BIFACTOR: Bifactor analysis
In EFA.dimensions: Exploratory Factor Analysis Functions for Assessing Dimensionality
BIFACTOR R Documentation
Bifactor analysis
Description
Bifactor analysis with multiple options for data entry and analysis
Usage
BIFACTOR(loadings = NULL,
rawdata = NULL,
cormat = NULL, Ncases = NULL, corkind = 'pearson',
Nfactors = 4,
bifactor_kind = 'bifactorT',
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,
verbose = TRUE)
Arguments
loadings
(optional) loadings can be either a bifactor loading matrix or an EFA
loading matrix. See the Details and Examples sections below.
rawdata
(optional) An all-numeric dataframe where the rows are cases & the columns are
the variables. Required only when loadings and cormat are not provided.
Nfactors
(optional) The number of factors to extract, including the general factor.
Nfactors is = 1 (for the general factor) + the number of group factors.
cormat
(optional) A correlation matrix with ones on the diagonal.
Required only when loadings and rawdata are not provided.
Ncases
(optional) The number of cases. Required only when cormat is provided.
corkind
(optional) The kind of correlation matrix to be used when rawdata is provided.
The options are 'pearson', 'kendall', 'spearman', 'gamma', and 'polychoric'.
bifactor_kind
(optional) Specify one of the following possible bifactor methods:
'bifactorT', 'bifactorQ', 'bigeominT', 'bigeominQ', 'SL', 'SLiD', 'DSL',
'CFA', 'ESEM', or 'none'.
Use 'bifactor_kind = "none"' only when loadings is (already) a bifactor loading matrix.
Example: bifactor_kind = 'bifactorT'
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', 'N_group_factors',
'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.
verbose
Should detailed results be displayed in console? TRUE (default) or FALSE
Details
The bifactor analyses can be conducted for three possible data input scenarios.
-
When "loadings" is provided and when it is (already) a bifactor loading matrix,
then bifactor rotations are not conducted and the function merely provides a variety
of bifactor model, factor, and item statistics. "bifactor_kind" must be set
to "none" for the function to recognize that loadings is (already) a
bifactor loading matrix.
-
When "loadings" is provided and when it consists of EFA loadings (not bifactor
loadings), then the function will conduct the requested kind of bifactor
analysis and provide the bifactor loadings and statistics.
-
if either "rawdata" or "cormat" are provided, the function will conduct the
preliminary EFA, the bifactor analyses, and produce the bifactor loadings and
statistics. "loadings" must be NULL for this to occur.
The factor extraction computations for the following methods are conducted
using the psych package (Revelle, 2026): 'alpha', 'gls', 'minres', 'ols', 'uls', and 'wls'.
The factor extraction computations for 'fullinfo' are conducted
using the mirt package (Chalmers, 2012). Full-information methods are considered more
appropriate for item-level data than other factor extraction methods (Wirth & Edwards, 2007).
The factor rotation computations for the following methods are conducted
using the GPArotation package (Bernaards & Jennrich, 2005, 2026): 'bentlerQ',
'bentlerT', 'entropy', 'geominQ', 'geominT', 'oblimax', 'oblimin', 'quartimax',
'quartimin', and 'simplimax'.
The 'bifactorT', 'bifactorQ', 'bigeominQ', and 'bigeominQ' computations
are conducted using the GPArotation package (Bernaards & Jennrich, 2005, 2026).
The 'SL' and 'DSL' bifactor computations
are conducted using the psych package (Revelle, 2026). The 'SLiD' bifactor
computations are conducted using code from Garcia-Garzon et al. (2021).
The only possible extraction methods for 'SL', 'SLiD', and 'DSL' bifactor
computations are 'paf', 'minres', and 'ml'.
For reviews of bifactor analyses, see Bornovalova (2020),
Garcia-Garzon et al. (2021), & Reise et al. (2018).
