sirt (version 0.31-20)

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, Moore & Haviland, 2010).

Usage

greenyang.reliability(object.tetra, nfactors)

Arguments

object.tetra

Object as the output of the function tetrachoric or fa.parallel.poly from the psych package. This object can also be created as a list by the user where the tetrachoric correlation must must be in the list entry

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, ECV) explained by the common factor is based on the D-dimensional but does not take item thresholds into account.
• dimensions
  Number of dimensions
• estimate
  Reliability estimate

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., 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

##################################################################
# Reliability estimation of reading dataset
library(psych)
set.seed(789)
data( data.read )
dat <- data.read

# calculate matrix of tetrachoric correlations
dat.tetra <- tetrachoric(dat)      # using tetrachoric from psych package
dat.tetra2 <- tetrachoric2(dat)	   # using tetrachoric2 from sirt package

# perform parallel factor analysis
fap <- 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 <- fa.parallel(dat.tetra$rho , n.obs=nrow(dat) ,  n.iter = 10 )
## 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

# calculation of Green-Yang-Reliability based on tetrachoric2 generated matrix
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 )