Generalized full-information item bifactor analysis.

Full-information item bifactor analysis is an important statistical method in psychological and educational measurement. Current methods are limited to single-group analysis and inflexible in the types of item response models supported. We propose a flexible multiple-group item bifactor analysis framework that supports a variety of multidimensional item response theory models for an arbitrary mixing of dichotomous, ordinal, and nominal items. The extended item bifactor model also enables the estimation of latent variable means and variances when data from more than 1 group are present. Generalized user-defined parameter restrictions are permitted within or across groups. We derive an efficient full-information maximum marginal likelihood estimator. Our estimation method achieves substantial computational savings by extending Gibbons and Hedeker's (1992) bifactor dimension reduction method so that the optimization of the marginal log-likelihood requires only 2-dimensional integration regardless of the dimensionality of the latent variables. We use simulation studies to demonstrate the flexibility and accuracy of the proposed methods. We apply the model to study cross-country differences, including differential item functioning, using data from a large international education survey on mathematics literacy. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Cognitive psychology meets psychometric theory: On the relation between process models for decision making and latent variable models for individual differences.

This article analyzes latent variable models from a cognitive psychology perspective. We start by discussing work by Tuerlinckx and De Boeck (2005), who proved that a diffusion model for 2-choice response processes entails a 2-parameter logistic item response theory (IRT) model for individual differences in the response data. Following this line of reasoning, we discuss the appropriateness of IRT for measuring abilities and bipolar traits, such as pro versus contra attitudes. Surprisingly, if a diffusion model underlies the response processes, IRT models are appropriate for bipolar traits but not for ability tests. A reconsideration of the concept of ability that is appropriate for such situations leads to a new item response model for accuracy and speed based on the idea that ability has a natural zero point. The model implies fundamentally new ways to think about guessing, response speed, and person fit in IRT. We discuss the relation between this model and existing models as well as implications for psychology and psychometrics. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Using item response theory to study the convergent and discriminant validity of three questionnaires measuring cigarette dependence.

To determine whether the Cigarette Dependence Scale, the Fagerstr?m Test for Nicotine Dependence, and the Nicotine Dependence Syndrome Scale (NDSS) reliably and correctly assessed both weakly and severely dependent individuals, the authors collected data via Internet from 2,435 current smokers, from 2004 to 2007. They used a 2-parameter item response model to determine the difficulty and discrimination of each question and used correlations between latent scores to assess convergent and discriminant validity. The reliability of all scales was close to or exceeded .70. Both the Cigarette Dependence Scale and the Fagerstr?m Test for Nicotine Dependence had 1 misfitting item. Each NDSS scale had at least 2 misfitting items. The information curve of each of the questionnaires peaked between -2 and 2 and was low at both extremes. All questionnaires had adequate reliability and were more informative for a medium level of the underlying cigarette dependence continuum than for both extremes of this continuum. The correlations between latent scores indicated good convergent validity between questionnaires and low discriminant validity between NDSS subscales, except for Tolerance. This result suggests that nicotine dependence may not be composed of 5 dimensions but may be unidimensional and distinct from reduced sensitivity to the effects of smoking (Tolerance). (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How Do Respondents Construe Ambiguous Response Formats of Affect Items?

Ambiguous response formats predict correlations from -.467 to -1 between opposite items, depending on whether the respondent's interpretation of the format is unipolar or bipolar. The authors present a procedure to investigate the proper interpretation in each case. It consists of applying nonparametric and parametric item response theory models (the Mokken and the graded response models) to pairs of opposite items in order to find the locations of the response options along the latent scale and, therefore, identify the response format construction. The authors tested this procedure on 4 samples (Ns=142-1,150) and 2 item pairs ("relaxed"-"tense" and "optimistic"-"pessimistic"). The results revealed that respondents constructed the formats as bipolar and supported the bipolarity of the item pairs. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

How many IRT parameters does it take to model psychopathology items?