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 the
theseanalyses. 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 one of the following commands for more detailed descriptions of the
above extraction, rotation, and bifactor methods:
RShowDoc("EFA_BIFACTOR_vignettes", package = "EFA.dimensions")
vignette("EFA_BIFACTOR_vignettes")
Value
A list with the bifactor loadings and statistics, including omegas, ECV,
ARPB, FD, coef_H, and rmsr.
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.
https://doi.org/10.1177/0013164404272507
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
Bornovalova, M. A., Choate, A. M., Fatimah, H., Petersen, K. J., &
Wiernik, B. M. (2020). Appropriate Use of Bifactor Analysis in Psychopathology
Research: Appreciating Benefits and Limitations.
Biological psychiatry, 88(1), 1827.
Chalmers, R. P. (2012). mirt: A Multidimensional Item Response Theory
Package for the R Environment.
Journal of Statistical Software, 48(6), 129. doi:10.18637/jss.v048.i06.
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.
Giordano, C., Ones, D. S., Waller, N. G., & Stanek, K. C. (2020).
Exploratory bifactor measurement models in vocational behavior research.
Journal of Vocational Behavior, 120, Article 103430.
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
Markon K. E. (2019). Bifactor and Hierarchical Models: Specification,
Inference, and Interpretation. Annual review of clinical psychology, 15, 5169.
Mulaik, S. A. (2010). Foundations of factor analysis (2nd ed.). Boca Raton, FL: Chapman
and Hall/CRC Press, Taylor & Francis Group.
Reise, S.P., Bonifay, W., & Haviland, M.G. (2018). Bifactor Modelling and
the Evaluation of Scale Scores. In P. Irwing, T. Booth& D.J. Hughes (eds.),
The Wiley Handbook of Psychometric Testing. John Wiley & Sons.
Revelle, W. (2026). psych: Procedures for Psychological, Psychometric, and
Personality Research. R package version 2.6.5, https://CRAN.R-project.org/package=psych
Sellbom, M., & Tellegen, A. (2019). Factor analysis in psychological assessment research:
Common pitfalls and recommendations.
Psychological Assessment, 31(12), 1428-1441. https://doi.org/10.1037/pas0000623
Watts, A. L., Greene, A. L., Ringwald, W., Forbes, M. K., Brandes, C. M.,
Levin-Aspenson, H. F., & Delawalla, C. (2023). Factor analysis in personality
disorders research: Modern issues and illustrations of practical recommendations.
Personality Disorders: Theory, Research, and Treatment, 14(1), 105-117.
https://doi.org/10.1037/per0000581
Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: current
approaches and future directions. Psychological methods, 12(1), 58-79.
https://doi.org/10.1037/1082-989X.12.1.58
Examples
# using only EFA loadings as input
efa_loadings <- EFA(data=data_RSE, Nfactors=3, extraction = 'ml', verbose=FALSE)$pattern
BIFACTOR(loadings = efa_loadings)
# when a correlation matrix is provided, but not loadings or rawdata
BIFACTOR(cormat = cor(data_RSE), Ncases = 800, Nfactors = 4,
bifactor_kind = 'SL',
schmid_options = list(extraction = 'minres',
rotation = 'oblimin'))
# when rawdata is provided, but not loadings or cormat
BIFACTOR(rawdata = data_RSE, Nfactors = 3,
bifactor_kind = 'bifactorT',
EFA_options = list(extraction = 'minres', rotation = 'oblimin'))
# confirmatory bifactor analyses
BIFACTOR(rawdata = data_RSE,
bifactor_kind = 'CFA',
LV_options = list(group_keys = c(1, 1, 2, 1, 2, 1, 1, 2, 2, 2),
N_group_factors = NULL,
estimator = 'WLSMV',
rotation = 'bigeomin',
resid_correls = NULL,
LV_names=NULL,
ordered = TRUE),
min_loading = .0001)
# Run this command for additional Examples: vignette("EXAMPLES_vignettes")
EFA.dimensions documentation built on Sept. 14, 2026, 9:08 a.m.
