EFAtools (version 0.3.0)

OMEGA: McDonald's omega

Description

This function finds omega total, omega hierarchical, and omega subscale from a Schmid-Leiman (SL) solution or lavaan single factor, second-order (see below), or bifactor solution. The SL-based omegas can either be found from a psych::schmid, SL, or, in a more flexible way, by leaving model = NULL and specifying additional arguments. By setting the type argument, results from psych::omega can be reproduced.

Usage

OMEGA(
  model = NULL,
  type = c("EFAtools", "psych"),
  g_name = "g",
  group_names = NULL,
  factor_corres = NULL,
  var_names = NULL,
  fac_names = NULL,
  g_load = NULL,
  s_load = NULL,
  u2 = NULL,
  cormat = NULL,
  pattern = NULL,
  Phi = NULL,
  variance = c("correlation", "sums_load")
)

Arguments

model

class SL, class schmid, or class lavaan object. That is, an output object from SL or psych::schmid, or a lavaan fit object with a single factor, second-order, or bifactor solution. If of class lavaan, only g_name needs to be specified additionally. If of class SL or schmid, only the arguments factor_corres and cormat need to be specified additionally.

type

character. Either "EFAtools" (default) or "psych" (see details)

g_name

character. The name of the general factor from the lavaan solution. This needs only be specified if model is a lavaan second-order or bifactor solution. Default is "g".

group_names

character. An optional vector of group names. The length must correspond to the number of groups for which the lavaan model was fitted.

factor_corres

matrix. A logical matrix or a numeric matrix containing 0's and 1's that indicates which variable corresponds to which group factor. Must have the same dimensions as the matrix of group factor loadings from the SL solution. Cross-loadings are allowed here. See examples for use.

var_names

character. A vector with subtest names in the order of the rows from the SL solution. This needs only be specified if model is left NULL.

fac_names

character. An optional vector of group factor names in the order of the columns of the SL solution. If left NULL, names of the group factors from the entered solution are taken.

g_load

numeric. A vector of general factor loadings from an SL solution. This needs only be specified if model is left NULL.

s_load

matrix. A matrix of group factor loadings from an SL solution. This needs only be specified if model is left NULL.

u2

numeric. A vector of uniquenesses from an SL solution. This needs only be specified if model is left NULL.

cormat

matrix. A correlation matrix to be used when variance = "correlation". If left NULL and an SL output is entered in model, the correlation matrix is taken from the output. If left NULL and a psych::schmid output is entered, the correlation matrix will be found based on the pattern matrix and Phi from the psych::schmid output using psych::factor.model. If left NULL and model is also left NULL, the correlation matrix is found based on the pattern matrix and Phi entered. However, if the correlation matrix is available, cormat should be specified instead of Phi and pattern.

pattern

matrix. Pattern coefficients from an oblique factor solution. This needs only be specified if model is left NULL, variance = "correlation" and cormat is also left NULL.

Phi

matrix. Factor intercorrelations from an oblique factor solution. This needs only be specified if model is left NULL, variance = "correlation" and cormat is also left NULL.

variance

character. If "correlation" (default), then total variances for the whole scale as well as for the subscale composites are calculated based on the correlation matrix. If "sums_load", then total variances are calculated using the squared sums of general factor loadings and group factor loadings and the sum of uniquenesses (see details).

Value

If found for an SL or lavaan second-order of bifactor solution without multiple groups: A matrix with omegas for the whole scale and for the subscales.

tot

Omega total.

hier

Omega hierarchical.

sub

Omega subscale.

If found for a lavaan single factor solution without multiple groups: A vector with omega total for the single factor.

If found for a lavaan output from a multiple group analysis: A list containing the output described above for each group.

Details

If model is a lavaan second-order or bifactor solution, only the name of the general factor from the lavaan model needs to be specified additionally with the g_name argument. It is then determined whether this general factor is a second-order factor (second-order model assumed) or a breadth factor (bifactor model assumed). In case of a second-order solution, a Schmid-Leiman transformation is performed on the first- and second-order loadings and omega coefficents are obtained from the transformed (orthogonalized) solution (see SL for more information on Schmid-Leiman transformation). There is also the possibility to enter a lavaan single factor solution. In this case, g_name is not needed. Finally, if a solution from a lavaan multiple group analysis is entered, the omegas are computed for each group. The type argument is not evaluated if model is of class lavaan.

If model is of class SL or psych::schmid only the type and, depending on the type (see below), the factor_corres arguments need to be specified additionally. If model is of class psych::schmid and variance = "correlation" (default), it is recommended to also provide the original correlation matrix in cormat to get more accurate results. Otherwise, the correlation matrix will be found based on the pattern matrix and Phi from the psych::schmid output using the psych::factor.model function.

