item.omega: Coefficient Omega, Hierarchical Omega, and Categorical Omega

Description

This function computes point estimate and confidence interval for the coefficient omega (McDonald, 1978), hierarchical omega (Kelley & Pornprasertmanit, 2016), and categorical omega (Green & Yang, 2009) along with standardized factor loadings and omega if item deleted.

Usage

item.omega(..., data = NULL, rescov = NULL, type = c("omega", "hierarch", "categ"),
           exclude = NULL, std = FALSE, na.omit = FALSE,
           print = c("all", "omega", "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
model.fit: fitted lavaan object (mod.fit)
result: list with result tables, i.e., alpha for a table with coefficient omega and itemstat for a table with item statistics

Arguments

...: a matrix or data frame. Note that at least three items are needed for computing omega. Alternatively, an expression indicating the variable names in data e.g., item.omega(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 or data frame for the argument ....
rescov: a character vector or a list of character vectors for specifying residual covariances when computing coefficient omega, e.g. rescov = c("x1", "x2") for specifying a residual covariance between items x1 and x2 or rescov = list(c("x1", "x2"), c("x3", "x4")) for specifying residual covariances between items x1 and x2, and items x3 and x4.
type: a character string indicating the type of omega to be computed, i.e., omega (default) for coefficient omega, hierarch for hierarchical omega, and categ for categorical omega.
exclude: a character vector indicating items to be excluded from the analysis.
std: logical: if TRUE, the standardized coefficient omega is computed.
na.omit: logical: if TRUE, incomplete cases are removed before conducting the analysis (i.e., listwise deletion); if FALSE, full information maximum likelihood (FIML) is used for computing coefficient omega or hierarchical omega, while pairwise deletion is used for computing categorical omega.
print: a character vector indicating which results to show, i.e. "all" (default), for all results "omega" for omega, and "item" for item statistics.
digits: an integer value indicating the number of decimal places to be used for displaying omega and standardized factor loadings.
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

Omega is computed by estimating a confirmatory factor analysis model using the cfa() function in the lavaan package by Yves Rosseel (2019). Maximum likelihood ("ML") estimator is used for computing coefficient omega and hierarchical omega, while diagonally weighted least squares estimator ("DWLS") is used for computing categorical omega.

Approximate confidence intervals are computed using the procedure by Feldt, Woodruff and Salih (1987). 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

Feldt, L. S., Woodruff, D. J., & Salih, F. A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11 93-103.

Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74, 155-167. https://doi.org/10.1007/s11336-008-9099-3

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. http://dx.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

McDonald, R. P. (1978). Generalizability in factorable domains: Domain validity and generalizability. Educational and Psychological Measurement, 38, 75-79.

Examples

Run this code

if (FALSE) {
dat <- data.frame(item1 = c(5, 2, 3, 4, 1, 2, 4, 2),
                  item2 = c(5, 3, 3, 5, 2, 2, 5, 1),
                  item3 = c(4, 2, 4, 5, 1, 3, 5, 1),
                  item4 = c(5, 1, 2, 5, 2, 3, 4, 2))

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

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

# Example 2: Compute unstandardized coefficient omega with a residual covariance
# and item statistics
item.omega(dat, rescov = c("item1", "item2"))

# Example 3: Compute unstandardized coefficient omega with residual covariances
# and item statistics
item.omega(dat, rescov = list(c("item1", "item2"), c("item1", "item3")))

# Example 4: Compute unstandardized hierarchical omega and item statistics
item.omega(dat, type = "hierarch")

# Example 5: Compute categorical omega and item statistics
item.omega(dat, type = "categ")

# Example 6: Compute standardized coefficient omega and item statistics
item.omega(dat, std = TRUE)

# Example 7: Compute unstandardized coefficient omega
item.omega(dat, print = "omega")

# Example 8: Compute item statistics
item.omega(dat, print = "item")

# Example 9: Compute unstandardized coefficient omega and item statistics while excluding item3
item.omega(dat, exclude = "item3")

# Example 10: Summary of the CFA model used to compute coefficient omega
lavaan::summary(item.omega(dat, output = FALSE)$model.fit,
                fit.measures = TRUE, standardized = TRUE)

# Example 11a: Write results into a text file
item.omega(dat, write = "Omega.txt")

# Example 11b: Write results into a Excel file
item.omega(dat, write = "Omega.xlsx")

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

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