In standard item response theory (IRT) applications, the latent variable is typically assumed to be normally distributed. If the normality assumption is violated, the item parameter estimates can become biased. Summed score likelihood-based statistics may be useful for testing latent variable distribution fit. We develop Satorra-Bentler type moment adjustments to approximate the test statistics' tail-area probability. A simulation study was conducted to examine the calibration and power of the unadjusted and adjusted statistics in various simulation conditions. Results show that the proposed indices have tail-area probabilities that can be closely approximated by central chi-squared random variables under the null hypothesis. Furthermore, the test statistics are focused. They are powerful for detecting latent variable distributional assumption violations, and not sensitive (correctly) to other forms of model misspecification such as multidimensionality. As a comparison, the goodness-of-fit statistic M-2 has considerably lower power against latent variable nonnormality than the proposed indices. Empirical data from a patient-reported health outcomes study are used as illustration.

Despite the growing popularity of diagnostic classification models (e.g., Rupp et al., 2010, Diagnostic measurement: theory, methods, and applications, Guilford Press, New York, NY) in educational and psychological measurement, methods for testing their absolute goodness of fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full-information test statistics such as Pearson's X2 and the likelihood ratio statistic G2 suffer from sparseness in the underlying contingency table from which they are computed. Recently, limited-information fit statistics such as Maydeu-Olivares and Joe's (2006, Psychometrika, 71, 713) M2 have been found to be quite useful in testing the overall goodness of fit of item response theory models. In this study, we applied Maydeu-Olivares and Joe's (2006, Psychometrika, 71, 713) M2 statistic to diagnostic classification models. Through a series of simulation studies, we found that M2 is well calibrated across a wide range of diagnostic model structures and was sensitive to certain misspecifications of the item model (e.g., fitting disjunctive models to data generated according to a conjunctive model), errors in the Q-matrix (adding or omitting paths, omitting a latent variable), and violations of local item independence due to unmodelled testlet effects. On the other hand, M2 was largely insensitive to misspecifications in the distribution of higher-order latent dimensions and to the specification of an extraneous attribute. To complement the analyses of the overall model goodness of fit using M2 , we investigated the utility of the Chen and Thissen (1997, J. Educ. Behav. Stat., 22, 265) local dependence statistic XLD2 for characterizing sources of misfit, an important aspect of model appraisal often overlooked in favour of overall statements. The XLD2 statistic was found to be slightly conservative (with Type I error rates consistently below the nominal level) but still useful in pinpointing the sources of misfit. Patterns of local dependence arising due to specific model misspecifications are illustrated. Finally, we used the M2 and XLD2 statistics to evaluate a diagnostic model fit to data from the Trends in Mathematics and Science Study, drawing upon analyses previously conducted by Lee et al., (2011, IJT, 11, 144).

Despite the growing popularity of diagnostic classification models (e.g., Rupp et al ., 2010, Diagnostic measurement: theory, methods, and applications , Guilford Press, New York, NY) in educational and psychological measurement, methods for testing their absolute goodness of fit to real data remain relatively underdeveloped. For tests of reasonable length and for realistic sample size, full-information test statistics such as Pearson's X 2 and the likelihood ratio statistic G 2 suffer from sparseness in the underlying contingency table from which they are computed. Recently, limited-information fit statistics such as Maydeu-Olivares and Joe's (2006, Psychometrika , 71, 713) M 2 have been found to be quite useful in testing the overall goodness of fit of item response theory models. In this study, we applied Maydeu-Olivares and Joe's (2006, Psychometrika , 71, 713) M 2 statistic to diagnostic classification models. Through a series of simulation studies, we found that M 2 is well calibrated across a wide range of diagnostic model structures and was sensitive to certain misspecifications of the item model (e.g., fitting disjunctive models to data generated according to a conjunctive model), errors in the Q-matrix (adding or omitting paths, omitting a latent variable), and violations of local item independence due to unmodelled testlet effects. On the other hand, M 2 was largely insensitive to misspecifications in the distribution of higher-order latent dimensions and to the specification of an extraneous attribute. To complement the analyses of the overall model goodness of fit using M 2 , we investigated the utility of the Chen and Thissen (1997, J. Educ. Behav. Stat ., 22, 265) local dependence statistic for characterizing sources of misfit, an important aspect of model appraisal often overlooked in favour of overall statements. The statistic was found to be slightly conservative (with Type I error rates consistently below the nominal level) but still useful in pinpointing the sources of misfit. Patterns of local dependence arising due to specific model misspecifications are illustrated. Finally, we used the M 2 and statistics to evaluate a diagnostic model fit to data from the Trends in Mathematics and Science Study, drawing upon analyses previously conducted by Lee et al., (2011, IJT , 11, 144).

INTRODUCTIONThe positive emotional and sensory expectancies of cigarette smoking include improved cognitive abilities, positive affective states, and pleasurable sensorimotor sensations. This paper describes development of Positive Emotional and Sensory Expectancies of Smoking item banks that will serve to standardize the assessment of this construct among daily and nondaily cigarette smokers.METHODSData came from daily (N = 4,201) and nondaily (N =1,183) smokers who completed an online survey. To identify a unidimensional set of items, we conducted item factor analyses, item response theory analyses, and differential item functioning analyses. Additionally, we evaluated the performance of fixed-item short forms (SFs) and computer adaptive tests (CATs) to efficiently assess the construct.RESULTSEighteen items were included in the item banks (15 common across daily and nondaily smokers, 1 unique to daily, 2 unique to nondaily). The item banks are strongly unidimensional, highly reliable (reliability = 0.95 for both), and perform similarly across gender, age, and race/ethnicity groups. A SF common to daily and nondaily smokers consists of 6 items (reliability = 0.86). Results from simulated CATs indicated that, on average, less than 8 items are needed to assess the construct with adequate precision using the item banks.CONCLUSIONSThese analyses identified a new set of items that can assess the positive emotional and sensory expectancies of smoking in a reliable and standardized manner. Considerable efficiency in assessing this construct can be achieved by using the item bank SF, employing computer adaptive tests, or selecting subsets of items tailored to specific research or clinical purposes.

The PROMIS Smoking Initiative developed an assessment toolkit that enables the measurement of current adult smokers' standing in domains of importance to smoking research, including nicotine dependence and using smoking to cope with stress.

INTRODUCTION:Smokers' health-related outcome expectancies are associated with a number of important constructs in smoking research, yet there are no measures currently available that focus exclusively on this domain. This paper describes the development and evaluation of item banks for assessing the health expectancies of smoking. METHODS:Using data from a sample of daily (N = 4,201) and nondaily (N = 1,183) smokers, we conducted a series of item factor analyses, item response theory analyses, and differential item functioning analyses (according to gender, age, and race/ethnicity) to arrive at a unidimensional set of health expectancies items for daily and nondaily smokers. We also evaluated the performance of short forms (SFs) and computer adaptive tests (CATs) to efficiently assess health expectancies. RESULTS:A total of 24 items were included in the Health Expectancies item banks; 13 items are common across daily and nondaily smokers, 6 are unique to daily, and 5 are unique to nondaily. For both daily and nondaily smokers, the Health Expectancies item banks are unidimensional, reliable (reliability = 0.95 and 0.96, respectively), and perform similarly across gender, age, and race/ethnicity groups. A SF common to daily and nondaily smokers consists of 6 items (reliability = 0.87). Results from simulated CATs showed that health expectancies can be assessed with good precision with an average of 5-6 items adaptively selected from the item banks. CONCLUSIONS:Health expectancies of smoking can be assessed on the basis of these item banks via SFs, CATs, or through a tailored set of items selected for a specific research purpose.