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| BIFACTOR | R Documentation |
Bifactor analysis
Description
Bifactor analysis with multiple options for data entry and analysis
Usage
BIFACTOR(loadings = NULL,
rawdata = NULL,
cormat = NULL, Ncases = NULL, corkind = 'pearson',
Nfactors = 4,
bifactor_kind = 'bifactorT',
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,
verbose = TRUE)Arguments
loadings |
(optional) loadings can be either a bifactor loading matrix or an EFA loading matrix. See the Details and Examples sections below. |
rawdata |
(optional) An all-numeric dataframe where the rows are cases & the columns are the variables. Required only when loadings and cormat are not provided. |
Nfactors |
(optional) The number of factors to extract, including the general factor.
|
cormat |
(optional) A correlation matrix with ones on the diagonal. Required only when loadings and rawdata are not provided. |
Ncases |
(optional) The number of cases. Required only when cormat is provided. |
corkind |
(optional) The kind of correlation matrix to be used when rawdata is provided. The options are 'pearson', 'kendall', 'spearman', 'gamma', and 'polychoric'. |
bifactor_kind |
(optional) Specify one of the following possible bifactor methods:
'bifactorT', 'bifactorQ', 'bigeominT', 'bigeominQ', 'SL', 'SLiD', 'DSL',
'CFA', 'ESEM', or 'none'.
Use 'bifactor_kind = "none"' only when loadings is (already) a bifactor loading matrix.
|
EFA_options |
(optional) A list with EFA options when rawdata is provided. The list elements
include values for 'extraction' and 'rotation'.
|
LV_options |
(optional) A list with cfa options when bifactor_kind = 'CFA'. The possible list elements are 'group_keys', 'N_group_factors', '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'.
|
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. |
verbose |
Should detailed results be displayed in console? TRUE (default) or FALSE |
Details
The bifactor analyses can be conducted for three possible data input scenarios.
-
When "loadings" is provided and when it is (already) a bifactor loading matrix, then bifactor rotations are not conducted and the function merely provides a variety of bifactor model, factor, and item statistics. "bifactor_kind" must be set to "none" for the function to recognize that loadings is (already) a bifactor loading matrix.
-
When "loadings" is provided and when it consists of EFA loadings (not bifactor loadings), then the function will conduct the requested kind of bifactor analysis and provide the bifactor loadings and statistics.
-
if either "rawdata" or "cormat" are provided, the function will conduct the preliminary EFA, the bifactor analyses, and produce the bifactor loadings and statistics. "loadings" must be NULL for this to occur.
The factor extraction computations for the following methods are conducted using the psych package (Revelle, 2026): 'alpha', 'gls', 'minres', 'ols', 'uls', and 'wls'.
The factor extraction computations for 'fullinfo' are conducted using the mirt package (Chalmers, 2012). Full-information methods are considered more appropriate for item-level data than other factor extraction methods (Wirth & Edwards, 2007).
The factor rotation computations for the following methods are conducted using the GPArotation package (Bernaards & Jennrich, 2005, 2026): 'bentlerQ', 'bentlerT', 'entropy', 'geominQ', 'geominT', 'oblimax', 'oblimin', 'quartimax', 'quartimin', and 'simplimax'.
The 'bifactorT', 'bifactorQ', 'bigeominQ', and 'bigeominQ' computations are conducted using the GPArotation package (Bernaards & Jennrich, 2005, 2026). The 'SL' and 'DSL' bifactor computations are conducted using the psych package (Revelle, 2026). The 'SLiD' bifactor computations are conducted using code from Garcia-Garzon et al. (2021).
The only possible extraction methods for 'SL', 'SLiD', and 'DSL' bifactor
computations are 'paf', 'minres', and 'ml'.
For reviews of bifactor analyses, see Bornovalova (2020), Garcia-Garzon et al. (2021), & Reise et al. (2018).
