OmegaG {OmegaG}

Composite Reliability Coefficient Omega-Generic

Description

This function is used to estimate the composite reliability coefficient Omega-generic (Mai, Srivastava, & Krull, 2021), given factor loadings, factor covariance matrix, and covariance matrix of item residuals.

Usage

OmegaG(
  Lambda = NULL,
  Phi = NULL,
  Psi = NULL,
  items.index = NULL,
  factor.index = NULL,
  scale.structure = NULL,
  modeltype = c("correlated-factor", "bi-factor")
)

Arguments

Lambda

The input factor lading matrix. Each row contains the loadings of one item on factors. Each column includes the loadings of one factor. In the case of bi-factor structure, the first column of loadings is on the global factor.

Phi

The input factor covariance matrix.

Psi

The input covariance matrix of item residuals. Typically, Psi is a diagonal matrix.

items.index

The vector indexing the items of which the composite reliability is being estimated. It is an optional argument. If it is specified, the argument scale.structure is not effective. If it is not specified, the the argument scale.structure is expected to be specified and effective.

factor.index

The vector indexing the factor(s)/construct(s) regarding which the composite reliability is being estimated. It is an optional argument. If it is not specified, the function will estimate the composite reliability regarding each factor/construct.

scale.structure

The scale structure in a list or a Boolean matrix form. In a list form, each element is a vector of items (names) of a subscale. If in a boolean form, the element on the i-th row and the j-th column indicates whether the i-th item is within the j-th subscale. If both the argument scale.structure and Lambda include colnames and rownames, the names must be match with each other. This argument scale.structure is optional. Only when item-index is not specified, this argument is effective.

modeltype

The type of factor structure ("corr-factor" or "bi-factor"). The current version supports correlated-factor structure and bi-factor structure. A bi-factor model typically assumes factors are uncorrelated. The default is correlated-factor structure.

Value

The estimated composite reliability coefficient OmegaG.

Author(s)

Yujiao Mai, Deo Kumar Srivastava, and Kevin R Krull

References

Mai, Y., Srivastava, D.K., & Krull, K.R. (2021). Estimating Composite reliability of Multidimensional Measurement with Overlapping Items. Present at the 2021 Eastern North American Region (ENAR) Spring Virtual Meeting.

Examples

#### Example 1:
OmegaG(Lambda = PedsQLMFS$ESEM$Lambda,
                       Phi = PedsQLMFS$ESEM$Phi,
                        Psi = PedsQLMFS$ESEM$Psi,
                        modeltype = "correlated-factor",
                        scale.structure = PedsQLMFS$ScaleStructure
                        )

#  Model type = correlated-factor
#
#  CR of each subscale:
#       GeneralFatigue :    0.770
#         SleepFatigue :    0.690
#     CognitiveFatigue :    0.777


#### Example 2:
 OmegaG(Lambda = PedsQLMFS$biESEM$Lambda,
                Phi = PedsQLMFS$biESEM$Phi,
                Psi = PedsQLMFS$biESEM$Psi,
                modeltype = "bi-factor",
                scale.structure = PedsQLMFS$ScaleStructure
 )

# Model type = bi-factor
#
# Hierarchy and Hierarchical-subscale CR:
#                          GlobalFatigue :    0.806
#                         GeneralFatigue :    0.174
#                           SleepFatigue :    0.361
#                       CognitiveFatigue :    0.190
#
# Scale Total and Subscale CR:
#   GlobalFatigue + all sepcific factors :    0.926
#         GlobalFatigue + GeneralFatigue :    0.859
#           GlobalFatigue + SleepFatigue :    0.758
#       GlobalFatigue + CognitiveFatigue :    0.839


# Example 3:
 OmegaG::OmegaG(Lambda = PedsQLMFS$biESEM$Lambda,
       Phi = PedsQLMFS$biESEM$Phi,
       Psi = PedsQLMFS$biESEM$Psi,
       modeltype = "bi-factor",
       items.index = 1:6,factor.index = 2
 )

# Model type = bi-factor
#
# CR of Items 1 2 3 4 5 6 regarding factor 2:
#                      GeneralFatigue :    0.174


# Example 4:
  OmegaG::OmegaG(Lambda = PedsQLMFS$ESEM$Lambda,
                 Phi = PedsQLMFS$ESEM$Phi,
                  Psi = PedsQLMFS$ESEM$Psi,
                 modeltype = "correlated-factor",
                  items.index = 7:12,factor.index = 2
   )

# Model type = correlated-factor
#
# CR of Items 7 8 9 10 11 12 regarding factor 2:
#   SleepFatigue :    0.690