A general structural equation model with dichotomous,ordered categorical,and continuous latent variable indicators

A structural equation model is proposed with a generalized measurement part, allowing for dichotomous and ordered categorical variables (indicators) in addition to continuous ones. A computationally feasible three-stage estimator is proposed for any combination of observed variable types. This approach provides large-sample chi-square tests of fit and standard errors of estimates for situations not previously covered. Two multiple-indicator modeling examples are given. One is a simultaneous analysis of two groups with a structural equation model underlying skewed Likert variables. The second is a longitudinal model with a structural model for multivariate probit regressions.This research was supported by Grant No. 81-IJ-CX-0015 from the National Institute of Justice, by Grant No. DA 01070 from the U.S. Public Health Service, and by Grant No. SES-8312583 from the National Science Foundation. I thank Julie Honig for drawing the figures. Requests for reprints should be sent to Bengt Muthén, Graduate School of Education, University of California, Los Angeles, California 90024.     

The associations of cultural worldviews,political orientation,and trust with COVID-19 risk beliefs in the U.S.

Given that risk beliefs predict engagement in behaviors to prevent disease, it is important to understand the factors associated with risk beliefs. In the present paper, we conducted path analyses to investigate the associations of belief systems (political orientation and cultural worldviews of individualism and hierarchy) with COVID-19 risk beliefs (i.e., perceived likelihood, perceived severity, and worry about disease; Studies 1 and 2), and the indirect effect through trust in information sources in these relationships (Study 1). Two online panels of U.S. adults were surveyed at three timepoints during the COVID-19 pandemic (Study 1: baseline n = 1,667, 1-year follow-up n = 551; Study 2: n = 404). Results of path analyses indicated that, across studies and timepoints, when controlling for political orientation, trust, and demographic factors, greater individualism had consistent significant direct effects on lower perceived severity and worry about COVID-19, whereas greater hierarchy had consistent significant direct effects on lower perceived severity. However, after accounting for cultural worldviews of individualism and hierarchy (and trust and demographic factors), none of the associations among political orientation and any of the three COVID-19 risk beliefs were significant. The test of indirect effects indicated that individualism and hierarchy were indirectly associated with lower perceived severity of and worry about COVID-19 through less trust. The findings suggest that cultural worldviews of individualism and hierarchy play a role in shaping people's risk beliefs.     

Behavioral extremity moderates the association between certainty in attitudes about COVID and willingness to engage in mitigation-related behaviors

People generally intend to act more on beliefs and attitudes about which they have greater certainty. However, we introduce a boundary condition to the positive association between certainty and behavioral intentions—behavioral extremity. Uncertainty about a threatening issue like COVID-19 can be disconcerting, and we propose that uncertain people cope in part through increased openness to extreme actions like accepting risky medical treatments and aggression toward those defying mitigation policies. Testing this, we compiled and analyzed all the data on certainty about COVID-19 mitigation policies and willingness to engage in mitigation-related behaviors that our lab collected during the pandemic (6 samples, 20 behaviors, Ns up to 1496). External ratings of the behaviors' extremity moderated certainty-willingness associations: whereas greater certainty was associated with increased willingness to engage in moderate behaviors (the typical result), lower certainty was associated with increased willingness to engage in extreme behaviors, especially among those worried about becoming ill.     

Internal consistency and reliability of alternate short forms of the college women's assertion sample: Clinical and research implications

Assertive behavior is most often assessed with self-report or role-play measures. The latter modality is preferred because it provides for the sampling of the structure of behavior and for the consideration of the situational context. MacDonald (1978) has developed such an assessment device but it is limited by the length of time for administration and scoring. Two studies were conducted to reconstruct reliable alternate short forms. The first study describes the selection of items and demonstrates the internal consistency of the alternate forms. The second study demonstrates the alternate form and retest reliability and provides normative statistics. We conclude that reliable alternate short forms have been constructed to be used in research in clinical applications.This research was supported by the Marie Wilson Howells Fund.Alternate short forms of the CWAS may be obtained from the first author.     

The substitutability of reinforcers

Substitutability is a construct borrowed from microeconomics that describes a continuum of possible interactions among the reinforcers in a given situation. Highly substitutable reinforcers, which occupy one end of the continuum, are readily traded for each other due to their functional similarity. Complementary reinforcers, at the other end of the continuum, tend to be consumed jointly in fairly rigid proportion, and therefore cannot be traded for one another except to achieve that proportion. At the center of the continuum are reinforcers that are independent with respect to each other; consumption of one has no influence on consumption of another. Psychological research and analyses in terms of substitutability employ standard operant conditioning paradigms in which humans and nonhumans choose between alternative reinforcers. The range of reinforcer interactions found in these studies is more readily accommodated and predicted when behavior-analytic models of choice consider issues of substitutability. New insights are gained into such areas as eating and drinking, electrical brain stimulation, temporal separation of choice alternatives, behavior therapy, drug use, and addictions. Moreover, the generalized matching law (Baum, 1974) gains greater explanatory power and comprehensiveness when measures of substitutability are included.     

