Social scientists are frequently interested in identifying latent subgroups within the population, based on a set of observed variables. One of the more common tools for this purpose is latent class analysis (LCA), which models a scenario involving k finite and mutually exclusive classes within the population. An alternative approach to this problem is presented by the grade of membership (GoM) model, in which individuals are assumed to have partial membership in multiple population subgroups. In this respect, it differs from the hard groupings associated with LCA. The current Monte Carlo simulation study extended on prior work on the GoM by investigating its ability to recover underlying subgroups in the population for a variety of sample sizes, latent group size ratios, and differing group response profiles. In addition, this study compared the performance of GoM with that of LCA. Results demonstrated that when the underlying process conforms to the GoM model form, the GoM approach yielded more accurate classification results than did LCA. In addition, it was found that the GoM modeling paradigm yielded accurate results for samples as small as 200, even when latent subgroups were very unequal in size. Implications for practice were discussed.S – χ 2 is a popular item fit index that is available in commercial software packages such as flexMIRT. However, no research has systematically examined the performance of S – χ 2 for detecting item misfit within the context of the multidimensional graded response model (MGRM). The primary goal of this study was to evaluate the performance of S – χ 2 under two practical misfit scenarios first, all items are misfitting due to model misspecification, and second, a small subset of items violate the underlying assumptions of the MGRM. Simulation studies showed that caution should be exercised when reporting item fit results of polytomous items using S – χ 2 within the context of the MGRM, because of its inflated false positive rates (FPRs), especially with a small sample size and a long test. S – χ 2 performed well when detecting overall model misfit as well as item misfit for a small subset of items when the ordinality assumption was violated. However, under a number of conditions of model misspecification or items violating the homogeneous discrimination assumption, even though true positive rates (TPRs) of S – χ 2 were high when a small sample size was coupled with a long test, the inflated FPRs were generally directly related to increasing TPRs. There was also a suggestion that performance of S – χ 2 was affected by the magnitude of misfit within an item. There was no evidence that FPRs for fitting items were exacerbated by the presence of a small percentage of misfitting items among them.A number of psychometricians have suggested that parallel analysis (PA) tends to yield more accurate results in determining the number of factors in comparison with other statistical methods. Nevertheless, all too often PA can suggest an incorrect number of factors, particularly in statistically unfavorable conditions (e.g., small sample sizes and low factor loadings). Because of this, researchers have recommended using multiple methods to make judgments about the number of factors to extract. Implicit in this recommendation is that, when the number of factors is chosen based on PA, uncertainty nevertheless exists. We propose a Bayesian parallel analysis (B-PA) method to incorporate the uncertainty with decisions about the number of factors. B-PA yields a probability distribution for the various possible numbers of factors. 2-Aminoethyl manufacturer We implement and compare B-PA with a frequentist approach, revised parallel analysis (R-PA), in the contexts of real and simulated data. Results show that B-PA provides relevant information regarding the uncertainty in determining the number of factors, particularly under conditions with small sample sizes, low factor loadings, and less distinguishable factors. Even if the indicated number of factors with the highest probability is incorrect, B-PA can show a sizable probability of retaining the correct number of factors. Interestingly, when the mode of the distribution of the probabilities associated with different numbers of factors was treated as the number of factors to retain, B-PA was somewhat more accurate than R-PA in a majority of the conditions.Many approaches have been proposed to jointly analyze item responses and response times to understand behavioral differences between normally and aberrantly behaved test-takers. Biometric information, such as data from eye trackers, can be used to better identify these deviant testing behaviors in addition to more conventional data types. Given this context, this study demonstrates the application of a new method for multiple-group analysis that concurrently models item responses, response times, and visual fixation counts collected from an eye-tracker. It is hypothesized that differences in behavioral patterns between normally behaved test-takers and those who have different levels of preknowledge about the test items will manifest in latent characteristics of the different data types. A Bayesian estimation scheme is used to fit the proposed model to experimental data and the results are discussed.Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the ubiquity of correlated residuals and imperfect model specification. Our research focuses on a scale evaluation context and the performance of four standard model fit indices root mean square error of approximate (RMSEA), standardized root mean square residual (SRMR), comparative fit index (CFI), and Tucker-Lewis index (TLI), and two equivalence test-based model fit indices RMSEAt and CFIt. We use Monte Carlo simulation to generate and analyze data based on a substantive example using the positive and negative affective schedule (N = 1,000). We systematically vary the number and magnitude of correlated residuals as well as nonspecific misspecification, to evaluate the impact on model fit indices in fitting a two-factor exploratory factor analysis.