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, 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(x, resid.cov = 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, check = TRUE, output = TRUE)

Arguments

x	a matrix or data frame. Note that at least three items are needed for computing omega.
resid.cov	a character vector or a list of character vectors for specifying residual covariances when computing coefficient omega, e.g. resid.cov = c("x1", "x2") for specifying a residual covariance between items x1 and x2 or resid.cov = 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 for writing the results into a Excel file naming a file with or without file extension '.xlsx', e.g., "Results.xlsx" or "Results".
check	logical: if TRUE, argument specification is checked.
output	logical: if TRUE, output is shown.

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).

Value

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

call	function call
type	type of analysis
data	matrix or data frame specified in x
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

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.

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.

See Also

write.result, item.alpha, item.cfa, item.reverse, item.scores

Examples

## Not run: 
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))

# Compute unstandardized coefficient omega and item statistics
item.omega(dat)

# Compute unstandardized coefficient omega with a residual covariance
# and item statistics
item.omega(dat, resid.cov = c("item1", "item2"))

# Compute unstandardized coefficient omega with residual covariances
# and item statistics
item.omega(dat, resid.cov = list(c("item1", "item2"), c("item3", "item4")))

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

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

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

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

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

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

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

# Write Results into a Excel file
item.omega(dat, write = "Omega.xlsx")

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

## End(Not run)

misty documentation built on Nov. 15, 2023, 1:06 a.m.