ci.var: (Bootstrap) Confidence Intervals for Variances and Standard Deviations

Description

The function ci.var computes and plots confidence intervals for variances, and the function ci.sd computes confidence intervals for the standard deviations, optionally by a grouping and/or split variable. These functions also supports three types of bootstrap confidence intervals (e.g., bias-corrected (BC) percentile bootstrap or bias-corrected and accelerated (BCa) bootstrap confidence intervals) and plots the bootstrap samples with histograms and density curves.

Usage

ci.var(data, ..., method = c("chisq", "bonett"),
       boot = c("none", "perc", "bc", "bca"), nrep = 1000, seed = NULL,
       alternative = c("two.sided", "less", "greater"),
       conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
       na.omit = FALSE, digits = 2, as.na = NULL, plot = c("none", "ci", "boot"),
       hist = TRUE, density = TRUE, point = TRUE, ci = TRUE, line = TRUE,
       filename = NULL, width = NA, height = NA, dpi = 600, write = NULL,
       append = TRUE, check = TRUE, output = TRUE)
ci.sd(data, ..., method = c("chisq", "bonett"),
      boot = c("none", "perc", "bc", "bca"), nrep = 1000, seed = NULL,
      alternative = c("two.sided", "less", "greater"),
      conf.level = 0.95, group = NULL, split = NULL, sort.var = FALSE,
      na.omit = FALSE, digits = 2, as.na = NULL, plot = c("none", "ci", "boot"),
      hist = TRUE, density = TRUE, point = TRUE, ci = TRUE, line = TRUE,
      filename = NULL, width = NA, height = NA, dpi = 600, write = NULL,
      append = TRUE, check = TRUE, output = TRUE)

Value

Returns an object of class misty.object, which is a list with following entries:

call: function call
type: type of analysis
data: list with the input specified in ..., data, group, and split
args: specification of function arguments
boot: data frame with bootstrap replicates of the variance or standard deviation when bootstrapping was requested
plot: ggplot2 object for plotting the results and the data frame used for plotting
result: result table

Arguments

data: a numeric vector or data frame with numeric variables, i.e., factors and character variables are excluded from data before conducting the analysis.
...: an expression indicating the variable names in data, e.g., ci.var(dat, x1, x2, x3). Note that the operators +, -, ~, :, ::, and ! can also be used to select variables, see 'Details' in the df.subset function.
method: a character string specifying the method for computing the confidence interval, must be one of "chisq", or "bonett" (default).
boot: a character string specifying the type of bootstrap confidence intervals (CI), i.e., "none" (default) for not conducting bootstrapping, "perc", for the percentile bootstrap CI "bc" (default) for the bias-corrected (BC) percentile bootstrap CI (without acceleration), and "bca" for the bias-corrected and accelerated (BCa) bootstrap CI, see 'Details' in the ci.cor function.
nrep: a numeric value indicating the number of bootstrap replicates (default is 1000).
seed: a numeric value specifying seeds of the pseudo-random numbers used in the bootstrap algorithm when conducting bootstrapping.
alternative: a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".
conf.level: a numeric value between 0 and 1 indicating the confidence level of the interval.
group: either a character string indicating the variable name of the grouping variable in data, or a vector representing the grouping variable.
split: either a character string indicating the variable name of the split variable in 'data', or a vector representing the split variable.
sort.var: logical: if TRUE, output table is sorted by variables when specifying group.
na.omit: logical: if TRUE, incomplete cases are removed before conducting the analysis (i.e., listwise deletion) when specifying more than one outcome variable.
digits: an integer value indicating the number of decimal places to be used.
as.na: a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis. Note that as.na() function is only applied to data, but not to group or split.
plot: a character string indicating the type of the plot to display, i.e., "none" (default) for not displaying any plots, "ci" for displaying confidence intervals for variances or standard deviations, "boot" for displaying bootstrap samples with histograms and density curves when the argument "boot" is other than "none".
hist: logical: if TRUE (default), histograms are drawn when plotting bootstrap samples (plot = "boot").
density: logical: if TRUE (default), density curves are drawn when plotting bootstrap samples (plot = "boot").
point: logical: if TRUE (default), vertical lines representing the point estimate of the variance or standard deviation are drawn when plotting bootstrap samples (plot = "boot").
ci: logical: if TRUE (default), vertical lines representing the bootstrap confidence intervals of the variance or standard deviation are drawn when plotting bootstrap samples (plot = "boot").
line: logical: if TRUE, a horizontal line is drawn when plot = "ci" or a vertical line is drawn when plot = "boot"
filename: a character string indicating the filename argument including the file extension in the ggsave function. Note that one of ".eps", ".ps", ".tex", ".pdf" (default), ".jpeg", ".tiff", ".png", ".bmp", ".svg" or ".wmf" needs to be specified as file extension in the file argument. Note that plots can only be saved when plot = "ci" or plot = "boot".
width: a numeric value indicating the width argument (default is the size of the current graphics device) in the ggsave function.
height: a numeric value indicating the height argument (default is the size of the current graphics device) in the ggsave function.
dpi: a numeric value indicating the dpi argument (default is 600) in the ggsave function.
write: a character string naming a file for writing the output into either a text file with file extension ".txt" (e.g., "Output.txt") or Excel file with file extension ".xlsx" (e.g., "Output.xlsx"). If the file name does not contain any file extension, an Excel file will be written.
append: logical: if TRUE (default), output will be appended to an existing text file with extension .txt specified in write, if FALSE existing text file will be overwritten.
check: logical: if TRUE (default), argument specification is checked.
output: logical: if TRUE (default), output is shown on the console.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

