The unique correspondence of the item response function and item category response functions in polytomously scored item response models

The item response function (IRF) for a polytomously scored item is defined as a weighted sum of the item category response functions (ICRF, the probability of getting a particular score for a randomly sampled examinee of ability ). This paper establishes the correspondence between an IRF and a unique set of ICRFs for two of the most commonly used polytomous IRT models (the partial credit models and the graded response model). Specifically, a proof of the following assertion is provided for these models: If two items have the same IRF, then they must have the same number of categories; moreover, they must consist of the same ICRFs. As a corollary, for the Rasch dichotomous model, if two tests have the same test characteristic function (TCF), then they must have the same number of items. Moreover, for each item in one of the tests, an item in the other test with an identical IRF must exist. Theoretical as well as practical implications of these results are discussed.This research was supported by Educational Testing Service Allocation Projects No. 79409 and No. 79413. The authors wish to thank John Donoghue, Ming-Mei Wang, Rebecca Zwick, and Zhiliang Ying for their useful comments and discussions. The authors also wish to thank three anonymous reviewers for their comments.     

Component analysis in cross-sectional and longitudinal data

An extension of component analysis to longitudinal or cross-sectional data is presented. In this method, components are derived under the restriction of invariant and/or stationary compositing weights. Optimal compositing weights are found numerically. The method can be generalized to allow differential weighting of the observed variables in deriving the component solution. Some choices of weightings are discussed. An illustration of the method using real data is presented.Preparation of this article was supported in part by PSC-CUNY Grant #665365 to Roger E. Millsap and by National Institute of Aging Grant NIA-AG03164-03 to William Meredith. The authors thank John Nesselroade for permitting the use of the data presented in the article.     

A new estimator of the uniqueness in factor analysis

A closed form estimator of the uniqueness (unique variance) in factor analysis is proposed. It has analytically desirable properties—consistency, asymptotic normality and scale invariance. The estimation procedure is given through the application to the two sets of Emmett's data and Holzinger and Swineford's data. The new estimator is shown to lead to values rather close to the maximum likelihood estimator.     

The effects of interval duration on temporal tracking and alternation learning

On cyclic-interval reinforcement schedules, animals typically show a postreinforcement pause that is a function of the immediately preceding time interval (temporal tracking). Animals, however, do not track single-alternation schedules-when two different intervals are presented in strict alternation on successive trials. In this experiment, pigeons were first trained with a cyclic schedule consisting of alternating blocks of 12 short intervals (5 s or 30 s) and 12 long intervals (180 s), followed by three different single-alternation interval schedules: (a) 30 s and 180 s, (b) 5 s and 180 s, and (c) 5 s and 30 s. Pigeons tracked both schedules with alternating blocks of 12 intervals. With the single-alternation schedules, when the short interval duration was 5 s, regardless of the duration of the longer interval, pigeons learned the alternation pattern, and their pause anticipated the upcoming interval. When the shorter interval was 30 s, even when the ratio of short to long intervals was kept at 6:1, pigeons did not initially show anticipatory pausing-a violation of the principle of timescale invariance.     

Measuring sport fantasy proneness and deflated reality in sport and performance: Development and validation of two context-specific instruments

Fantasy-prone personalities and generalized states of pessimism and hopelessness have been linked to various behavioural, cognitive, and health related outcomes in the general population. Nevertheless, to date, knowledge of sport-specific fantasy proneness and athletes’ perception of deflated reality in sport is scarce, possibly due to a lack of appropriate psychometric instruments to examine these two important context-specific constructs. In this research, we developed the Sport Fantasy Proneness Scale (SFPS) and the Deflated Reality in Sport Scale (DRSS), first assessing the content validity of items for the instruments following a rigorous process. Through two cross-sectional samples (Study 1: Sample 1 N = 255, Sample 2 N = 260) and one longitudinal sample (Study 2: Sample 3 N = 118) of competitive athletes in the UK, we then examined factorial, convergent, discriminant, and concurrent validity and measurement invariance (Study 1), as well as internal consistency, and test-retest reliability (Study 2) of the two new scales. Results revealed robust construct validity and reliability of scores on the two instruments and suggested very good invariance when implementing the new scales to athletes from different sports and competitive levels and good invariance for cross-gender comparisons. The new scales fill a gap in the sport psychology literature and provide researchers and practitioners with robust psychometric instruments to examine new research questions and tackle issues relevant to athletes’ sport-specific fantasy proneness and perceptions of deflated reality.     

