Constructing the exact significance level for a person fit statistic

This paper uses an extension of the network algorithm originally introduced by Mehta and Patel to construct exact tail probabilities for testing the general hypothesis that item responses are distributed according to the Rasch model. By assuming that item difficulties are known, the algorithm is applicable to the statistical tests either given the maximum likelihood ability estimate or conditioned on the total score. A simulation study indicates that the network algorithm is an efficient tool for computing the significance level of a person fit statistic based on test lengths of 30 items or less.     

A quasi-nonmetric method for multidimensional scaling VIA an extended euclidean model

An Extended Two-Way Euclidean Multidimensional Scaling (MDS) model which assumes both common and specific dimensions is described and contrasted with the standard (Two-Way) MDS model. In this Extended Two-Way Euclidean model then stimuli (or other objects) are assumed to be characterized by coordinates onR common dimensions. In addition each stimulus is assumed to have a dimension (or dimensions) specific to it alone. The overall distance between objecti and objectj then is defined as the square root of the ordinary squared Euclidean distance plus terms denoting the specificity of each object. The specificity,s _j , can be thought of as the sum of squares of coordinates on those dimensions specific to objecti, all of which have nonzero coordinatesonly for objecti. (In practice, we may think of there being just one such specific dimension for each object, as this situation is mathematically indistinguishable from the case in which there are more than one.)We further assume that _ij =F(d _ij ) +e _ij where _ij is the proximity value (e.g., similarity or dissimilarity) of objectsi andj,d _ij is the extended Euclidean distance defined above, whilee _ij is an error term assumed i.i.d.N(0, ²).F is assumed either a linear function (in the metric case) or a monotone spline of specified form (in the quasi-nonmetric case). A numerical procedure alternating a modified Newton-Raphson algorithm with an algorithm for fitting an optimal monotone spline (or linear function) is used to secure maximum likelihood estimates of the paramstatistics) can be used to test hypotheses about the number of common dimensions, and/or the existence of specific (in addition toR common) dimensions.This approach is illustrated with applications to both artificial data and real data on judged similarity of nations.     

Nonconvergence,improper solutions,and starting values in lisrel maximum likelihood estimation

In the framework of a robustness study on maximum likelihood estimation with LISREL three types of problems are dealt with: nonconvergence, improper solutions, and choice of starting values. The purpose of the paper is to illustrate why and to what extent these problems are of importance for users of LISREL. The ways in which these issues may affect the design and conclusions of robustness research is also discussed.     

Statistical consistency and hypothesis testing for nonmetric multidimensional scaling

The properties of nonmetric multidimensional scaling (NMDS) are explored by specifying statistical models, proving statistical consistency, and developing hypothesis testing procedures. Statistical models with errors in the dependent and independent variables are described for quantitative and qualitative data. For these models, statistical consistency often depends crucially upon how error enters the model and how data are collected and summarized (e.g., by means, medians, or rank statistics). A maximum likelihood estimator for NMDS is developed, and its relationship to the standard Shepard-Kruskal estimation method is described. This maximum likelihood framework is used to develop a method for testing the overall fit of the model.     

On structural equation modeling with data that are not missing completely at random

A general latent variable model is given which includes the specification of a missing data mechanism. This framework allows for an elucidating discussion of existing general multivariate theory bearing on maximum likelihood estimation with missing data. Here, missing completely at random is not a prerequisite for unbiased estimation in large samples, as when using the traditional listwise or pairwise present data approaches. The theory is connected with old and new results in the area of selection and factorial invariance. It is pointed out that in many applications, maximum likelihood estimation with missing data may be carried out by existing structural equation modeling software, such as LISREL and LISCOMP. Several sets of artifical data are generated within the general model framework. The proposed estimator is compared to the two traditional ones and found superior.The research of the first author was supported by grant No. SES-8312583 from the National Science Foundation and by a Spencer Foundation grant. We wish to thank Chuen-Rong Chan for drawing the path diagram.     

A note on the computation of the second-order derivatives of the elementary symmetric functions in the rasch model

Jansen (1984) gave explicit formulas for the computation of the second-order derivatives of the elementary symmetric functions. But they are only applicable to those pairs of items which have unequal parameters. It is shown here that for equal parameters similar explicit formulas do exist, too, facilitating the application of the Newton-Raphson procedure to estimate the parameters in the Rasch model and related models according to the conditional maximum likelihood principle.The author wishes to thank the reviewers for their helpful comments on an earlier draft of this paper.     

Estimation for structural equation models with missing data

A direct method in handling incomplete data in general covariance structural models is investigated. Asymptotic statistical properties of the generalized least squares method are developed. It is shown that this approach has very close relationships with the maximum likelihood approach. Iterative procedures for obtaining the generalized least squares estimates, the maximum likelihood estimates, as well as their standard error estimates are derived. Computer programs for the confirmatory factor analysis model are implemented. A longitudinal type data set is used as an example to illustrate the results.This research was supported in part by Research Grant DAD1070 from the U.S. Public Health Service. The author is indebted to anonymous reviewers for some very valuable suggestions. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

Stylistic appearances and linguistic diversity

Philosophy is beginning to pay problems of linguistic justice the attention they deserve in today's heavily interconnected and migrant world. Contemporary philosophy itself, however, has a particular problem of linguistic justice that deserves metaphilosophical attention. At least in the philosophical tradition that is mainstream in much of the world today, viz., analytic philosophy, methodological and sociological mechanisms make it the case that the voices of non-(native) Anglophone philosophers are substantially less heard. Among the mechanisms responsible for this situation, argues this paper, is the emphasis given by influential philosophical institutions to linguistic style and appearances as signs of clarity, precision, and rigour in the treatment of philosophical problems. Such an emphasis is not justifiable, in part because it deprives philosophy of a wider variety of perspectives. The paper concludes by presenting and motivating a recent initiative that aims to foster greater linguistic and cultural diversity within the profession.     

Ideological Contestation on Twitter Over Diversity: Constructions of Diversity as Clashing Projects

The problematic of diversity today circulates a discourse on human differences and similarities which is also taken up by actors with controversial political agendas, notably right-wing populist and neoconservative movements. Focusing on contestation over the meaning of “diversity” by lay actors in social media, we suggest here that different constructions of diversity may be seen as clashing projects largely shaping each other through their emphasis on differences or similarities among people. In a qualitative analysis on the tweets mentioning diversity in Greek over a year, constructions of diversity were mirror images of each other across two independent ideological tensions, with distinct social stakes. Individualist constructions of diversity praising individuals' differences clashed over the legitimation of power with majoritarianist constructions emphasizing social homogeneity, and universalist constructions of diversity advocating the fundamental similarities of individuals clashed over the legitimation of social identities with particularist constructions praising cultural differences. Those constructions converse with basic social psychological models of diversity, suggesting that the emphasis on difference or similarity across people may stem from a dynamic context of political confrontation. The findings also suggest that right-wing populist representations may be channeled by the content of contestation and the positions held by the other side.     

Race in the Space: Clinical Considerations for Addressing Race in Treatment

During a period of intense racial unrest in the nation, we were working as clinicians delivering a manualized protocol to LGBTQ adults of varying racial and ethnic backgrounds. Intrigued by the differences in our modes of engagement with clients, we, a Black, cis female therapist and White, cis male therapist, set out to further explore how our positionalities informed our communications with, and expectations of, White and non-White clients during this time. In this paper, we reflect on these differences when delivering therapy in cross-racial and same-race dyads. We highlight where our experiences overlap as clinicians trained in the same program and where they diverge due to our respective worldviews. We conclude with considerations for practitioners to engage with race in psychotherapeutic treatment.