item.alpha: Coefficient Alpha and Item Statistics

Description

This function computes point estimate and confidence interval for the (ordinal) coefficient alpha (aka Cronbach's alpha) along with the corrected item-total correlation and coefficient alpha if item deleted.

Usage

item.alpha(..., data = NULL, exclude = NULL, std = FALSE, ordered = FALSE,
           na.omit = FALSE, print = c("all", "alpha", "item"), digits = 2,
           conf.level = 0.95, as.na = NULL, 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: data frame used for the current analysis
args: specification of function arguments
result: list with result tables, i.e., alpha for a table with coefficient alpha and itemstat for a table with item statistics

Arguments

...: a matrix, data frame, variance-covariance or correlation matrix. Note that raw data is needed to compute ordinal coefficient alpha, i.e., ordered = TRUE. Alternatively, an expression indicating the variable names in data e.g., item.alpha(x1, x2, x3, data = dat). Note that the operators ., +, -, ~, :, ::, and ! can also be used to select variables, see 'Details' in the df.subset function.
data: a data frame when specifying one or more variables in the argument .... Note that the argument is NULL when specifying a matrix, data frame, variance-covariance or correlation matrix for the argument ....
exclude: a character vector indicating items to be excluded from the analysis.
std: logical: if TRUE, the standardized coefficient alpha is computed.
ordered: logical: if TRUE, variables are treated as ordered (ordinal) variables to compute ordinal coefficient alpha.
na.omit: logical: if TRUE, incomplete cases are removed before conducting the analysis (i.e., listwise deletion); if FALSE (default), pairwise deletion is used.
print: a character vector indicating which results to show, i.e. "all" (default), for all results "alpha" for the coefficient alpha, and "item" for item statistics.
digits: an integer value indicating the number of decimal places to be used for displaying coefficient alpha and item-total correlations.
conf.level: a numeric value between 0 and 1 indicating the confidence level of the interval.
as.na: a numeric vector indicating user-defined missing values, i.e. these values are converted to NA before conducting the analysis.
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.

Author

Takuya Yanagida takuya.yanagida@univie.ac.at

Details

Ordinal coefficient alpha was introduced by Zumbo, Gadermann and Zeisser (2007) which is obtained by applying the formula for computing coefficient alpha to the polychoric correlation matrix instead of the variance-covariance or product-moment correlation matrix. Note that Chalmers (2018) highlighted that the ordinal coefficient alpha should be interpreted only as a hypothetical estimate of an alternative reliability, whereby a test's ordinal categorical response options have be modified to include an infinite number of ordinal response options and concludes that coefficient alpha should not be reported as a measure of a test's reliability. However, Zumbo and Kroc (2019) argued that Chalmers' critique of ordinal coefficient alpha is unfounded and that ordinal coefficient alpha may be the most appropriate quantifier of reliability when using Likert-type measurement to study a latent continuous random variable. Confidence intervals are computed using the procedure by Feldt, Woodruff and Salih (1987). When computing confidence intervals using pairwise deletion, the average sample size from all pairwise samples is used. Note that there are at least 10 other procedures for computing the confidence interval (see Kelley and Pornprasertmanit, 2016), which are implemented in the ci.reliability() function in the MBESSS package by Ken Kelley (2019).

References

Chalmers, R. P. (2018). On misconceptions and the limited usefulness of ordinal alpha. Educational and Psychological Measurement, 78, 1056-1071. https://doi.org/10.1177/0013164417727036

Cronbach, L.J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297-334. https://doi.org/10.1007/BF02310555

Cronbach, L.J. (2004). My current thoughts on coefficient alpha and successor procedures. Educational and Psychological Measurement, 64, 391-418. https://doi.org/10.1177/0013164404266386

Feldt, L. S., Woodruff, D. J., & Salih, F. A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11 93-103. https://doi.org/10.1177/014662168701100107

Kelley, K., & Pornprasertmanit, S. (2016). Confidence intervals for population reliability coefficients: Evaluation of methods, recommendations, and software for composite measures. Psychological Methods, 21, 69-92. https://doi.org/10.1037/a0040086.

Ken Kelley (2019). MBESS: The MBESS R Package. R package version 4.6.0. https://CRAN.R-project.org/package=MBESS

Zumbo, B. D., & Kroc, E. (2019). A measurement is a choice and Stevens' scales of measurement do not help make it: A response to Chalmers. Educational and Psychological Measurement, 79, 1184-1197. https://doi.org/10.1177/0013164419844305

Zumbo, B. D., Gadermann, A. M., & Zeisser, C. (2007). Ordinal versions of coefficients alpha and theta for Likert rating scales. Journal of Modern Applied Statistical Methods, 6, 21-29. https://doi.org/10.22237/jmasm/1177992180

Examples

Run this code

dat <- data.frame(item1 = c(4, 2, 3, 4, 1, 2, 4, 2),
                  item2 = c(4, 3, 3, 3, 2, 2, 4, 1),
                  item3 = c(3, 2, 4, 2, 1, 3, 4, 1),
                  item4 = c(4, 1, 2, 3, 2, 3, 4, 2))

# Example 1a: Compute unstandardized coefficient alpha and item statistics
item.alpha(dat)

# Example 1b: Alternative specification using the 'data' argument
item.alpha(., data = dat)

# Example 2: Compute standardized coefficient alpha and item statistics
item.alpha(dat, std = TRUE)

# Example 3: Compute unstandardized coefficient alpha
item.alpha(dat, print = "alpha")

# Example 4: Compute item statistics
item.alpha(dat, print = "item")

# Example 5: Compute unstandardized coefficient alpha and item statistics while excluding item3
item.alpha(dat, exclude = "item3")

# Example 6: Compute variance-covariance matrix
dat.cov <- cov(dat)
# Compute unstandardized coefficient alpha based on the variance-covariance matrix
item.alpha(dat.cov)

# Compute correlation matrix
dat.cor <- cor(dat)
# Example 7: Compute standardized coefficient alpha based on the correlation matrix
item.alpha(dat.cor)

# Example 8: Compute ordinal coefficient alpha
item.alpha(dat, ordered = TRUE)

if (FALSE) {
# Example 9a: Write results into a text file
result <- item.alpha(dat, write = "Alpha.txt")

# Example 9b: Write results into a Excel file
result <- item.alpha(dat, write = "Alpha.xlsx")

result <- item.alpha(dat, output = FALSE)
write.result(result, "Alpha.xlsx")
}

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