The many null distributions of person fit indices

This paper deals with the situation of an investigator who has collected the scores ofn persons to a set ofk dichotomous items, and wants to investigate whether the answers of all respondents are compatible with the one parameter logistic test model of Rasch. Contrary to the standard analysis of the Rasch model, where all persons are kept in the analysis and badly fittingitems may be removed, this paper studies the alternative model in which a small minority ofpersons has an answer strategy not described by the Rasch model. Such persons are called anomalous or aberrant. From the response vectors consisting ofk symbols each equal to 0 or 1, it is desired to classify each respondent as either anomalous or as conforming to the model. As this model is probabilistic, such a classification will possibly involve false positives and false negatives. Both for the Rasch model and for other item response models, the literature contains several proposals for a person fit index, which expresses for each individual the plausibility that his/her behavior follows the model. The present paper argues that such indices can only provide a satisfactory solution to the classification problem if their statistical distribution is known under the null hypothesis that all persons answer according to the model. This distribution, however, turns out to be rather different for different values of the person's latent trait value. This value will be called ability parameter, although our results are equally valid for Rasch scales measuring other attributes.As the true ability parameter is unknown, one can only use its estimate in order to obtain an estimated person fit value and an estimated null hypothesis distribution. The paper describes three specifications for the latter: assuming that the true ability equals its estimate, integrating across the ability distribution assumed for the population, and conditioning on the total score, which is in the Rasch model the sufficient statistic for the ability parameter.Classification rules for aberrance will be worked out for each of the three specifications. Depending on test length, item parameters and desired accuracy, they are based on the exact distribution, its Monte Carlo estimate and a new and promising approximation based on the moments of the person fit statistic. Results for the likelihood person fit statistic are given in detail, the methods could also be applied to other fit statistics. A comparison of the three specifications results in the recommendation to condition on the total score, as this avoids some problems of interpretation that affect the other two specifications.The authors express their gratitude to the reviewers and to many colleagues for comments on an earlier version.     

Generalized Rough Sets (Preclusivity Fuzzy-Intuitionistic (BZ) Lattices)

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the "elementary" sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out.The rough approximation of any fixed subset of the universe is the pair consisting of the best "open" approximation from the bottom and the best "closed" approximation from the top. The properties of this generalized rough approximation mapping are studied in the context of quasi-BZ lattice structures of "closed-open" ordered pairs (the "algebraic logic" of generalized rough set theory), comparing the results with the standard Pawlak approach. A particular weak form of rough representation is also studied.     

Intuitionistic Autoepistemic Logic

In this paper we address the problem of combining a logic with nonmonotonic modal logic. In particular we study the intuitionistic case. We start from a formal analysis of the notion of intuitionistic consistency via the sequent calculus. The epistemic operator M is interpreted as the consistency operator of intuitionistic logic by introducing intuitionistic stable sets. On the basis of a bimodal structure we also provide a semantics for intuitionistic stable sets.     

Rules of Existential Quantification into "Intensional Contexts"

Propositional and notional attitudes are construed as relations (-in-intension) between individuals and constructions (rather than propositrions etc,). The apparatus of transparent intensional logic (Tichy) is applied to derive two rules that make it possible to export existential quantifiers without conceiving attitudes as relations to expressions (sententialism).     

A critical review of theS/L reliability index

The meaning and properties of a commonly used index of reliability, S/L,were examined critically. It was found that the index does not reflect any conventional concept of reliability. When used for an identical behavioral observation session, it is not statistically correlated with other reliability indices. Within an observation session, the standardizing measure of Lis beyond the control of the investigator. Furthermore, the reason for the choice of Las the standard is unclear. The role of chance agreement in S/Lis not known. The exact interpretation of the index depends on which observer reports L.Overall the conceptual and mathematical meaning of S/Lis dubious. It is suggested that the S/Lindex should not be used until its nature is shown to be a measure of reliability. Other approaches such as the intraclass correlations and generalizability coefficients should be used instead.The authors are indebted to Johnny Matson for his critique of an earlier version of this paper.