Details

The confidence interval based on the chi-square distribution is computed by specifying method = "chisq", while the Bonett (2006) confidence interval is requested by specifying method = "bonett". By default, the Bonett confidence interval interval is computed which performs well under moderate departure from normality, while the confidence interval based on the chi-square distribution is highly sensitive to minor violations of the normality assumption and its performance does not improve with increasing sample size. Note that at least four valid observations are needed to compute the Bonett confidence interval.

References

Rasch, D., Kubinger, K. D., & Yanagida, T. (2011). Statistics in psychology - Using R and SPSS. John Wiley & Sons.

Canty, A., & Ripley, B. (2024). boot: Bootstrap R (S-Plus) Functions. R package version 1.3-31.

Bonett, D. G. (2006). Approximate confidence interval for standard deviation of nonnormal distributions. Computational Statistics and Data Analysis, 50, 775-782. https://doi.org/10.1016/j.csda.2004.10.003

Examples

Run this code

#————————————————————————————————————————————————————————————————————————————
# Confidence Interval (CI) for the Variance

# Example 1a: Two-Sided 95% CI
ci.var(mtcars)

# Example 1b: One-Sided 99% CI based on the chi-square distribution
ci.var(mtcars, alternative = "less", method = "chisq")

#————————————————————————————————————————————————————————————————————————————
# Confidence Interval (CI) for the Standard Deviation

# Example 2a: Two-Sided 95% CI
ci.sd(mtcars)

# Example 2b: One-Sided 99% CI based on the chi-square distribution
ci.sd(mtcars, alternative = "less", method = "chisq")

if (FALSE) {
#————————————————————————————————————————————————————————————————————————————
# Bootstrap Confidence Interval (CI)

# Example 3a: Bias-corrected (BC) percentile bootstrap CI
ci.var(mtcars, boot = "bc")

# Example 3b: Bias-corrected and accelerated (BCa) bootstrap CI,
# 5000 bootstrap replications, set seed of the pseudo-random number generator
ci.var(mtcars, boot = "bca", nrep = 5000, seed = 42)

#————————————————————————————————————————————————————————————————————————————
# Grouping and Split Variable

# Example 4a: Grouping variable
ci.var(mtcars, mpg, cyl, disp, group = "vs")

# Alternative specification without using the '...' argument
ci.var(mtcars[, c("mpg", "cyl", "disp")], group = mtcars$vs)

# Example 4b: Split variable
ci.var(mtcars, mpg, cyl, disp, split = "am")

# Alternative specification without using the '...' argument
ci.var(mtcars[, c("mpg", "cyl", "disp")], split = mtcars$am)

# Example 4c: Grouping and split variable
ci.var(mtcars, mpg, cyl, disp, group = "vs", split = "am")

# Alternative specification without using the '...' argument
ci.var(mtcars[, c("mpg", "cyl", "disp")], group = mtcars$vs, split = mtcars$am)

#————————————————————————————————————————————————————————————————————————————
# Plot Confidence Intervals

# Example 6a: Two-Sided 95
ci.var(mtcars, plot = "ci")

# Example 6b: Grouping variable
ci.var(mtcars, disp, hp, group = "vs", plot = "ci")

# Example 6c: Split variable
ci.var(mtcars, disp, hp, split = "am", plot = "ci")

# Example 6d: Plot results using the plot() function, use additional arguments
# see Details in the help page of the function plot.misty.object
object <- ci.var(mtcars, disp, hp, plot = "ci")
plot(object, ybreaks = seq(0, 25000, by = 2500), title = "Confidence Intervals")

#————————————————————————————————————————————————————————————————————————————
# Plot Bootstrap Samples

# Example 7a: Two-Sided 95
ci.var(mtcars, disp, hp, boot = "bc", plot = "boot")

# Example 7b: Grouping variable
ci.var(mtcars, disp, hp, group = "vs", boot = "bc", plot = "boot")

# Example 7c: Split variable
ci.var(mtcars, disp, hp, split = "am", boot = "bc", plot = "boot")

# Example 7d: Plot results using the plot() function, use additional arguments
# see Details in the help page of the function plot.misty.object
object <- ci.var(mtcars, disp, hp, boot = "bc", plot = "boot")
plot(object, fill = "gray30", title = "Bootstrap Samples")

#————————————————————————————————————————————————————————————————————————————
# Write Results and Save Plot

# Example 8a: Write results into a text file
ci.var(mtcars, disp, write = "CI_Var.txt")

# Example 8b: Write results into an Excel file
ci.var(mtcars, disp, write = "CI_Var.xlsx")

# Example 8c: Save plot as PNG file
ci.var(mtcars, disp, plot = "ci", filename = "CI_Var.png",
        width = 9, height = 6)
}

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