These assumptions include a monotonic relationship between the probability of responding to an item correctly and the latent trait, the unidimensionality of the latent trait, local independence of items, and invariance in the item parameters and the latent trait across different subgroups in a population.
RM is designed to estimate the subject's level on the latent trait, net of item characteristics, and items' net of subjects.
σ: variance of the latent trait; J: number of items.
The student response distributions on the origin of traits items provide an interesting pattern in students' responses to the matched item pairs.
Hence when designing a study, the most important parameters for reliable power determination using this ratio when a Rasch model is intended to be used to analyse PRO data appear to be the variance of the latent trait and the number of items regardless of the values of the group effect and items parameters (δj, j = 1,…,J).
Taken together, it is possible to achieve fine control over where and how well a given item set measures a latent trait along the latent trait distribution (subject to the availability of items with the desired parameters).
The distribution of student responses to the fitness, genetic origin of traits, and transformationist items indicated significant differences in how students responded to those items.
In all cases, marginal maximum likelihood estimation provided, as expected, unbiased estimates of the mean of the latent trait (μIRT1) and of item parameters, when needed.
This score reflects the hierarchical order of items across the trait.
Multi-trait scaling analyses supported the grouping of items into dimensions for 26 of the 36 items as their corrected item-total correlations exceeded the correlations with other dimension scores; scaling success rates ranging between 73-100% (Table 2, Table 3).
We specified two models of the relationship of items to latent trait(s) but used Item Response Theory (IRT) Graded Response Models (GRMs) [ 48] instead of the SEM approach used by Reise and colleagues [ 47].
