It follows that for a fixed number of items, higher C α is associated with smaller measurement error of items through higher inter-item correlation ρ.
Additionally, there was a correlation between the errors of item 4, "shopping" and item 8, "moving a table".
The tests of content validity measure the fit of individual items to the model, the estimation errors of item parameter values, and the spacing and range of item parameter values, relative to the distribution of person parameter values.
δ average item challenge, SE standard error of the item challenge, Infit infit mean square statistic, Oufit outfit mean square statistic aThe original item 9 was reversed in these analyses Note.
Error terms of item 2 (hearing loss) and item 3 (speech impairment) correlated highly which made conceptual sense.
Large correlation was found between error terms of item 4 (emotional distress) and item 6 (caregiver concerns) which also made conceptual sense.
In these analyses no correlations between measurement errors of items were allowed within or across subscales.
Together with the values of these threshold parameters, the standard error of the item steps are shown, showing that the values are relatively low (0.06, 0.03, 0.02 and 0.03).
In addition, the interpretation of the resulting reliability coefficient depends on some strong assumptions being met: most notably in the context of the current study, there is the assumption that the measurement error of each item is random (i.e. uncorrelated with anything else).
In order to check Type I error of the item-fit residuals and the generalized residuals for first-order marginals and second-order marginals, we simulated data that look like the above-mentioned NAEP data sets but fit the model perfectly.
