OMEGA: Omega internal consistency reliability coefficients

In EFA.dimensions: Exploratory Factor Analysis Functions for Assessing Dimensionality

Omega internal consistency reliability coefficients

Description

Total and hierarchical omega internal consistency reliability coefficients computed using multiple possible methods

Usage

OMEGA(data, corkind = 'pearson',  
      Nfactors = 4,
      bifactor_kind = c('SL', 'SLiD', 'DSL', 'bifactorT', 'bigeominT'),
      EFA_options = list(extraction = 'minres', rotation = 'oblimin'),
      LV_options = list(group_keys = NULL, 
                        estimator = 'MLR', 
                        rotation = 'bigeomin',
                        resid_correls = NULL, 
                        LV_names = NULL,
                        ordered = FALSE),
      schmid_options = list(extraction = 'minres', rotation = 'oblimin'),
      GPA_options = list(delta = .01, 
                         epsilon = .00001, 
                         normalize = FALSE, 
                         maxit = 1000, 
                         randomStarts = 50),
      min_loading = .2, display = 2)

Arguments

data	An all-numeric dataframe where the rows are cases & the columns are the variables, or a correlation matrix with ones on the diagonal. The function internally determines whether the data are a correlation matrix.
corkind	The kind of correlation matrix to be used if data is not a correlation matrix. The options are 'pearson', 'kendall', 'spearman', 'gamma', and 'polychoric'.
Nfactors	(optional) The number of factors to extract, including the general factor. Nfactors is = 1 (for the general factor) + the number of group factors.
bifactor_kind	The bifactor method(s) to be used. The options are 'SL', 'SLiD', 'DSL', 'bifactorQ', 'bifactorT', 'bigeominQ', 'bigeominT', 'CFA', and 'ESEM'. Multiple methods can be specified.
EFA_options	(optional) A list with EFA options when rawdata is provided. The list elements include values for 'extraction' and 'rotation'. The possibilities for extraction are: 'minres'(the default), 'alpha', 'fullinfo', 'gls', 'image', 'ml', 'ols', 'paf', 'uls', and 'wls'. The possibilities for rotation are: 'varimax', 'bentlerT', 'entropy', 'equamax', 'geominT', 'quartimax', 'promax', 'bentlerQ', 'geominQ', 'oblimin' (the default, 'oblimax', 'quartimin', 'simplimax', and 'none'.
LV_options	(optional) A list with cfa options when bifactor_kind = 'CFA'. The possible list elements are 'group_keys', 'estimator', 'rotation', 'resid_correls', 'LV_names', and 'ordered'. See the Details section below for information on each element.
schmid_options	(optional) A list with schmid function (from the psych package) options when bifactor_kind is one of 'SL', 'SLiD', or 'DSL'. The list elements include values for 'extraction' and 'rotation'. The possibilities for extraction are: 'minres'(the default), 'paf', 'pc', and 'ml'. The possibilities for rotation are: 'oblimin' (the default), 'simplimax', 'Promax', 'promax' and 'none'.
GPA_options	(optional) A list with options for when a GPArotation is used. See the Details section below.
min_loading	The minimum value of a group factor loading for an item to be considered to have a non-negligible contribution to a group factor. min_loading only plays a role in the computations for PUC and for some group factor statistics.
display	The results to be displayed in the console: 0 = nothing 1 = only the omega and scale coefficients 2 (default) = detailed output, including the bifactor model loadings and statistics

Details

For the bifactor_kind argument:

• bifactorT is an orthogonal bifactor rotation designed for situations where a single, overarching global dimension is expected alongside separate sub-domains, and when all factors should be uncorrelated.

• bifactorQ is an oblique bifactor rotation designed for when a strong, overarching global dimension is expected alongside separate sub-domains that are allowed to correlate with each other.

• bigeominT is an orthogonal bifactor rotation designed for situations where a single, overarching global dimension is expected alongside separate sub-domains, and when all factors should be uncorrelated.

• bigeominQ is an oblique bifactor rotation designed for when a strong, overarching global dimension is expected alongside separate sub-domains that are allowed to correlate with each other.

• SL is an oblique bifactor rotation designed for where there is a broad, overarching factor alongside sub-domains that are allowed to overlap.

• SLiD an orthogonal bifactor rotation method designed for exploratory bifactor analysis that tries to ensure that once the general factor's variance is pulled out, each item loads onto only one specific group factor.

• DSL entropy is an orthogonal factor rotation that pushes factor loadings to be either strongly dominant (close to 1.0) or cleanly absent (close to 0.0), reducing the overall informational "noise" of the matrix.

• CFA confirmatory bifactor analyses are conducted using the cfa function from the lavaan package. All items are assumed to load on the general factor. The items that load on the group factors are indicated using "group_keys" for the LV_options argument.

• ESEM rxploratory structural equation modeling bifactor analyses conducted using the cfa function from the lavaan package. All items are assumed to load on the general factor. The items that load on the group factors can be indicated using "group_keys" for the LV_options argument.
  

For the LV_options argument:

When bifactor_kind = 'CFA' or 'ESEM', then LV_options is a list with information for these analyses. The possible list elements are 'group_keys', 'estimator', 'rotation', 'resid_correls', 'LV_names', and 'ordered'.

