This study conducted a comprehensive comparison of Item Response Theory (IRT) linking methods applied to a bifactor model, examining their performance on both multiple choice (MC) and mixed format tests within the common item nonequivalent group design framework. Four distinct multidimensional IRT linking approaches were explored, consisting of…

The forced-choice response format is often considered superior to the standard Likert-type format for controlling social desirability in personality inventories. We performed simulations and found that the trait information based on the two formats converges when the number of items is high and forced-choice items are mixed with regard to…

This study proposes a Bayesian method for diagnostic classification models (DCMs) for a partially known Q-matrix setting between exploratory and confirmatory DCMs. This Q-matrix setting is practical and useful because test experts have pre-knowledge of the Q-matrix but cannot readily specify it completely. The proposed method employs priors for…

In selected-response assessments such as attitude surveys with Likert-type rating scales, examinees often select from rating scale categories to reflect their locations on a construct. Researchers have observed that some examinees exhibit "response styles," which are systematic patterns of responses in which examinees are more likely to…

To evaluate multidimensional factor structure, a popular method that combines features of confirmatory and exploratory factor analysis is Bayesian structural equation modeling with small-variance normal priors (BSEM-N). This simulation study evaluated BSEM-N as a variable selection and parameter estimation tool in factor analysis with sparse…

Determining the number of dimensions is extremely important in applying item response theory (IRT) models to data. Traditional and revised parallel analyses have been proposed within the factor analysis framework, and both have shown some promise in assessing dimensionality. However, their performance in the IRT framework has not been…

A Monte Carlo simulation study was conducted to examine the performance of [alpha], [lambda]2, [lambda][subscript 4], [lambda][subscript 2], [omega][subscript T], GLB[subscript MRFA], and GLB[subscript Algebraic] coefficients. Population reliability, distribution shape, sample size, test length, and number of response categories were varied…

Statistical process control (SPC) charts have been widely used in the field of educational measurement. The cumulative sum (CUSUM) is an established SPC method to detect aberrant responses for educational assessments. There are many studies that investigated the performance of CUSUM in different test settings. This paper describes the CUSUM…

The detection of differential item functioning (DIF) is important in psychological and behavioral sciences. Standard DIF detection methods perform an item-by-item test iteratively, often assuming that all items except the one under investigation are DIF-free. This article proposes a Bayesian adaptive Lasso method to detect DIF in graded response…

A new index of item discrimination power (IDP), dimension-corrected Somers' D (D2) is proposed. Somers' D is one of the superior alternatives for item-total- (Rit) and item-rest correlation (Rir) in reflecting the real IDP with items with scales 0/1 and 0/1/2, that is, up to three categories. D also reaches the extreme value +1 and -1 correctly…

To address response style or bias in rating scales, forced-choice items are often used to request that respondents rank their attitudes or preferences among a limited set of options. The rating scales used by raters to render judgments on ratees' performance also contribute to rater bias or errors; consequently, forced-choice items have recently…

In real-world situations, multidimensional data may appear on large-scale tests or attitudinal surveys. A simple structure, multidimensional model may be used to evaluate the items, ignoring the cross-loading of some items on the secondary dimension. The purpose of this study was to investigate the influence of structure complexity magnitude of…

In exploratory factor analysis, although the researchers decide which items belong to which factors by considering statistical results, the decisions taken sometimes can be subjective in case of having items with similar factor loadings and complex factor structures. The aim of this study was to examine the validity of classifying items into…

Scores estimated from multidimensional item response theory (IRT) models are not necessarily comparable across dimensions. In this article, the concept of aligned dimensions is formalized in the context of Rasch models, and two methods are described--delta dimensional alignment (DDA) and logistic regression alignment (LRA)--to transform estimated…

A log-linear model (LLM) is a well-known statistical method to examine the relationship among categorical variables. This study investigated the performance of LLM in detecting differential item functioning (DIF) for polytomously scored items via simulations where various sample sizes, ability mean differences (impact), and DIF types were…