The authors compared the fit of the 2- and 3-parameter logistic models (2PLM; 3PLM) on 15 unidimensional factor scales derived from the Minnesota Multiphasic Personality Inventory--Adolescent item pool. Log-likelihood chi-square deviance tests indicated that a 3PLM provided an improved fit. However, residual statistics Indicated that the difference in fit between the 2 models was negligible. An unexpected finding was that from 10% to 30% of the items had substantial lower asymptote parameters (c ≥ .10) when the scales were scored in the pathology or nonpathology directions. The authors argue that the large lower asymptote parameters are attributable to item-content ambiguity possibly caused by item-level multidimensionality. These findings suggest that the direction of scoring can critically affect an item response theory analysis. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Ramsay-curve item response theory (RC-IRT) to detect and correct for nonnormal latent variables.

Popular methods for fitting unidimensional item response theory (IRT) models to data assume that the latent variable is normally distributed in the population of respondents, but this can be unreasonable for some variables. Ramsay-curve IRT (RC-IRT) was developed to detect and correct for this nonnormality. The primary aims of this article are to introduce RC-IRT less technically than it has been described elsewhere; to evaluate RC-IRT for ordinal data via simulation, including new approaches for model selection; and to illustrate RC-IRT with empirical examples. The empirical examples demonstrate the utility of RC-IRT for real data, and the simulation study indicates that when the latent distribution is skewed, RC-IRT results can be more accurate than those based on the normal model. Along with a plot of candidate curves, the Hannan-Quinn criterion is recommended for model selection. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Bifactor and item response theory analyses of interviewer report scales of cognitive impairment in schizophrenia.

A psychometric analysis of 2 interview-based measures of cognitive deficits was conducted: the 21-item Clinical Global Impression of Cognition in Schizophrenia (CGI-CogS; Ventura et al., 2008), and the 20-item Schizophrenia Cognition Rating Scale (SCoRS; Keefe et al., 2006), which were administered on 2 occasions to a sample of people with schizophrenia. Traditional psychometrics, bifactor analysis, and item response theory methods were used to explore item functioning and dimensionality and to compare instruments. Despite containing similar item content, responses to the CGI-CogS demonstrated superior psychometric properties (e.g., higher item intercorrelations, better spread of ratings across response categories) relative to the SCoRS. The authors argue that these differences arise mainly from the differential use of prompts and how the items are phrased and scored. Bifactor analysis demonstrated that although both measures capture a broad range of cognitive functioning (e.g., working memory, social cognition), the common variance on each is overwhelmingly explained by a single general factor. Item response theory analyses of the combined pool of 41 items showed that measurement precision is peaked in the mild to moderate range of cognitive impairment. Finally, simulated adaptive testing revealed that only about 10 to 12 items are necessary to achieve latent trait level estimates with reasonably small standard errors for most individuals. This suggests that these interview-based measures of cognitive deficits could be shortened without loss of measurement precision. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

A nonlinear mixed model framework for item response theory.

Mixed models take the dependency between observations based on the same cluster into account by introducing 1 or more random effects. Common item response theory (IRT) models introduce latent person variables to model the dependence between responses of the same participant. Assuming a distribution for the latent variables, these IRT models are formally equivalent with nonlinear mixed models. It is shown how a variety of IRT models can be formulated as particular instances of nonlinear mixed models. The unifying framework offers the advantage that relations between different IRT models become explicit and that it is rather straightforward to see how existing IRT models can be adapted and extended. The approach is illustrated with a self-report study on anger. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Development and Validation of a Rasch-Derived CES-D Short Form.

