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Resumen El objetivo de este trabajo es aportar nuevas evidencias de calidad psicométrica para la adaptación argentina de la versión reducida del Cuestionario de Personalidad de Eysenck (EPQ-RS). Participaron 1136 personas de población general (52.5% femenino, edad media = 29.6 años, DE = 11.9) residentes en Buenos Aires, Argentina. La adaptación argentina se compone de 42 ítems con formato de respuesta dicotómica. Se realizó un análisis factorial confirmatorio a partir de la matriz de correlaciones tetracóricas. Esto permitió replicar la estructura propuesta por Eysenck para el modelo PEN (Psicoticismo-Extraversión-Neuroticismo) y la escala Sinceridad. Posteriormente, se ajustó el modelo logístico de dos parámetros por separado para los ítems de cada escala. Los ítems no mostraron funcionamiento diferencial según género. La discriminación de los ítems resultó moderada-alta. Los parámetros b se localizaron en rangos acotados de cada uno de los rasgos medidos, lo que originó que la precisión de las escalas varíe en el recorrido de los continuos. La escala Neuroticismo aporta más información en niveles medios del rasgo, Psicoticismo en los medio-bajos y Extraversión en los medio-altos. La escala Sinceridad mostró una función de información relativamente plana en todo el recorrido del rasgo. Se brindan evidencias de validez basadas en la relación con otras pruebas que miden facetas del neuroticismo y sintomatología. Las evidencias de validez y confiabilidad obtenidas ofrecen garantías de calidad suficientes para la aplicación de este instrumento en el contexto local y confirman la vigencia del modelo teórico que operacionaliza el EPQ-RS.

Abstract The aim of this work is to provide new evidence of psychometric quality for the Argentinean adaptation of the brief version of the Eysenck Personality Questionnaire (EPQ-RS). 1136 people from the general population (52.5% female, mean age = 29.6 years, SD = 11.9) residing in Buenos Aires, Argentina participated. The Argentinean adaptation consists of 42 items with dichotomous response format. A confirmatory factor analysis was performed from the tetrachoric correlation matrix. This allowed replicating the structure proposed by Eysenck for the PEN model (Psychoticism - Extroversion - Neuroticism) and the Lie scale. Subsequently, the two-parameter logistic model was adjusted separately for the items of each scale. The items did not show differential functioning by gender. Items discrimination was moderate-high. Parameters b were located in narrow ranges of each one of the measured traits, which caused the precision of the scales to vary along the trait continuums. The Neuroticism scale provides more information at medium levels of the trait, Psychoticism in the medium-low and Extraversion in the medium-high. The Lie scale showed a relatively flat information function throughout the trait. Evidence of validity based on the relationship with other tests that measure facets of neuroticism and symptomatology is provided. The evidence of validity and reliability obtained offers sufficient quality guarantees for the application of this instrument in the local context and confirms topicality of the theoretical model that operationalizes the EPQ-RS.

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Functional Somatic Symptoms (FSS) are physical symptoms that cannot be attributed to underlying pathology. Their severity is often measured with sum scores on questionnaires; however, this may not adequately reflect FSS severity in subgroups of patients. We aimed to identify the items of the somatization section of the Composite International Diagnostic Interview that best discriminate FSS severity levels, and to assess their functioning in sex and age subgroups. We applied the two-parameter logistic model to 19 items in a population-representative cohort of 962 participants. Subsequently, we examined differential item functioning (DIF). "Localized (muscle) weakness" was the most discriminative item of FSS severity. "Abdominal pain" consistently showed DIF by sex, with males reporting it at higher FSS severity. There was no consistent DIF by age, however, "Joint pain" showed poor discrimination of FSS severity in older adults. These findings could be helpful for the development of better assessment instruments for FSS, which can improve both future research and clinical care.

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What to do when item response data are multidimensional but a unidimensional model is preferred in terms of statistical simplicity and ease of interpretability? The projection method for the compensatory logistic multidimensional item response model for dichotomous data leads to a two parameter logistic model with local item dependence. Despite the local item dependence, the model is unidimensional for many practical purposes. Here, Ip's projection method is generalized to the case of the graded response model for polytomous variables, extending the applicability of the method to Likert-type response formats. A secondary aim of the paper is the study of rotation techniques intended for use prior to projection. In contrast to rotations aiming at a simple structure of factor loadings, the proposed techniques increase the variance explained before or after projection, facilitate the interpretation of the projected dimension by variants of target rotations or a mix of both. The method is illustrated with an application to the Highly Sensitive Person Scale and R code is provided.

