Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis

In the last decade several algorithms for computing the greatest lower bound to reliability or the constrained minimum-trace communality solution in factor analysis have been developed. In this paper convergence properties of these methods are examined. Instead of using Lagrange multipliers a new theorem is applied that gives a sufficient condition for a symmetric matrix to be Gramian. Whereas computational pitfalls for two methods suggested by Woodhouse and Jackson can be constructed it is shown that a slightly modified version of one method suggested by Bentler and Woodward can safely be applied to any set of data. A uniqueness proof for the solution desired is offered.The authors are obliged to Charles Lewis and Dirk Knol for helpful comments, and to Frank Brokken and Henk Camstra for developing computer programs.     

Estimating the standard errors of rotated factor loadings by jackknifing

The jackknife by groups and modifications of the jackknife by groups are used to estimate standard errors of rotated factor loadings for selected populations in common factor model maximum likelihood factor analysis. Simulations are performed in whicht-statistics based upon these jackknife estimates of the standard errors are computed. The validity of thet-statistics and their associated confidence intervals is assessed. Methods are given through which the computational efficiency of the jackknife may be greatly enhanced in the factor analysis model.Computing assistance was obtained from the Health Sciences Computing Facility, UCLA, sponsored by NIH Special Research Resources Grant RR-3.The author wishes to thank his doctoral committee co-chairmen, Drs James W. Frane and Robert I. Jennrich, UCLA, for their contributions to this research.     

Estimation of covariance structure models with parameters subject to functional restraints

This paper demonstrates the feasibility of using the penalty function method to estimate parameters that are subject to a set of functional constraints in covariance structure analysis. Both types of inequality and equality constraints are studied. The approaches of maximum likelihood and generalized least squares estimation are considered. A modified Scoring algorithm and a modified Gauss-Newton algorithm are implemented to produce the appropriate constrained estimates. The methodology is illustrated by its applications to Heywood cases in confirmatory factor analysis, quasi-Weiner simplex model, and multitrait-multimethod matrix analysis.The author is indebted to several anonymous reviewers for creative suggestions for improvement of this paper. Computer funding is provided by the Computer Services Centre, The Chinese University of Hong Kong.     

A feasible method for standard errors of estimate in maximum likelihood factor analysis

A jackknife-like procedure is developed for producing standard errors of estimate in maximum likelihood factor analysis. Unlike earlier methods based on information theory, the procedure developed is computationally feasible on larger problems. Unlike earlier methods based on the jackknife, the present procedure is not plagued by the factor alignment problem, the Heywood case problem, or the necessity to jackknife by groups. Standard errors may be produced for rotated and unrotated loading estimates using either orthogonal or oblique rotation as well as for estimates of unique factor variances and common factor correlations. The total cost for larger problems is a small multiple of the square of the number of variables times the number of observations used in the analysis. Examples are given to demonstrate the feasibility of the method.The research done by R. I. Jennrich was supported in part by NSF Grant MCS 77-02121. The research done by D. B. Clarkson was supported in part by NSERC Grant A3109.     

Quasi‐Experimental Single‐Subject Design: Comparing Seeking Safety and Canine‐Assisted Therapy Interventions Among Mentally Ill Female Inmates

This repeated measures quasi‐experimental study evaluated the effectiveness of 2 interventions, Seeking Safety and canine‐assisted therapy, with female prisoners with trauma histories on a mental health unit. Results indicate both are effective at reducing anxiety, depression, and posttraumatic stress disorder.     

Applied Political Philosophy at the Rubicon: Will Kymlica's Multicultural Citizenship

Will Kymlicka's Multicultural Citizenship represents an extraordinary attempt to put applied political philosophy to work in the empirical context of contemporary political debates about immigration and ethnic minorities in western society. This paper explores the methodological and interpretative difficulties of combining normative and empirical goals, in a critical discussion of the examples Kymlicka makes of multicultural issues in France, Britain and the US. It goes on to argue that these weaknesses lie in the Rawlsian influence in Kymlicka's work, and that political philosophers may have to rethink their methodological approach if they wish to pursue further the kind of applied work which Kymlicka is aiming for.     

Critiques of Casuistry and Why They Are Mistaken

Casuistic methods of reasoning in medical ethics have been criticized by a number of authors. At least five main objections to casuistry have been put forward: (1) it requires a uniformity of views that is not present in contemporary pluralistic society; (2) it cannot achieve consensus on controversial issues; (3) it is unable to examine critically intuitions about cases; (4) it yields different conclusions about cases when alternative paradigms are chosen; and (5) it cannot articulate the grounds of its conclusions. Two main versions of casuistry have been put forward, and the responses to these objections depend in part on which version one is defending. Jonsen has advocated a version modeled on the approach to casuistry used by moral theologians in the 15th and 16th century, involving comparison of the case at hand with a single paradigm and a lineup of cases. The present author has advocated another version, drawn from experience with cases in clinical ethics, which involves comparing the case at hand with two or more paradigms. Four of the five objections are unsuccessful when directed against Jonsen'sapproach, and all of them are unsuccessful when directed against the approach involving comparison with two or more paradigms.