The current study presents a Rasch-derived short form of the Center for Epidemiologic Studies-Depression scale (CES-D) for use as a depression screening tool in the general population. In contrast to short forms developed with reliance on classical measurement techniques, those developed using techniques based on item response theory produce a measure that offers true interval scaling, provide enhanced information about responders with extreme scores, and expand understanding of the underlying latent structure. Cross-validation of the Rasch-derived CES-D short form supported its utility and structural validity across samples. Tests of structural validity using latent variable modeling methodology indicated that a hierarchical, single-factor model of depression had the best fit for the original full form and the Rasch-derived short form of the CES-D. This finding challenges depression researchers and theorists to reconsider the interfactor relationships in the study and assessment of depression. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

A parametric model for local dependence among test items.

A framework is presented to model instances of local dependence between items within the context of unidimensional item response theory (IRT). A distinction is made between item main effects and item interactions. Four types of models for interdependent items are considered, on the basis of the distinction between order dependency and combination dependency on the one hand, and dimension-dependent versus constant interaction on the other hand. For each of the 4 model types, variants of the 1-parameter logistic model can be formulated as well as variants of the 2-parameter logistic model. A number of existing IRT models for polytomous items that are variants of the partial credit model may be reconsidered in these terms. Two examples are given to demonstrate the approach. (PsycINFO Database Record (c) 2011 APA, all rights reserved)     

Psychometric properties of the MMPI-2-RF Somatic Complaints (RC1) Scale.

The MMPI-2 Restructured Form (MMPI-2-RF; Tellegen & Ben-Porath, 2008) was designed to be psychometrically superior to its MMPI-2 counterpart. However, the test has yet to be extensively evaluated in diverse clinical settings. The purpose of this study was to examine the psychometric properties of the MMPI-2-RF Somatic Complaints (RC1) scale in a clinically relevant population. Participants were 399 patients diagnosed with either epilepsy or psychogenic nonepileptic seizures on the basis of video–electroencephalograph monitoring. The internal structure of the MMPI-2-RF was evaluated using taxometric, confirmatory factor analysis, and item response theory procedures. Data from 4 content-specific scales directly related to RC1 (Malaise, Gastrointestinal Complaints, Head Pain Complaints, and Neurological Complaints) indicated that the latent construct of somatization is a dimensional variable with a bifactor structure. However, consistent with the scale's construction, a unidimensional model also provided adequate fit. A 2-parameter logistic item response theory model better accounted for observed item responses than did 1- or 3-parameter models. Results suggest that the RC1 scale is most precise for T score estimates between 55 and 90. Overall, the scale appears to be well suited for the assessment of somatization. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Item response theory analysis of diagnostic criteria for alcohol and cannabis use disorders in adolescents: Implications for DSM-V.

Item response theory (IRT) has advantages over classical test theory in evaluating diagnostic criteria. In this study, the authors used IRT to characterize the psychometric properties of Diagnostic and Statistical Manual of Mental Disorders, 4th edition (DSM-IV; American Psychiatric Association, 1994) alcohol and cannabis use disorder symptoms among 472 clinical adolescents. For both substances, DSM-IV symptoms fit a model specifying a unidimensional latent trait of problem severity. Threshold (severity) parameters did not distinguish abuse and dependence symptoms. Abuse symptoms of legal problems and hazardous use, and dependence symptoms of tolerance, unsuccessful attempts to quit, and physical-psychological problems, showed relatively poor discrimination of problem severity. There were gender differences in thresholds for hazardous use, legal problems, and physical-psychological problems. The results illustrate limitations of DSM-IV criteria for alcohol and cannabis use disorders when applied to adolescents. The development process for the fifth edition (DSM-V) should be informed by statistical models such as those used in this study. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Effects of estimation methods on making trait-level inferences from ordered categorical items for assessing psychopathology.

