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

In misty: Miscellaneous Functions 'T. Yanagida'

Coefficient Omega, Hierarchical Omega, and Categorical Omega

Description

This function computes point estimate and confidence interval for the coefficient omega (McDonald, 1999), hierarchical coefficient omega (Kelley & Pornprasertmanit, 2016), and categorical coefficient omega (Green & Yang, 2009) along with standardized factor loadings and omega if item deleted. By default, the function computes coefficient omega based on maximum likelihood parameter (ML) estimates using full information maximum likelihood (FIML) method in the presence of missing data.

Usage

item.omega(data, ..., rescov = NULL, type = c("omega", "hierarch", "categ"),
           exclude = NULL, std = FALSE,
           estimator = c("ML", "GLS", "WLS", "DWLS", "ULS", "PML"),
           missing = c("listwise", "pairwise", "fiml"),
           print = c("all", "omega", "item"), digits = 2, r.digits = 3,
           conf.level = 0.95, as.na = NULL, write = NULL, append = TRUE,
           check = TRUE, output = TRUE)

Arguments

data	a data frame. Note that at least three items are needed for computing coefficient omega
...	an expression indicating the variable names in data e.g., item.omega(dat, x1, x2, x3). Note that the operators +, -, ~, :, ::, and ! can also be used to select variables, see 'Details' in the df.subset function.
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 coefficient omega, and categ for categorical coefficient omega.
exclude	a character vector indicating items to be excluded from the analysis.
std	logical: if TRUE, the standardized coefficient omega is computed.
estimator	a character string indicating the estimator to be used (see 'Details' in the item.cfa function). By default, "ML" is used for computing (hierarchical) coefficient omega and "DWLS" is used for computing ordinal coefficient omega.
missing	a character string indicating how to deal with missing data. (see 'Details' in the item.cfa function). By default, full information maximum likelihood method (missing = "fiml") is used for computing (hierarchical) coefficient omega and pairwise deletion (missing = "pairwise") is used to compute coefficient omega.
print	a character vector indicating which results to show, i.e. "all" for all results "omega" (default) for the coefficient omega, and "item" for item statistics.
digits	an integer value indicating the number of decimal places to be used for displaying mean, standard deviation, minimum, and maximum.
r.digits	an integer value indicating the number of decimal places to be used for displaying alpha 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.

Details

Coefficient Omega

This function computes the coefficient omega by conducting a confirmatory factor analysis based on the congeneric measurement model (Graham, 2006) using the cfa() function in the lavaan package by Yves Rosseel (2019).

Confidence Interval

The confidence interval for the (ordinal) coefficient alpha is computed using the procedure by Feldt et al. (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).

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., omega for a table with coefficient omega and itemstat for a table with item statistics

Note

Computation of the hierarchical and categorical omega is based on the ci.reliability() function in the MBESS package by Ken Kelley (2019).

Author(s)

Takuya Yanagida [e-mail]

References

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

Graham, J. M. (2006). Congeneric and (essentially) tau-equivalent estimates of score reliability: What they are and how to use them. Educational and Psychological Measurement, 66(6), 930–944. https://doi.org/10.1177/0013164406288165

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

McDonald, R. P. (1999). Test theory: A unified treatment. Lawrence Erlbaum Associates Publishers.

See Also

item.omega, item.cfa, item.invar, item.reverse, item.scores, write.result

Examples

## Not run: 

# Load data set "HolzingerSwineford1939" in the lavaan package
data("HolzingerSwineford1939", package = "lavaan")

#————————————————————————————————————————————————————————————————————————————
# Continuous Data

# Example 1a: Coefficient omega
item.omega(HolzingerSwineford1939, x1::x9)

# Example 1b: Coefficient omega and item statistics after excluding 'x3'
item.omega(HolzingerSwineford1939, x1::x9, exclude = "x3", print = "all")

# Example 2: Hierarchical Omega
item.omega(HolzingerSwineford1939, x1::x9, type = "hierarch")

# Example 3a: Residual covariance between 'x1' and 'x2'
item.omega(HolzingerSwineford1939, x1::x9, rescov = c("x1", "x2"))

# Example 3b: Residual covariances between 'x1' and 'x2', and 'x2' and 'x3'
item.omega(HolzingerSwineford1939, x1::x9, rescov = list(c("x1", "x2"), c("x2", "x3")))

# Example 4: Summary of the CFA model used to compute coefficient omega
lavaan::summary(item.omega(HolzingerSwineford1939, x1::x9, output = FALSE)$model.fit,
                standardized = TRUE)

#————————————————————————————————————————————————————————————————————————————
# Polytomous Data

# Example 5: Ordinal coefficient omega and item statistics
item.omega(data.items, pitem1, pitem2r, pitem3r, pitem4::pitem6, type = "categ",
           print = "all")

#————————————————————————————————————————————————————————————————————————————
# Write Results

# Example 6a: Write Results into a text file
item.omega(HolzingerSwineford1939, x1::x9, print = "all", write = "Omega.txt")

# Example 6b: Write Results into an Excel file
item.omega(HolzingerSwineford1939, x1::x9, print = "all", write = "Omega.xlsx")

## End(Not run)

misty documentation built on Aug. 2, 2026, 9:06 a.m.