If model = NULL, the arguments type, factor_corres (depending on the type, see below), var_names, g_load, s_load, and u2 and either cormat (recommended) or Phi and pattern need to be specified. If Phi and pattern are specified instead of cormat, the correlation matrix is found using the psych::factor.model function.

The only difference between type = "EFAtools" and type = "psych" is the determination of variable-to-factor correspondences. type = "psych" reproduces the psych::omega results, where variable-to-factor correspondences are found by taking the highest group factor loading for each variable as the relevant group factor loading. To do this, factor_corres must be left NULL.

The calculation of the total variance (for the whole scale as well as the subscale composites) can also be controlled in this function using the variance argument. For both types---"EFAtools" and "psych" ---variance is set to "correlation" by default, which means that total variances are found using the correlation matrix. If variance = "sums_load" the total variance is calculated using the squared sums of general loadings and group factor loadings and the sum of the uniquenesses. This will only get comparable results to variance = "correlation" if no cross-loadings are present and simple structure is well-achieved in general with the SL solution (i.e., the uniquenesses should capture almost all of the variance not explained by the general factor and the variable's allocated group factor).

Examples

# NOT RUN {
## Use with lavaan outputs

# Create and fit bifactor model in lavaan (assume all variables have SDs of 1)
mod <- 'F1 =~ V1 + V2 + V3 + V4 + V5 + V6
        F2 =~ V7 + V8 + V9 + V10 + V11 + V12
        F3 =~ V13 + V14 + V15 + V16 + V17 + V18
        g =~ V1 + V2 + V3 + V4 + V5 + V6 + V7 + V8 + V9 + V10 + V11 + V12 +
             V13 + V14 + V15 + V16 + V17 + V18'
fit_bi <- lavaan::cfa(mod, sample.cov = test_models$baseline$cormat,
                      sample.nobs = 500, estimator = "ml", orthogonal = TRUE)

# Compute omega for bifactor solution
OMEGA(fit_bi, g_name = "g")

# Create and fit second-order model in lavaan (assume all variables have SDs of 1)
mod <- 'F1 =~ V1 + V2 + V3 + V4 + V5 + V6
        F2 =~ V7 + V8 + V9 + V10 + V11 + V12
        F3 =~ V13 + V14 + V15 + V16 + V17 + V18
        g =~ F1 + F2 + F3'
fit_ho <- lavaan::cfa(mod, sample.cov = test_models$baseline$cormat,
                      sample.nobs = 500, estimator = "ml")

# Compute omega for second-order solution
OMEGA(fit_ho, g_name = "g")
# }
# NOT RUN {
## Use with an output from the SL function, with type EFAtools
efa_mod <- EFA(test_models$baseline$cormat, N = 500, n_factors = 3,
               type = "EFAtools", method = "PAF", rotation = "promax")
sl_mod <- SL(efa_mod, type = "EFAtools", method = "PAF")

# Two examples how to specify the indicator-to-factor correspondences:

# Based on a specific salience threshold for the loadings (here: .20):
factor_corres_1 <- sl_mod$sl[, c("F1", "F2", "F3")] >= .2

# Or more flexibly (could also be TRUE and FALSE instead of 0 and 1):
factor_corres_2 <- matrix(c(rep(0, 12), rep(1, 6), rep(0, 6), rep(1, 6),
                         rep(0, 6), rep(1, 6), rep(0, 12)), ncol = 3,
                         byrow = FALSE)

OMEGA(sl_mod, type = "EFAtools", factor_corres = factor_corres_1)

## Use with an output from the psych::schmid function, with type psych for
## OMEGA
schmid_mod <- psych::schmid(test_models$baseline$cormat, nfactors = 3,
                            n.obs = 500, fm = "pa", rotate = "Promax")
# Find correlation matrix from phi and pattern matrix from psych::schmid output
OMEGA(schmid_mod, type = "psych")
# Use specified correlation matrix
OMEGA(schmid_mod, type = "psych", cormat = test_models$baseline$cormat)

## Manually specify components (useful if omegas should be computed for a SL
## or bifactor solution found with another program)
## As an example, we extract the elements from an SL output here. This gives
## the same results as in the second example above.

efa_mod <- EFA(test_models$baseline$cormat, N = 500, n_factors = 3,
               type = "EFAtools", method = "PAF", rotation = "promax")
sl_mod <- SL(efa_mod, type = "EFAtools", method = "PAF")

factor_corres <- matrix(c(rep(0, 12), rep(1, 6), rep(0, 6), rep(1, 6),
                        rep(0, 6), rep(1, 6), rep(0, 12)), ncol = 3,
                        byrow = FALSE)

OMEGA(model = NULL, type = "EFAtools", var_names = rownames(sl_mod$sl),
      g_load = sl_mod$sl[, "g"], s_load = sl_mod$sl[, c("F1", "F2", "F3")],
      u2 = sl_mod$sl[, "u2"], cormat = test_models$baseline$cormat,
      factor_corres = factor_corres)

# }