIME=German_Switzerland.1252
#>
#> attached base packages:
#> [1] stats graphics grDevices utils datasets methods base
#>
#> other attached packages:
#> [1] zipfR_0.6-10 scales_1.0.0 ggplot2_3.1.1 usethis_1.5.0
#> [5] devtools_2.0.2
#>
#> loaded via a namespace (and not attached):
#> [1] Rcpp_1.0.1 RColorBrewer_1.1-2 highr_0.8
#> [4] pillar_1.3.1 plyr_1.8.4 compiler_3.6.0
#> [7] prettyunits_1.0.2 remotes_2.0.4 tools_3.6.0
#> [10] testthat_2.1.1 digest_0.6.18 pkgbuild_1.0.3
#> [13] pkgload_1.0.2 tibble_2.1.1 evaluate_0.13
#> [16] memoise_1.1.0 gtable_0.3.0 pkgconfig_2.0.2
#> [19] rlang_0.3.4 cli_1.1.0 curl_3.3
#> [22] xfun_0.6 dplyr_0.8.0.1 withr_2.1.2
#> [25] stringr_1.4.0 httr_1.4.0 knitr_1.22
#> [28] desc_1.2.0 fs_1.3.0 tidyselect_0.2.5
#> [31] rprojroot_1.3-2 grid_3.6.0 glue_1.3.1
#> [34] R6_2.4.0 processx_3.3.0 sessioninfo_1.1.1
#> [37] purrr_0.3.2 callr_3.2.0 magrittr_1.5
#> [40] backports_1.1.4 ps_1.3.0 assertthat_0.2.1
#> [43] colorspace_1.4-1 labeling_0.3 stringi_1.4.3
#> [46] lazyeval_0.2.2 munsell_0.5.0 crayon_1.3.4
