BifactorIndicesCalculator (version 0.2.2)

bifactorIndices: bifactorIndices

Description

Computes all available bifactor indices for the input given.

Usage

bifactorIndices(
  Lambda,
  Theta = NULL,
  UniLambda = NULL,
  standardized = TRUE,
  Phi = NULL,
  Thresh = NULL
)

Arguments

Lambda

is a matrix of factor loadings or an object that can be converted to a matrix of factor loadings by getLambda. Currently fitted lavaan objects and fitted mirt objects are supported in addition to raw factor loading matrix input. For Mplus output files, use bifactorIndicesMplus.

Theta

is a vector of residual variances. If omitted, Theta will be computed from input for Lambda.

UniLambda

is a matrix of factor loadings or an object that can be converted to a matrix of factor loadings such as a fitted lavaan objects or fitted mirt object. Defaults to NULL, as UniLambda is only required if you wish to compute ARPB.

standardized

lets the function know whether to look for standardized or unstandardized results from lavaan and defaults to TRUE. If Lambda is not a lavaan object, then standardized will be ignored.

Phi

is the correlation matrix of factors and defaults to NULL. User should generally ignore this parameter. If not provided, bifactorIndices will try to determine Phi from Lambda when Lambda is a fitted lavaan model or will assume it is the identity matrix otherwise.

Thresh

is a list of vectors of item thresholds, used only when items are categorical.bifactorIndices will try to determine Thresh from Lambda when Lambda is a fitted lavaan model and the indicators are categorical. Thresh defaults to null, which indicates items are continuous.

Value

A list of bifactor indices, including three different ECV indices, IECV, PUC, Omega, OmegaH, Factor Determinacy (FD), Construct Replicability (H) and ARPB. Please note that many of these indices are interpretable even when the model being used is not a bifactor model; some indices may be useful for two-tier, trifactor, correlated traits, and even unidimensional models.

Details

Currently, factor loading matrices, fitted lavaan objects, and fitted mirt objects are supported. For Mplus output, see bifactorIndicesMplus. IRT parameters from mirt are converted to standardized factor loadings via the correspondence described in Kamata & Bauer (2008). If you wish to use standardized coefficients, item error variance will be computed directly from standardized factor loadings. ARPB will only be computed if the factor loadings from a unidimensional model are included, while ECV_GS and ECV_SG will only be computed for models with a general factor, and PUC will only be conputed for a true bifactor model. Note that if a correlated traits model is provided, the omega indices will simply be the regular omega values for those factors. Interpretations for individual indices as well as details about their computation can be found in the man page for the individual indices.

Formulas for all indices can be found in Rodriguez et al. (2016). When indicators are categorical, the methodology of Green and Yang (2009) is used for computing Omega and OmegaH.

References

Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74(1), 155-167 10.1007/s11336-008-9099-3.

Kamata, A., & Bauer, D. J. (2008). A note on the relation between factor analytic and item response theory models. Structural Equation Modeling: A Multidisciplinary Journal, 15 (1), 136-153.

#' Rodriguez, A., Reise, S. P., & Haviland, M. G. (2016). Evaluating bifactor models: calculating and interpreting statistical indices. Psychological Methods, 21(2), 137 10.1037/met0000045.

See Also

bifactorIndicesMplus, bifactorIndices_expl, bifactorIndicesMplus_expl, bifactorIndicesMplus_ESEM, ECV_SS, ECV_SG, ECV_GS, IECV, PUC, Omega_S, Omega_H, cat_Omega_S, cat_Omega_H, H, FD, ARPB

Examples

# NOT RUN {
# Computing bifactor indices from fitted lavaan object
# (using mirt object is similar). Use of the unidimensional
# model is optional; it is only used to compute ARPB.

