GENTLE TEACHING AND APPLIED BEHAVIOR ANALYSIS: A CRITICAL REVIEW

In recent years, there has been a growing controversy surrounding gentle teaching. This paper explores the nature of this controversy with particular reference to the relationship between gentle teaching and applied behavior analysis. Advantages and disadvantages of this approach are discussed, and it is suggested that gentle teaching and applied behavior analysis need not be regarded as mutually exclusive approaches to working with persons with mental retardation.     

Choice in situations of time-based diminishing returns: immediate versus delayed consequences of action.

Pigeons chose between two schedules of food presentation, a fixed-interval schedule and a progressive-interval schedule that began at 0 s and increased by 20 s with each food delivery provided by that schedule. Choosing one schedule disabled the alternate schedule and stimuli until the requirements of the chosen schedule were satisfied, at which point both schedules were again made available. Fixed-interval duration remained constant within individual sessions but varied across conditions. Under reset conditions, completing the fixed-interval schedule not only produced food but also reset the progressive interval to its minimum. Blocks of sessions under the reset procedure were interspersed with sessions under a no-reset procedure, in which the progressive schedule value increased independent of fixed-interval choices. Median points of switching from the progressive to the fixed schedule varied systematically with fixed-interval value, and were consistently lower during reset than during no-reset conditions. Under the latter, each subject's choices of the progressive-interval schedule persisted beyond the point at which its requirements equaled those of the fixed-interval schedule at all but the highest fixed-interval value. Under the reset procedure, switching occurred at or prior to that equality point. These results qualitatively confirm molar analyses of schedule preference and some versions of optimality theory, but they are more adequately characterized by a model of schedule preference based on the cumulated values of multiple reinforcers, weighted in inverse proportion to the delay between the choice and each successive reinforcer.     

Factor analysis for clustered observations

Classical factor analysis assumes a random sample of vectors of observations. For clustered vectors of observations, such as data for students from colleges, or individuals within households, it may be necessary to consider different within-group and between-group factor structures. Such a two-level model for factor analysis is defined, and formulas for a scoring algorithm for estimation with this model are derived. A simple noniterative method based on a decomposition of the total sums of squares and crossproducts is discussed. This method provides a suitable starting solution for the iterative algorithm, but it is also a very good approximation to the maximum likelihood solution. Extensions for higher levels of nesting are indicated. With judicious application of quasi-Newton methods, the amount of computation involved in the scoring algorithm is moderate even for complex problems; in particular, no inversion of matrices with large dimensions is involved. The methods are illustrated on two examples.Suggestions and corrections of three anonymous referees and of an Associate Editor are acknowledged. Discussions with Bob Jennrich on computational aspects were very helpful. Most of research leading to this paper was carried out while the first author was a visiting associate professor at the University of California, Los Angeles.     

Dynamic factor analysis of nonstationary multivariate time series

A dynamic factor model is proposed for the analysis of multivariate nonstationary time series in the time domain. The nonstationarity in the series is represented by a linear time dependent mean function. This mild form of nonstationarity is often relevant in analyzing socio-economic time series met in practice. Through the use of an extended version of Molenaar's stationary dynamic factor analysis method, the effect of nonstationarity on the latent factor series is incorporated in the dynamic nonstationary factor model (DNFM). It is shown that the estimation of the unknown parameters in this model can be easily carried out by reformulating the DNFM as a covariance structure model and adopting the ML algorithm proposed by Jöreskog. Furthermore, an empirical example is given to demonstrate the usefulness of the proposed DNFM and the analysis.     

The EM algorithm for latent class analysis with equality constraints

The EM algorithm is a popular iterative method for estimating parameters in the latent class model where at each step the unknown parameters can be estimated simply as weighted sums of some latent proportions. The algorithm may also be used when some parameters are constrained to equal given constants or each other. It is shown that in the general case with equality constraints, the EM algorithm is not simple to apply because a nonlinear equation has to be solved. This problem arises, mainly, when equality constrints are defined over probabilities indifferent combinations of variables and latent classes. A simple condition is given in which, although probabilities in different variable-latent class combinations are constrained to be equal, the EM algorithm is still simple to apply.The authors are grateful to the Editor and the anonymous reviewers for their helpful comments on an earlier draft of this paper. C. C. Clogg and R. Luijkx are also acknowledged for verifying our results with their computer programs MLLSA and LCAG, respectively.     