• group_keys is a vector indicating which item (i.e., which variable in data) goes with which group factor (which can be named or numbered).
  Example: group_keys = c(1, 1, 2, 1, 2, 1, 1, 2, 2, 2)

• estimator is the name of the lavaan estimator to be used in the analyses. The options for basic estimators (continuous data) are ML, GLS, WLS, DWLS, ULS, DLS, and PML. The options for robust estimators are MLM, MLMVS, MLMV, MLF, MLR, WLSM, WLSMVS, WLSMV, ULSM, ULSMVS, and ULSMV.
  Example: estimator = 'ML'

• rotation is the kind of lavaan bifactor rotation. The two options are 'bigeomin' or 'biquartimin'.

• resid_correls is a vector with the pairs of correlated error terms (if any).
  Example: resid_correls = c('Q1 ~~ Q2', 'Q9 ~~ Q10')

• LV_names is a vector of names for the latent variables

• ordered are the variables in rawdata (if provided) ordered? For example, Likert scale responses are usually ordered. The function will produce notices when the data are not consistent with the "ordered" status.

Examples of LV_options:

  LV_options = list(group_keys = c(1, 1, 2, 1, 2, 1, 1, 2, 2, 2),
                     resid_correls = NULL, estimator = 'WLSMVS')
  

  LV_options = list(group_keys = c(Q1=1, Q2=1, Q3_R=2, Q4=1,   Q5_R=2, 
                                    Q6=1, Q7=1, Q8_R=2, Q9_R=2, Q10_R=2)),
                     resid_correls = c('Q1 ~~ Q2', 'Q9 ~~ Q10'), 
                     estimator = 'WLSMVS')

For the GPA_options argument:

A list with options for when a GPArotation is used. The list elements are 'delta', 'epsilon', 'normalize', 'maxit', and 'randomStarts'.

• delta is a small positive number that is added to the squared factor loadings in the (geomin) optimization denominator to prevent division by zero and control the sharpness of the penalty near zero. (Note: In MPLus, delta is called "epsilon".)

• epsilon is the numeric rotational convergence tolerance threshold. It controls how precise or strict the stopping rule is for the rotation algorithm. The gradient projection algorithm stops optimizing and assumes the rotation has converged when the norm of the gradient falls below this value.

• normalize specifies whether and how the loadings matrix is normalized prior to rotation and denormalized after rotation. The possibilities are FALSE (the default) for no normalization, or TRUE, for the Kaiser/Horst normalization.

• maxit is the maximum number of iterations.

• randomStarts is an integer that specifies the number of random starting configurations used to optimize the factor rotation. It helps avoid getting trapped in local minima during factor rotation optimization. It runs the gradient projection algorithm multiple timeseach using a different random orthogonal or oblique starting rotation matrix (Tmat) generated via QR decomposition. It returns the rotated factor loadings matrix and results corresponding to the run with the lowest objective criterion value among all attempts.

Run the following command for detailed descriptions of the omega-total and omega-hierarchical internal consistency reliability coefficients and other statistics produced by this function:

• RShowDoc("Coefficient_descriptions_vignettes", package = "EFA.dimensions")
  

• vignette("Coefficient_descriptions_vignettes")
  

Value

A list with the omega coefficients, the factor loadings, and model fit statistics.

Author(s)

Brian P. O'Connor

References

Bernaards, C. A., & Jennrich, R. I. (2005). Gradient Projection Algorithms and Software for Arbitrary Rotation Criteria in Factor Analysis. Educational and Psychological Measurement, 65(5), 676-696.

Bernaards, C. A., & Jennrich, R. I. (2026). GPArotation: Gradient Projection Factor Rotation. R package version 2026.4-1, https://CRAN.R-project.org/package=GPArotation

Educational Content Team. (2026). McDonald's Omega. Cogn-IQ Encyclopedia. https://pubscience.org/cqep.2025.0048

Flora, D. B. (2020). Your coefficient alpha is probably wrong, but which coefficient omega is right? A tutorial on using R to obtain better reliability estimates. Advances in Methods and Practices in Psychological Science, 3(4), 484501.

Garcia-Garzon, E., Abad, F. J., & Garrido, L. E. (2021). On omega hierarchical estimation: A Comparison of Exploratory Bi-Factor Analysis Algorithms. Multivariate Behavioral Research, 56(1), 101-119.

Jennrich, R. I. (2018). Rotation. In P. Irwing, T. Booth, & D. J. Hughes (Eds.), The Wiley handbook of psychometric testing: A multidisciplinary reference on survey, scale and test development (pp. 279304). Wiley Blackwell. https://doi.org/10.1002/9781118489772.ch10

Kalkbrenner, M. T. (2024). Choosing Between Cronbachs Coefficient Alpha, McDonalds Coefficient Omega, and Coefficient H: Confidence Intervals and the Advantages and Drawbacks of Interpretive Guidelines. Measurement and Evaluation in Counseling and Development, 57(2), 93105.

McNeish, D. (2018). Thanks coefficient alpha, we'll take it from here. Psychological Methods, 23(3), 412433.

Revelle, W. (2026). psych: Procedures for Psychological, Psychometric, and Personality Research. R package version 2.6.5, https://CRAN.R-project.org/package=psych

Revelle, W., & Condon, D. M. (2019). Reliability from alpha to omega: A tutorial. Psychological Assessment, 31(12), 13951411.

Waller, N. G. (2018) Direct Schmid-Leiman Transformations and Rank-Deficient Loadings Matrices. Psychometrika, 83(4), 858870.

Examples

OMEGA(data_RSE, Nfactors = 3, display = 1)

EFA.dimensions documentation built on Sept. 14, 2026, 9:08 a.m.