# }
# NOT RUN {
SRS_UnidimensionalModel <-
  "SRS =~ SRS_1  + SRS_2  + SRS_3  + SRS_4  + SRS_5  +
          SRS_6  + SRS_7  + SRS_8  + SRS_9  + SRS_10 +
          SRS_11 + SRS_12 + SRS_13 + SRS_14 + SRS_15 +
          SRS_16 + SRS_17 + SRS_18 + SRS_19 + SRS_20"

SRS_Unidimensional <- lavaan::cfa(SRS_UnidimensionalModel,
                                 SRS_data,
                                 ordered = paste0("SRS_", 1:20),
                                 orthogonal = TRUE)


SRS_BifactorModel <-
"SRS =~ SRS_1  + SRS_2  + SRS_3  + SRS_4  + SRS_5  +
        SRS_6  + SRS_7  + SRS_8  + SRS_9  + SRS_10 +
        SRS_11 + SRS_12 + SRS_13 + SRS_14 + SRS_15 +
        SRS_16 + SRS_17 + SRS_18 + SRS_19 + SRS_20
 Function     =~ SRS_5  + SRS_9  + SRS_12 + SRS_15 + SRS_18
 Pain         =~ SRS_1  + SRS_2  + SRS_8  + SRS_11 + SRS_17
 SelfImage    =~ SRS_4  + SRS_6  + SRS_10 + SRS_14 + SRS_19
 MentalHealth =~ SRS_3  + SRS_7  + SRS_13 + SRS_16 + SRS_20"

SRS_bifactor <- lavaan::cfa(SRS_BifactorModel,
                            SRS_data,
                            ordered = paste0("SRS_", 1:20),
                            orthogonal = TRUE)

bifactorIndices(SRS_bifactor, UniLambda = SRS_Unidimensional)
# }
# NOT RUN {

# Computing bifactor indices from standardized factor loading matrices
Lambda <-  matrix(c(.82, .10,   0,   0,
                    .77, .35,   0,   0,
                    .79, .32,   0,   0,
                    .66, .39,   0,   0,
                    .51,   0, .71,   0,
                    .56,   0, .43,   0,
                    .68,   0, .13,   0,
                    .60,   0, .50,   0,
                    .83,   0,   0, .47,
                    .60,   0,   0, .27,
                    .78,   0,   0, .28,
                    .55,   0,   0, .75),
                    ncol = 4, byrow = TRUE)
colnames(Lambda) <- c("General", "SF1", "SF2", "SF3")
bifactorIndices(Lambda)


# bifactorIndices can also be used on two-tier models
MTMM_model <- "
Trait1  =~ T1M1_1 + T1M1_2 + T1M1_3 +
           T1M2_1 + T1M2_2 + T1M2_3 +
           T1M3_1 + T1M3_2 + T1M3_3
Trait2  =~ T2M1_1 + T2M1_2 + T2M1_3 +
           T2M2_1 + T2M2_2 + T2M2_3 +
           T2M3_1 + T2M3_2 + T2M3_3
Trait3  =~ T3M1_1 + T3M1_2 + T3M1_3 +
           T3M2_1 + T3M2_2 + T3M2_3 +
           T3M3_1 + T3M3_2 + T3M3_3

Method1  =~ T1M1_1 + T1M1_2 + T1M1_3 +
            T2M1_1 + T2M1_2 + T2M1_3 +
            T3M1_1 + T3M1_2 + T3M1_3
Method2  =~ T1M2_1 + T1M2_2 + T1M2_3 +
            T2M2_1 + T2M2_2 + T2M2_3 +
            T3M2_1 + T3M2_2 + T3M2_3
Method3  =~ T1M3_1 + T1M3_2 + T1M3_3 +
            T2M3_1 + T2M3_2 + T2M3_3 +
            T3M3_1 + T3M3_2 + T3M3_3

Trait1 ~~ 0*Method1
Trait1 ~~ 0*Method2
Trait1 ~~ 0*Method3
Trait2 ~~ 0*Method1
Trait2 ~~ 0*Method2
Trait2 ~~ 0*Method3
Trait3 ~~ 0*Method1
Trait3 ~~ 0*Method2
Trait3 ~~ 0*Method3

Method1 ~~ 0*Method2
Method1 ~~ 0*Method3
Method2 ~~ 0*Method3"

MTMM_fit <- lavaan::cfa(MTMM_model, MTMM_data)
bifactorIndices(MTMM_fit)

# }