Abstract:
The study investigates the effects of response scales of items on results of item
response theory (IRT) models and multivariate statistical techniques. A total of
sixty-four datasets have been simulated under various conditions such as item
response format, number of dimensions underlying response scales, and sample
size using R package MIRT command: simdata (a, d, N, itenitype). Two main
statistical techniques - IRT models and Factor Analysis - are employed in
analysing the simulated datasets using standard R 3.4.3 codes. We find that there
is a direct relationship between parameters of IRT and those of factor models,
particularly item discrimination and factor loadings. The results also show that
the overall fitness of the item response model increases with increasing scale
points for higher dimensionality and sample size 150 and higher. The fitness
deteriorates over increasing scale points for small sample sizes for unidimensional IRT model. Again, the number of influential indicators on factors increases with increasing scale-points, which improves the fitness of the
model. The results indicate that unrealistic factor solution may be obtained if
we attempt to extract higher factor solution than the underlying dimensionality
on few scale-points with higher sample sizes. The study suggests that a fivepoint
response scale gives most reasonable results among various scales
examined. IRT analysis is recommended as a preliminary process to ascertain the observed features of items. The study also finds a sample size of 150 as adequate for a most plausible factor solution, under various conditions.