In assessments of attitudes, personality, and psychopathology, unidimensional scale scores are commonly obtained from Likert scale items to make inferences about individuals' trait levels. This study approached the issue of how best to combine Likert scale items to estimate test scores from the practitioner's perspective: Does it really matter which method is used to estimate a trait? Analyses of 3 data sets indicated that commonly used methods could be classified into 2 groups: methods that explicitly take account of the ordered categorical item distributions (i.e., partial credit and graded response models of item response theory, factor analysis using an asymptotically distribution-free estimator) and methods that do not distinguish Likert-type items from continuously distributed items (i.e., total score, principal component analysis, maximum-likelihood factor analysis). Differences in trait estimates were found to be trivial within each group. Yet the results suggested that inferences about individuals' trait levels differ considerably between the 2 groups. One should therefore choose a method that explicitly takes account of item distributions in estimating unidimensional traits from ordered categorical response formats. Consequences of violating distributional assumptions were discussed. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The measurement of consistency and occasion specificity with latent class models: A new model and its application to the measurement of affect.

After a short overview of different latent variable models for analyzing interindividual differences in intraindividual change, a latent class variability model is introduced. The model makes it possible to estimate the consistency of interindividual differences across naturally occurring situations. In addition, the contribution of latent trait variables and occasion-specific latent variables in predicting manifest responses can be analyzed, and the precision of predicting states by traits and occasion-specific effects can be assessed. The model is illustrated by an application to the measurement of positive affects. Finally, the model and its application are discussed with respect to conditional trait concepts in personality psychology and other potential areas of application. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Measurement equivalence: A comparison of methods based on confirmatory factor analysis and item response theory.

Current interest in the assessment of measurement equivalence emphasizes 2 major methods of analysis. The authors offer a comparison of a linear method (confirmatory factor analysis) and a nonlinear method (differential item and test functioning using item response theory) with an emphasis on their methodological similarities and differences. The 2 approaches test for the equality of true scores (or expected raw scores) across 2 populations when the latent (or factor) score is held constant. Both approaches can provide information about when measurrment nonequivalence exists and the extent to which it is a problem. An empirical example is used to illustrate the 2 approaches. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

The effect of ignoring item interactions on the estimated discrimination parameters in item response theory.

Most item response theory models assume conditional independence, and it is known that interactions between items affect the estimated item discrimination. In this article, this effect is further investigated from a theoretical perspective and by means of simulation studies. To this end, a parametric model for item interactions is introduced. Next, it is shown that ignoring a positive interaction results in an overestimation of the discrimination parameter in the two-parameter logistic model (2PLM), whereas ignoring a negative interaction leads to an underestimation of the parameter. Furthermore, it is demonstrated that in some cases the item characteristic curves of the 2PLM and of an item involved in an interaction are quite similar, indicating that the 2PLM can provide a good fit to data with interactions. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Confirmatory factor analysis of items with a dichotomous response format using the multidimensional Rasch model.

Two models that can be used for exploratory factor analysis of items with a dichotomous response format are discussed: threshold models and multidimensional item response models. The models arise from different traditions: The threshold model is rooted in the factor analytic tradition, the multidimensional item response model had its foundation in item response theory. Despite the different origins, it can be proved that both models are the same. Subsequently, the generalized multidimensional Rasch model is introduced. This model can be used for confirmatory factor analysis of items with a dichotomous response format. Stated otherwise, it is the confirmatory counterpart of the (exploratory) threshold and multidimensional item response models. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Modeling life-span growth curves of cognition using longitudinal data with multiple samples and changing scales of measurement.

The authors use multiple-sample longitudinal data from different test batteries to examine propositions about changes in constructs over the life span. The data come from 3 classic studies on intellectual abilities in which, in combination, 441 persons were repeatedly measured as many as 16 times over 70 years. They measured cognitive constructs of vocabulary and memory using 8 age-appropriate intelligence test batteries and explore possible linkage of these scales using item response theory (IRT). They simultaneously estimated the parameters of both IRT and latent curve models based on a joint model likelihood approach (i.e., NLMIXED and WINBUGS). They included group differences in the model to examine potential interindividual differences in levels and change. The resulting longitudinal invariant Rasch test analyses lead to a few new methodological suggestions for dealing with repeated constructs based on changing measurements in developmental studies. (PsycINFO Database Record (c) 2010 APA, all rights reserved)