sirt: greenyang.reliability – R documentation

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greenyang.reliability

Reliability for Dichotomous Item Response Data Using the Method of Green and Yang (2009)

Description

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).

Usage

greenyang.reliability(object.tetra, nfactors)

Arguments

`object.tetra`	Object as the output of the function `tetrachoric`, the `fa.parallel.poly` from the psych package or the `tetrachoric2` function (from sirt). This object can also be created as a list by the user where the tetrachoric correlation must must be in the list entry `rho` and the thresholds must be in the list entry `thresh`.
`nfactors`	Number of factors (dimensions)

Value

A data frame with columns:

`coefficient`	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.
`dimensions`	Number of dimensions
`estimate`	Reliability estimate

Note

This function needs the psych package.

References

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.

Examples

## Not run: 
#############################################################################
# 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 ) 
## End(Not run)

sirt

Supplementary Item Response Theory Models

v3.10-118

GPL (>= 2)

Authors

Alexander Robitzsch [aut,cre] (<https://orcid.org/0000-0002-8226-3132>)

Initial release

2021-09-22 17:45:34