As with any psychometric models, the validity of inferences from cognitive diagnosis models (CDMs) determines the extent to which these models can be useful. For inferences from CDMs to be valid, it is crucial that the fit of the model to the data is ascertained. Based on a simulation study, this study investigated the sensitivity of various fit statistics for absolute or relative fit under different CDM settings. The investigation covered various types of model–data misfit that can occur with the misspecifications of the Q-matrix, the CDM, or both. Six fit statistics were considered: –2 log likelihood (–2LL), Akaike's information criterion (AIC), Bayesian information criterion (BIC), and residuals based on the proportion correct of individual items (p), the correlations (r), and the log-odds ratio of item pairs (l). An empirical example involving real data was used to illustrate how the different fit statistics can be employed in conjunction with each other to identify different types of misspecifications. With these statistics and the saturated model serving as the basis, relative and absolute fit evaluation can be integrated to detect misspecification efficiently.

The development of statistical methods for detecting test collusion is a new research direction in the area of test security. Test collusion may be described as large-scale sharing of test materials, including answers to test items. Current methods of detecting test collusion are based on statistics also used in answer-copying detection. Therefore, in computerized adaptive testing (CAT) these methods lose power because the actual test varies across examinees. This article addresses that problem by introducing a new approach that works in two stages: in Stage 1, test centers with an unusual distribution of a person-fit statistic are identified via Kullback–Leibler divergence; in Stage 2, examinees from identified test centers are analyzed further using the person-fit statistic, where the critical value is computed without data from the identified test centers. The approach is extremely flexible. One can employ any existing person-fit statistic. The approach can be applied to all major testing programs: paper-and-pencil testing (P&P), computer-based testing (CBT), multiple-stage testing (MST), and CAT. Also, the definition of test center is not limited by the geographic location (room, class, college) and can be extended to support various relations between examinees (from the same undergraduate college, from the same test-prep center, from the same group at a social network). The suggested approach was found to be effective in CAT for detecting groups of examinees with item pre-knowledge, meaning those with access (possibly unknown to us) to one or more subsets of items prior to the exam.

Changing the order of items between alternate test forms to prevent copying and to enhance test security is a common practice in achievement testing. However, these changes in item order may affect item and test characteristics. Several procedures have been proposed for studying these item-order effects. The present study explores the use of descriptive and explanatory models from item response theory for detecting and modeling these effects in a one-step procedure. The framework also allows for consideration of the impact of individual differences in position effect on item difficulty. A simulation was conducted to investigate the impact of a position effect on parameter recovery in a Rasch model. As an illustration, the framework was applied to a listening comprehension test for French as a foreign language and to data from the PISA 2006 assessment.

This study demonstrated the equivalence between the Rasch testlet model and the three-level one-parameter testlet model and explored the Markov Chain Monte Carlo (MCMC) method for model parameter estimation in WINBUGS. The estimation accuracy from the MCMC method was compared with those from the marginalized maximum likelihood estimation (MMLE) with the expectation-maximization algorithm in ConQuest and the sixth-order Laplace approximation estimation in HLM6. The results indicated that the estimation methods had significant effects on the bias of the testlet variance and ability variance estimation, the random error in the ability parameter estimation, and the bias in the item difficulty parameter estimation. The Laplace method best recovered the testlet variance while the MMLE best recovered the ability variance. The Laplace method resulted in the smallest random error in the ability parameter estimation while the MCMC method produced the smallest bias in item parameter estimates. Analyses of three real tests generally supported the findings from the simulation and indicated that the estimates for item difficulty and ability parameters were highly correlated across estimation methods.

A vertical score scale is needed to measure growth across multiple tests in terms of absolute changes in magnitude. Since the warrant for subsequent growth interpretations depends upon the assumption that the scale has interval properties, the validation of a vertical scale would seem to require methods for distinguishing interval scales from ordinal scales. In taking up this issue, two different perspectives on educational measurement are contrasted: a metaphorical perspective and a classical perspective. Although the metaphorical perspective is more predominant, at present it provides no objective methods whereby the properties of a vertical scale can be validated. In contrast, when taking a classical perspective, the axioms of additive conjoint measurement can be used to test the hypothesis that the latent variable underlying a vertical scale is quantitative (supporting ratio or interval properties) rather than merely qualitative (supporting ordinal or nominal properties). The application of such an approach is illustrated with both a hypothetical example and by drawing upon recent research that has been conducted on the Lexile scale for reading comprehension.

This article considers potential problems that can arise in estimating a unidimensional item response theory (IRT) model when some test items are multidimensional (i.e., show a complex factorial structure). More specifically, this study examines (1) the consequences of model misfit on IRT item parameter estimates due to unintended minor item-level multidimensionality, and (2) whether a Projection IRT model can provide a useful remedy. A real-data example is used to illustrate the problem and also is used as a base model for a simulation study. The results suggest that ignoring item-level multidimensionality might lead to inflated item discrimination parameter estimates when the proportion of multidimensional test items to unidimensional test items is as low as 1:5. The Projection IRT model appears to be a useful tool for updating unidimensional item parameter estimates of multidimensional test items for a purified unidimensional interpretation.