Generating Multivariate Ordinal Data via Entropy Principles

When conducting robustness research where the focus of attention is on the impact of non-normality, the marginal skewness and kurtosis are often used to set the degree of non-normality. Monte Carlo methods are commonly applied to conduct this type of research by simulating data from distributions with skewness and kurtosis constrained to pre-specified values. Although several procedures have been proposed to simulate data from distributions with these constraints, no corresponding procedures have been applied for discrete distributions. In this paper, we present two procedures based on the principles of maximum entropy and minimum cross-entropy to estimate the multivariate observed ordinal distributions with constraints on skewness and kurtosis. For these procedures, the correlation matrix of the observed variables is not specified but depends on the relationships between the latent response variables. With the estimated distributions, researchers can study robustness not only focusing on the levels of non-normality but also on the variations in the distribution shapes. A simulation study demonstrates that these procedures yield excellent agreement between specified parameters and those of estimated distributions. A robustness study concerning the effect of distribution shape in the context of confirmatory factor analysis shows that shape can affect the robust \(\chi ^2\) and robust fit indices, especially when the sample size is small, the data are severely non-normal, and the fitted model is complex.     

Psychometric Models of Small Group Collaborations

The social combination theory of group problem solving is used to extend existing psychometric models to collaborative settings. A model for pairwise group work is proposed, the implications of the model for assessment design are considered, and its estimation is addressed. The results are illustrated with an empirical example in which dyads work together on a twelfth-grade level mathematics assessment. In conclusion, attention is given to avenues of research that seem most fruitful for advancing current initiatives concerning the assessment of collaboration, teamwork, and related constructs.     

Outliers and Influential Observations in Exponential Random Graph Models

We discuss measuring and detecting influential observations and outliers in the context of exponential family random graph (ERG) models for social networks. We focus on the level of the nodes of the network and consider those nodes whose removal would result in changes to the model as extreme or “central” with respect to the structural features that “matter”. We construe removal in terms of two case-deletion strategies: the tie-variables of an actor are assumed to be unobserved, or the node is removed resulting in the induced subgraph. We define the difference in inferred model resulting from case deletion from the perspective of information theory and difference in estimates, in both the natural and mean-value parameterisation, representing varying degrees of approximation. We arrive at several measures of influence and propose the use of two that do not require refitting of the model and lend themselves to routine application in the ERGM fitting procedure. MCMC p values are obtained for testing how extreme each node is with respect to the network structure. The influence measures are applied to two well-known data sets to illustrate the information they provide. From a network perspective, the proposed statistics offer an indication of which actors are most distinctive in the network structure, in terms of not abiding by the structural norms present across other actors.     

Religious Beliefs,Religious Contexts,and Perceived Interactions with Ex-Offenders

Religious institutions can provide a means of support and resources for many people, particularly, individuals who have criminal histories, specifically parolees, sex offenders, and insanity acquittees. When these individuals are released into the community, they often face difficulties in acquiring shelter, work, and social support. Out of their own volition or as a result of faith-based prison programs, they might turn to religious institutions for help reintegrating into the community. However, whether congregation members are more or less accepting of these individuals is unaddressed in the current literature. Two studies assess the relationship between religious beliefs, religious contexts, legal attitudes, and perceived social interactions with parolees, sex offenders, and insanity acquittees. Results suggest that religious beliefs, legal attitudes, and religious contexts play an important role in individuals’ perceived interactions with these individuals. Religious contexts, specifically, might facilitate more positive social interactions with parolees. Implications are discussed.     

Engaging with Buddhism

In his new book, Jay Garfield invites philosophers of all persuasions to engage with Buddhist philosophy. In part I of this paper, I raise some questions on behalf of the philosopher working in the analytic tradition about the way in which Buddhist philosophy understands itself. I then turn, in part II, to look at what Orthodox Buddhism has to say about the self. I examine the debate between the Buddhist position discussed and endorsed by Garfield and that of a lesser-known school that he mentions only briefly, the Pudgalavāda (“Personalists”). I suggest that the views of the Pudgalavādins are strikingly similar to a position held, in the twentieth century analytic philosophy, by Peter Strawson.