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 the theseanalyses. 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 one of the following commands for more detailed descriptions of the above extraction, rotation, and bifactor methods:
RShowDoc("EFA_BIFACTOR_vignettes", package = "EFA.dimensions")
vignette("EFA_BIFACTOR_vignettes")
Value
A list with the bifactor loadings and statistics, including omegas, ECV, ARPB, FD, coef_H, and rmsr.
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.
https://doi.org/10.1177/0013164404272507
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
Bornovalova, M. A., Choate, A. M., Fatimah, H., Petersen, K. J., &
Wiernik, B. M. (2020). Appropriate Use of Bifactor Analysis in Psychopathology
Research: Appreciating Benefits and Limitations.
Biological psychiatry, 88(1), 1827.
Chalmers, R. P. (2012). mirt: A Multidimensional Item Response Theory
Package for the R Environment.
Journal of Statistical Software, 48(6), 129. doi:10.18637/jss.v048.i06.
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.
Giordano, C., Ones, D. S., Waller, N. G., & Stanek, K. C. (2020).
Exploratory bifactor measurement models in vocational behavior research.
Journal of Vocational Behavior, 120, Article 103430.
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
Markon K. E. (2019). Bifactor and Hierarchical Models: Specification,
Inference, and Interpretation. Annual review of clinical psychology, 15, 5169.
Mulaik, S. A. (2010). Foundations of factor analysis (2nd ed.). Boca Raton, FL: Chapman
and Hall/CRC Press, Taylor & Francis Group.
Reise, S.P., Bonifay, W., & Haviland, M.G. (2018). Bifactor Modelling and
the Evaluation of Scale Scores. In P. Irwing, T. Booth& D.J. Hughes (eds.),
The Wiley Handbook of Psychometric Testing. John Wiley & Sons.
Revelle, W. (2026). psych: Procedures for Psychological, Psychometric, and
Personality Research. R package version 2.6.5, https://CRAN.R-project.org/package=psych
Sellbom, M., & Tellegen, A. (2019). Factor analysis in psychological assessment research:
Common pitfalls and recommendations.
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Watts, A. L., Greene, A. L., Ringwald, W., Forbes, M. K., Brandes, C. M.,
Levin-Aspenson, H. F., & Delawalla, C. (2023). Factor analysis in personality
disorders research: Modern issues and illustrations of practical recommendations.
Personality Disorders: Theory, Research, and Treatment, 14(1), 105-117.
https://doi.org/10.1037/per0000581
Wirth, R. J., & Edwards, M. C. (2007). Item factor analysis: current
approaches and future directions. Psychological methods, 12(1), 58-79.
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Examples
# using only EFA loadings as input
efa_loadings <- EFA(data=data_RSE, Nfactors=3, extraction = 'ml', verbose=FALSE)$pattern
BIFACTOR(loadings = efa_loadings)
# when a correlation matrix is provided, but not loadings or rawdata
BIFACTOR(cormat = cor(data_RSE), Ncases = 800, Nfactors = 4,
bifactor_kind = 'SL',
schmid_options = list(extraction = 'minres',
rotation = 'oblimin'))
# when rawdata is provided, but not loadings or cormat
BIFACTOR(rawdata = data_RSE, Nfactors = 3,
bifactor_kind = 'bifactorT',
EFA_options = list(extraction = 'minres', rotation = 'oblimin'))
# confirmatory bifactor analyses
BIFACTOR(rawdata = data_RSE,
bifactor_kind = 'CFA',
LV_options = list(group_keys = c(1, 1, 2, 1, 2, 1, 1, 2, 2, 2),
N_group_factors = NULL,
estimator = 'WLSMV',
rotation = 'bigeomin',
resid_correls = NULL,
LV_names=NULL,
ordered = TRUE),
min_loading = .0001)
# Run this command for additional Examples: vignette("EXAMPLES_vignettes")
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