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The South Oaks Gambling Screen-Revised Adolescent (SOGS-RA) is one of the most widely used screening tools for problem gambling among adolescents. In this study, item response theory was used for computing measures of problem gambling severity that took into account how much information the endorsed items provided about the presence of problem gambling. A zero-inflated mixture two-parameter logistic model was estimated on the responses of 4,404 adolescents to the South Oaks Gambling Screen-Revised Adolescent to compute the difficulty and discrimination of each item, and the problem gambling severity level (θ score) of each respondent. Receiver operating characteristic curve analysis was used to identify the cutoff on the θ scores that best distinguished daily and nondaily gamblers. This cutoff outperformed the common cutoff defined on the sum scores in identifying daily gamblers but fell behind it in identifying nondaily gamblers. When screening adolescents to be subjected to further investigations, the cutoff on the θ scores must be preferred to that on the sum scores.

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The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of omnibus model tenability. The argument is exemplified with a comparison of the widely used one-parameter and two-parameter logistic models. A theoretically and practically relevant setting illustrates how discounting local fit and concentrating instead on overall model fit may lead to incorrect model selection, even if a popular information criterion is also employed. The article concludes with the recommendation for routine examination of particular parameter constraints within latent variable models as part of their fit evaluation.

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This note raises caution that a finding of a marked pseudo-guessing parameter for an item within a three-parameter item response model could be spurious in a population with substantial unobserved heterogeneity. A numerical example is presented wherein each of two classes the two-parameter logistic model is used to generate the data on a multi-item measuring instrument, while the three-parameter logistic model is found to be associated with a considerable pseudo-guessing parameter estimate on an item. The implications of the reported results for empirical educational research are subsequently discussed.

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Multidimensional computerized adaptive testing (MCAT) is one of the widely discussed topics in psychometrics. Within the context of item replenishment in MCAT, it is important to identify the item-trait pattern for each replenished item, which indicates the set of the latent traits that are measured by each replenished item in the item pool. We propose a pattern recognition method based on the least absolute shrinkage and selection operator (LASSO) to detect the optimal item-trait patterns of the replenished items via an MCAT test. Simulation studies are conducted to investigate the performance of the proposed method in pattern recognition accuracy under different conditions across various latent trait correlation, item discrimination, test lengths, and item selection criteria in the test. Results show that the proposed method can accurately and efficiently identify the item-trait patterns of the replenished items in both the two-dimensional and three-dimensional item pools.

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Item calibration is a technique to estimate characteristics of questions (called items) for achievement tests. In computerized tests, item calibration is an important tool for maintaining, updating and developing new items for an item bank. To efficiently sample examinees with specific ability levels for this calibration, we use optimal design theory assuming that the probability to answer correctly follows an item response model. Locally optimal unrestricted designs have usually a few design points for ability. In practice, it is hard to sample examinees from a population with these specific ability levels due to unavailability or limited availability of examinees. To counter this problem, we use the concept of optimal restricted designs and show that this concept naturally fits to item calibration. We prove an equivalence theorem needed to verify optimality of a design. Locally optimal restricted designs provide intervals of ability levels for optimal calibration of an item. When assuming a two-parameter logistic model, several scenarios with D-optimal restricted designs are presented for calibration of a single item and simultaneous calibration of several items. These scenarios show that the naive way to sample examinees around unrestricted design points is not optimal.

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Analysing ordinal data is becoming increasingly important in psychology, especially in the context of item response theory. The generalized partial credit model (GPCM) is probably the most widely used ordinal model and has found application in many large-scale educational assessment studies such as PISA. In the present paper, optimal test designs are investigated for estimating persons' abilities with the GPCM for calibrated tests when item parameters are known from previous studies. We find that local optimality may be achieved by assigning non-zero probability only to the first and last categories independently of a person's ability. That is, when using such a design, the GPCM reduces to the dichotomous two-parameter logistic (2PL) model. Since locally optimal designs require the true ability to be known, we consider alternative Bayesian design criteria using weight distributions over the ability parameter space. For symmetric weight distributions, we derive necessary conditions for the optimal one-point design of two response categories to be Bayes optimal. Furthermore, we discuss examples of common symmetric weight distributions and investigate under what circumstances the necessary conditions are also sufficient. Since the 2PL model is a special case of the GPCM, all of these results hold for the 2PL model as well.

