A conceptualization of multiple-choice exams in terms of signal detection theory (SDT) leads to simple measures of item difficulty and item discrimination that are closely related to, but also distinct from, those used in classical item analysis (CIA). The theory defines a "true split," depending on whether or not examinees know an item,…

Discriminant Analysis (DA) is a tool commonly used for differentiating among 2 or more groups based on 2 or more predictor variables. DA works by finding 1 or more linear combinations of the predictors that yield maximal difference among the groups. One common goal of researchers using DA is to characterize the nature of group difference by…

Discrimination has traditionally been parameterized for items but not other empirical factors. Consequently, if person factors affect discrimination they cause misfit. However, by explicitly formulating the relationship between discrimination and the unit of a metric, it is possible to parameterize discrimination for person groups. This article…

This study examined the utility of the Minnesota Multiphasic Personality Inventory-2's (MMPI-2) malingering discriminant function index (M-DFI), recently developed by Bacchiochi and Bagby, in the detection of malingering in a forensic sample. Criminal defendants were divided into "malingering" and "not malingering" groups using…

In this article we extend and implement the forward search algorithm for identifying atypical subjects/observations in factor analysis models. The forward search has been mainly developed for detecting aberrant observations in regression models (Atkinson, 1994) and in multivariate methods such as cluster and discriminant analysis (Atkinson, Riani,…

The Personality Assessment Inventory (L. C. Morey, 1991) includes 3 measures for identifying overreporting of psychopathology: the Negative Impression scale (NIM), Malingering Index (MAL), and Rogers Discriminant Function (RDF). Meta-analysis revealed that each measure was a strong predictor of uncoached (NIM, d = 1.48, k = 23; MAL, d = 1.15, k =…

A method for robust canonical discriminant analysis via two robust objective loss functions is discussed. Majorization is used at several stages in the minimization procedure to obtain a monotonically convergent algorithm. A simulation study and empirical data illustrate the procedure. (SLD)

To assess the effect on discriminant analysis in terms of correct classification into two groups, the following parameters were systematically altered using Monte Carlo techniques: sample sizes; proportions of one group to the other; number of independent variables; and covariance matrices. The pairing of the off diagonals (or covariances) with…

An empirical comparison is made of three proposed indices of relative predictor variable contribution: (1) the scaled weights of the first discriminant function; (2) the total group estimates of the correlations between each predictor variable and the first function; and (3) the within-groups estimates of the correlations between each predictor…

Differential item functioning (DIF) continues to receive attention both in applied and methodological studies. Because DIF can be an indicator of irrelevant variance that can influence test scores, continuing to evaluate and improve the accuracy of detection methods is an essential step in gathering score validity evidence. Methods for detecting…

Simulations were conducted to investigate factors that influence the Mantel, generalized Mantel-Haenszel (GMH), and logistic discriminant function analysis (LDFA) methods in assessing differential item functioning (DIF) for polytomous items. The results show that the magnitude of DIF contamination in the matching score, as measured by the average…

This study presents an overview of Monte Carlo studies in discriminant analysis. Some common questions about the use of Monte Carlo techniques are answered through a brief literature review of articles on discriminant analysis in which Monte Carlo methods are used. The articles cover many research points, such as comparing error rate estimates,…

This paper discusses the principles underlying discriminant analysis and constructs a simulated data set to illustrate its methods. Discriminant analysis is a multivariate technique for identifying the best combination of variables to maximally discriminate between groups. Discriminant functions are established on existing groups and used to…

Statistical significance is misused in educational and psychological research when it is applied as a method to establish the reliability of research results. Other techniques have been developed which can be correctly utilized to establish the generalizability of findings. Methods that do provide such estimates are known as invariance or…