National glorification and attachment differentially predict support for intergroup conflict resolution: Scrutinizing cross-country generalizability

Research on national identity distinguishes between national glorification and attachment. We tested whether glorification and attachment differentially predicted support for military and diplomatic conflict resolution strategies (CRS) in response to international conflicts. Using data collected in seven countries (Australia, United States, United Kingdom, France, Germany, Israel, China; total N = 1784), we investigated whether glorification and attachment can be equivalently measured (using tests of measurement invariance) and whether their relationships with CRS were generalizable across countries. The results revealed metric, but not scalar, measurement invariance of the two-factor structure of national identification across six countries, excluding China. Among these six countries, glorification predicted more support for military CRS, whereas attachment predicted more support for diplomatic CRS. Our study is novel in scrutinizing the cross-cultural generalizability of the bi-dimensional model of national identification. Implications for studying national identification and intergroup conflict cross-culturally are discussed.     

The perceived vulnerability to disease scale: Cross-cultural measurement invariance and associations with fear of COVID-19 across 16 countries

Using cross-sectional data from N = 4274 young adults across 16 countries during the COVID-19 pandemic, we examined the cross-cultural measurement invariance of the perceived vulnerability to disease (PVD) scale and tested the hypothesis that the association between PVD and fear of COVID-19 is stronger under high disease threat [that is, absence of COVID-19 vaccination, living in a country with lower Human Development Index (HDI) or higher COVID-19 mortality]. Results supported a bi-factor Exploratory Structural Equation Modeling model where items loaded on a global PVD factor, and on the sub-factors of Perceived Infectability and Germ Aversion. However, cross-national invariance could only be obtained on the configural level with a reduced version of the PVD scale (PVD-r), suggesting that the concept of PVD may vary across nations. Moreover, higher PVD-r was consistently associated with greater fear of COVID-19 across all levels of disease threat, but this association was especially pronounced among individuals with a COVID-19 vaccine, and in contexts where COVID-19 mortality was high. The present research brought clarity into the dimensionality of the PVD measure, discussed its suitability and limitations for cross-cultural research, and highlighted the pandemic-related conditions under which higher PVD is most likely to go along with psychologically maladaptive outcomes, such as fear of COVID-19.     

A scale-invariant treatment for recursive path models

A reparameterization is formulated that yields estimates of scale-invariant parameters in recursive path models with latent variables, and (asymptotically) correct standard errors, without the use of constrained optimization. The method is based on the logical structure of the reticular action model.     

The Five Factor Model in personnel selection: Measurement equivalence between applicant and non-applicant groups

This study investigates the measurement equivalence of a Five Factor measure of personality between applicant and non-applicant samples. The Big Five Questionnaire-2 was administered in two samples: A group of volunteers (n = 903), who completed the test for research purposes, and a group applying for jobs, who completed the test during hiring procedures (n = 401). Multiple-group confirmatory factor analysis on item composites was conducted to test for the equivalence of factor covariance and mean structures of twenty facets of the Five Factors. Item-level analyses were carried out through analysis of variance to further examine the issue of measurement invariance. Findings suggested that personality facets have the same measurement unit across applicants and non-applicants, while a lack of equivalence was found in the origin of the scales. Similar results were found at the item-level. Implications for personality assessment are advanced and discussed.