greenyang.reliability.Rd
This function estimates the model-based reliability
of dichotomous data using the Green & Yang (2009) method.
The underlying factor model is \(D\)-dimensional where
the dimension \(D\) is specified by the argument
nfactors
. The factor solution is subject to the
application of the Schmid-Leiman transformation (see Reise, 2012;
Reise, Bonifay, & Haviland, 2013; Reise, Moore, & Haviland, 2010).
greenyang.reliability(object.tetra, nfactors)
object.tetra | Object as the output of the function |
---|---|
nfactors | Number of factors (dimensions) |
A data frame with columns:
Name of the reliability measure. omega_1
(Omega)
is the reliability estimate for the total score for dichotomous data
based on a one-factor model, omega_t
(Omega Total) is the
estimate for a \(D\)-dimensional model. For the nested factor model,
omega_h
(Omega Asymptotic) is the reliability of the general factor model,
omega_ha
(Omega Hierarchical Asymptotic) eliminates item-specific
variance. The explained common variance (ECV
) explained by the
common factor is based on the \(D\)-dimensional but does not take
item thresholds into account. The amount of explained
variance ExplVar
is defined as the quotient of the first
eigenvalue of the tetrachoric correlation matrix to the
sum of all eigenvalues. The statistic EigenvalRatio
is the ratio of the first and second eigenvalue.
Number of dimensions
Reliability estimate
Green, S. B., & Yang, Y. (2009). Reliability of summed item scores using structural equation modeling: An alternative to coefficient alpha. Psychometrika, 74, 155-167.
Reise, S. P. (2012). The rediscovery of bifactor measurement models. Multivariate Behavioral Research, 47, 667-696.
Reise, S. P., Bonifay, W. E., & Haviland, M. G. (2013). Scoring and modeling psychological measures in the presence of multidimensionality. Journal of Personality Assessment, 95, 129-140.
Reise, S. P., Moore, T. M., & Haviland, M. G. (2010). Bifactor models and rotations: Exploring the extent to which multidimensional data yield univocal scale scores, Journal of Personality Assessment, 92, 544-559.
This function needs the psych package.
See f1d.irt
for estimating the functional unidimensional
item response model.
This function uses reliability.nonlinearSEM
.
See also the MBESS::ci.reliability
function for estimating
reliability for polytomous item responses.
if (FALSE) { ############################################################################# # EXAMPLE 1: Reliability estimation of Reading dataset data.read ############################################################################# miceadds::library_install("psych") set.seed(789) data( data.read ) dat <- data.read # calculate matrix of tetrachoric correlations dat.tetra <- psych::tetrachoric(dat) # using tetrachoric from psych package dat.tetra2 <- sirt::tetrachoric2(dat) # using tetrachoric2 from sirt package # perform parallel factor analysis fap <- psych::fa.parallel.poly(dat, n.iter=1 ) ## Parallel analysis suggests that the number of factors=3 ## and the number of components=2 # parallel factor analysis based on tetrachoric correlation matrix ## (tetrachoric2) fap2 <- psych::fa.parallel(dat.tetra2$rho, n.obs=nrow(dat), n.iter=1 ) ## Parallel analysis suggests that the number of factors=6 ## and the number of components=2 ## Note that in this analysis, uncertainty with respect to thresholds is ignored. # calculate reliability using a model with 4 factors greenyang.reliability( object.tetra=dat.tetra, nfactors=4 ) ## coefficient dimensions estimate ## Omega Total (1D) omega_1 1 0.771 ## Omega Total (4D) omega_t 4 0.844 ## Omega Hierarchical (4D) omega_h 4 0.360 ## Omega Hierarchical Asymptotic (4D) omega_ha 4 0.427 ## Explained Common Variance (4D) ECV 4 0.489 ## Explained Variance (First Eigenvalue) ExplVar NA 35.145 ## Eigenvalue Ratio (1st to 2nd Eigenvalue) EigenvalRatio NA 2.121 # calculation of Green-Yang-Reliability based on tetrachoric correlations # obtained by tetrachoric2 greenyang.reliability( object.tetra=dat.tetra2, nfactors=4 ) # The same result will be obtained by using fap as the input greenyang.reliability( object.tetra=fap, nfactors=4 ) }