The microanalysis of fixed-interval responding

The fixed-interval schedule of reinforcement is one of the more widely studied schedules in the experimental analysis of behavior and is also a common baseline for behavior pharmacology. Despite many intensive studies, the controlling variables and the pattern of behavior engendered are not well understood. The present study examined the microstructure and superstructure of the behavior engendered by a fixed-interval 5- and a fixed-interval 15-minute schedule of food reinforcement in the pigeon. Analysis of performance typical of fixed-interval responding indicated that the scalloped pattern does not result from smooth acceleration in responding, but, rather, from renewed pausing early in the interval. Individual interresponse-time (IRT) analyses provided no evidence of acceleration. There was a strong indication of alternation in shorter-longer IRTs, but these shorter-longer IRTs did not occur at random, reflecting instead a sequential dependency in successive IRTs. Furthermore, early in the interval there was a high relative frequency of short IRTs. Such a pattern of early pauses and short IRTs does not suggest behavior typical of reinforced responding as exemplified by the pattern found near the end of the interval. Thus, behavior from clearly scalloped performance can be classified into three states: postreinforcement pause, interim behavior, and terminal behavior.     

Minimum rank and minimum trace of covariance matrices

This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented.     

The Headache Symptom Questionnaire: Discriminant classificatory ability and headache syndromes suggested by a factor analysis

A brief Headache Symptom Questionnaire was administered to 129 chronic headache Sufferers. The questionnaire accurately classified 68.42% of headache subjects in their proper diagnostic category, comparable to, but statistically less accurate than, the 86.4% agreement between expert headache diagnosticians using clinical interviews. Results of a factor analysis of the Headache Symptom Questionnaire lend support for their being two commonly accepted global headache categories—vascular/migraine and muscle contraction—and one headache dimension concerned with duration of headache pain. Combined migraine-muscle contraction headache was found to be related more to migraine than to muscle contraction headache, and cluster headaches emerged as a separate clinical entity, not loading positively on any factor and loading negatively on all three.This research was supported in part by Grant NS-15235 from the National Institute of Neurological and Communicative Disorders and Stroke.     

New assessment systems for residential treatment,management, research,and evaluation: A symposium

An introduction and overview are presented to new observational assessment systems for ongoing assessment and monitoring of both staff and resident (client or patient) functioning in residential treatment programs for emotionally disturbed and mentally retarded adults.Preparation of articles and the research and development on which the articles are based was supported, in part, by Public Health Service Grants MH-15553 and MH-25464 from the National Institute of Mental Health, and by grants from the Joyce Foundation and the Illinois Department of Mental Health and Developmental Disabilities.A symposium presented at the 87th Annual Meetings of the American Psychological Association, New York City, September 1979.     

Systems use to objectify program evaluation,clinical, and management decisions

The utility of the observational assessment systems at different levels — from local clinical to systemwide management — is outlined. An overview is provided of TSBC information applied to individualized problem identification and programming/monitoring, discharge and competency determinations, and both absolute and comparative program evaluation. The utility of SRIC information for prgoramming/monitoring and for staff training and evaluation is outlined in addition to the applied uses of the information of the assessment systems in combination. Once implemented, the continuous data from the systems allow for empirically based self-corrective improvements in the quality of mental health services while automatically providing a basis for legal documentation and accurate cost/effectiveness comparisons of mental health programs.Preparation of this article and the research and development on which the article is based were supported, in part, by Public Health Service Grants MH-15553 and MH-25464 from the National Institute of Mental Health, and by grants from The Joyce Foundation and the Illinois Department of Mental Health and Developmental Disabilities.Presented at the 87th Annual Meetings of the American Psychological Association, New York City, September 1979, as part of a symposium on New assessment systems for residential treatment, management, research, and evaluation.     

On rotating to smooth functions

Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. Simple structure is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.Portions of this research were supported by the National Research Council of Canada, Grant A8615 to the second author. We thank Jagdeth Sheth for supplying his raw data.     

Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study

In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log (N–1) and log {[n(n–1)/2]–[(i–1)n]}, whereN is the number of observations;n, the number of variables; andi, the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member.     

Comments on “the measurement of factorial indeterminacy”

Guttman's index of indeterminacy (2² – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation ² for predicting the factor from the observed variables is the average correlation _AB between independently selected alternative solutionsA andB, while var ( _AB )=(1 – ²)²/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, ² is the lower bound for E( _AB ); however, E( _AB ) need not be a modal value in the distribution of _AB . Guttman's index and E( _AB ) measure different aspects of the same indeterminacy problem.     

A look,by simulation,at the validity of some asymptotic distribution results for rotated loadings

In the last few years, a number of asymptotic results for the distribution of unrotated and rotated factor loadings have been given. This paper investigates the validity of some of these results based on simulation techniques. In particular, it looks at principal component extraction and quartimax rotation on a problem with 13 variables. The indication is that the asymptotic results are quite good.     

Who drops-out? Do measures of risk to self and to others predict unplanned endings in primary care counselling?

Aims: Unplanned endings, where clients unilaterally end therapy, are of concern for psychological therapy services generally as they raise questions about the appropriateness of the treatment and it's delivery for some clients. Limited available data indicates that those who drop-out often have more severe symptoms at entry, and have poorer clinical outcomes. This raises further questions about risk to self and others for those clients who leave therapy prematurely and how these clients might be identified and kept engaged. Method: This paper uses a large dataset of CORE data collected routinely in a primary care counselling service between 2000 and 2003. Logistic regression was utilised to consider different measures of risk and other client characteristics recorded at assessment to predict drop-out from the service. Results: These indicate that younger age, greater psychological distress at assessment, an addiction problem and greater risk to others, are associated with an unplanned ending. However, no reliable logistic regression model could be produced. This may be partly due to data quality issues or important characteristics not being available in the data. Implications for practice: The paper concludes that counsellors should actively seek to minimise unplanned endings, as amongst them may be represented the more distressed and risky clients referred to primary care counselling.