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Multidimensional computerized adaptive testing (MCAT) has received increasing attention over the past few years in educational measurement. Like all other formats of CAT, item replenishment is an essential part of MCAT for its item bank maintenance and management, which governs retiring overexposed or obsolete items over time and replacing them with new ones. Moreover, calibration precision of the new items will directly affect the estimation accuracy of examinees' ability vectors. In unidimensional CAT (UCAT) and cognitive diagnostic CAT, online calibration techniques have been developed to effectively calibrate new items. However, there has been very little discussion of online calibration in MCAT in the literature. Thus, this paper proposes new online calibration methods for MCAT based upon some popular methods used in UCAT. Three representative methods, Method A, the 'one EM cycle' method and the 'multiple EM cycles' method, are generalized to MCAT. Three simulation studies were conducted to compare the three new methods by manipulating three factors (test length, item bank design, and level of correlation between coordinate dimensions). The results showed that all the new methods were able to recover the item parameters accurately, and the adaptive online calibration designs showed some improvements compared to the random design under most conditions.

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Generalized fiducial inference (GFI) has been proposed as an alternative to likelihood-based and Bayesian inference in mainstream statistics. Confidence intervals (CIs) can be constructed from a fiducial distribution on the parameter space in a fashion similar to those used with a Bayesian posterior distribution. However, no prior distribution needs to be specified, which renders GFI more suitable when no a priori information about model parameters is available. In the current paper, we apply GFI to a family of binary logistic item response theory models, which includes the two-parameter logistic (2PL), bifactor and exploratory item factor models as special cases. Asymptotic properties of the resulting fiducial distribution are discussed. Random draws from the fiducial distribution can be obtained by the proposed Markov chain Monte Carlo sampling algorithm. We investigate the finite-sample performance of our fiducial percentile CI and two commonly used Wald-type CIs associated with maximum likelihood (ML) estimation via Monte Carlo simulation. The use of GFI in high-dimensional exploratory item factor analysis was illustrated by the analysis of a set of the Eysenck Personality Questionnaire data.

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Multidimensional-Method A (M-Method A) has been proposed as an efficient and effective online calibration method for multidimensional computerized adaptive testing (MCAT) (Chen & Xin, Paper presented at the 78th Meeting of the Psychometric Society, Arnhem, The Netherlands, 2013). However, a key assumption of M-Method A is that it treats person parameter estimates as their true values, thus this method might yield erroneous item calibration when person parameter estimates contain non-ignorable measurement errors. To improve the performance of M-Method A, this paper proposes a new MCAT online calibration method, namely, the full functional MLE-M-Method A (FFMLE-M-Method A). This new method combines the full functional MLE (Jones & Jin in Psychometrika 59:59-75, 1994; Stefanski & Carroll in Annals of Statistics 13:1335-1351, 1985) with the original M-Method A in an effort to correct for the estimation error of ability vector that might otherwise adversely affect the precision of item calibration. Two correction schemes are also proposed when implementing the new method. A simulation study was conducted to show that the new method generated more accurate item parameter estimation than the original M-Method A in almost all conditions.

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For item response theory (IRT) models, which belong to the class of generalized linear or non-linear mixed models, reliability at the scale of observed scores (i.e., manifest correlation) is more difficult to calculate than latent correlation based reliability, but usually of greater scientific interest. This is not least because it cannot be calculated explicitly when the logit link is used in conjunction with normal random effects. As such, approximations such as Fisher's information coefficient, Cronbach's α, or the latent correlation are calculated, allegedly because it is easy to do so. Cronbach's α has well-known and serious drawbacks, Fisher's information is not meaningful under certain circumstances, and there is an important but often overlooked difference between latent and manifest correlations. Here, manifest correlation refers to correlation between observed scores, while latent correlation refers to correlation between scores at the latent (e.g., logit or probit) scale. Thus, using one in place of the other can lead to erroneous conclusions. Taylor series based reliability measures, which are based on manifest correlation functions, are derived and a careful comparison of reliability measures based on latent correlations, Fisher's information, and exact reliability is carried out. The latent correlations are virtually always considerably higher than their manifest counterparts, Fisher's information measure shows no coherent behaviour (it is even negative in some cases), while the newly introduced Taylor series based approximations reflect the exact reliability very closely. Comparisons among the various types of correlations, for various IRT models, are made using algebraic expressions, Monte Carlo simulations, and data analysis. Given the light computational burden and the performance of Taylor series based reliability measures, their use is recommended.

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