Influence in canonical correlation analysis

The perturbation theory of the generalized eigenproblem is used to derive influence functions of each squared canonical correlation coefficient and the corresponding canonical vector pair. Three sample versions of these functions are described and some properties are noted. As particular applications, the influence function of the squared multiple correlation coefficient and influence functions of eigenvalues and eigenvectors in correspondence analysis are obtained. Three numerical examples are briefly discussed.We thank the Editor and the anonymous reviewers for their helpful comments. This research was carried out with the financial support of the Italian Ministry of the University and the National Research Council.     

The integration of multidimensional scaling and multivariate analysis with optimal transformations

The recent history of multidimensional data analysis suggests two distinct traditions that have developed along quite different lines. In multidimensional scaling (MDS), the available data typically describe the relationships among a set of objects in terms of similarity/dissimilarity (or (pseudo-)distances). In multivariate analysis (MVA), data usually result from observation on a collection of variables over a common set of objects. This paper starts from a very general multidimensional scaling task, defined on distances between objects derived from one or more sets of multivariate data. Particular special cases of the general problem, following familiar notions from MVA, will be discussed that encompass a variety of analysis techniques, including the possible use of optimal variable transformation. Throughout, it will be noted how certain data analysis approaches are equivalent to familiar MVA solutions when particular problem specifications are combined with particular distance approximations.This research was supported by the Royal Netherlands Academy of Arts and Sciences (KNAW). An earlier version of this paper was written during a stay at McGill University in Montréal; this visit was supported by a travel grant from the Netherlands Organization for Scientific Research (NWO). I am grateful to Jim Ramsay and Willem Heiser for their encouragement and helpful suggestions, and to the Editor and referees for their constructive comments.     

Symptom patterns in late luteal-phase dysphoric disorder

The symptom patterns of 180 women with prospectively confirmed late luteal-phase dysphoric disorder (LLPDD) were examined using a careful application of factor and cluster analytic techniques. Factor analysis of premenstrual change scores on 33 common premenstrual syndrome symptoms yielded four orthogonal factors that were consistent across two sets of menstrual cycle data. These were a negative affect dimension with concomitant behavioral changes, physical symptoms, agitation, and positive arousal. Cluster analysis of factor scores grouped patients into one of five symptom patterns, the most common of which is a general distress cluster, characterized by symptoms across all dimensions. The LLPDD symptom groups identified are remarkably consistent with those of earlier studies using both normative and clinic samples, and consideration of symptom pattern differences in future research may greatly increase our understanding of this disorder.     

Psychological and sexual functioning among outpatient sexual offenders against children: A Minnesota Multiphasic Personality Inventory (MMPI) cluster analytic study

Multivariate clustering procedures were used to identify homogeneous subgroups of outpatient sex offenders against children (n=110)on the basis of the Minnesota Multiphasic Personality Inventory (MMPI). Results indicated a five-subgroup solution. Two within-normal-limits and two clinically elevated profile subgroups replicated subtypes found in previous cluster analytic studies of child sex offenders. The fifth subgroup appeared similar in MMPI profile pattern and elevation to a previously identified subtype of rapists. Discriminant analyses showed that subgroups differed along dimensions of cognitive disturbance and sexual functioning. Furthermore, levels of psychopathology corresponded with levels of sexual pathology. Results are discussed with reference to previous MMPI cluster analytic studies of sex offenders and theories of sexual aggression.Portions of this paper were presented at the meeting of the Midwestern Psychological Association, 1992, Chicago, Illinois.     

Evaluating treatment effects in single-subject behavioral experiments using quality-control charts

Quality-control charts can be particularly useful in identifying treatment effects and patterns of behaviors in single-subject behavior-analytic experiments that cannot be determined by visual inspection of their graphs. Using an example from the behavior analysis literature the quality-control charts identified the presence of treatment effects across phases as well as the presence of trends within and between phases. The ease of their calculations suggest use of them by behavior analysts whenever the effects of particular interventions are questionable.