Application of posterior predictive checking for model fit testing of modified graded response model (m-grm) for the extrovert personality scale of undergraduate students
Abstract:
These research objectives were to develop a M-GRM parameter estimation
by using a posterior predictive model and to compare the performance of
the M-GRM parameter estimation between the posterior predictive model checking
and traditional methods for an extrovert personality scale in undergraduates.
The research procedure consisted of three stages, that is, 1) M-GRM development
process 2) the comparison of the M-GRM efficiency parameters using by five
conditions of Monte Carlo ( x x x x
n
)along 1,764 events (7x3x3x7x4), and
parameters = -2.5, -2, -1, 0, 1, 2, 2.5, = 0.1, 0.2, 0.3, = 0.3, 1.0, 1.7, = -3, -2, -1, 0,
1, 2, 3, and
n = 50, 100, 200, 400 and 3) The M-GRM model was checked for
the model fitting by using the posterior predictive checking method for the extrovert
personality scale in undergraduates.
The results were shown as follows:
1. The estimation process for the M-GRM parameter estimation by using the
posterior predictive model yielded b parameters of the M-GRM, which composed of
nine steps.
2. The posterior predictive model had a fitting model for 1,401 events,
while the traditional method yielded 568 fitted events suggesting that the posterior
predictive model checking method was more efficient than the traditional method.
When the sample size increased, the posterior predictive model checking method
tended to have a better efficient in examining a multidimensional property.
3. The model consistency of the extrovert personality scale of
undergraduate posed the multidimensional property with the slope value (
i
) was
1.00, the item difficulty value (
i b
) was -0.08 and the overall item threshold value (
i
c
)
was1.10, c2 was 0.86, c3 was -0.07 and c4 was -0.18, respectively. A probability for
zero ability of the respondent (
P( )
) was 0.58.