Some small sample results for maximum likelihood estimation in multidimensional scaling

Some aspects of the small sample behavior of maximum likelihood estimates in multidimensional scaling are investigated by Monte Carlo. An investigation of Model M2 in the MULTISCALE program package shows that the chi-square test of dimensionality requires a correction of tabled chi-square values to be unbiased. A formula for this correction in the case of two dimensions is estimated. The power of the test of dimensionality is acceptable with as few as two replications for 15 stimuli and as few as five replications for 10 stimuli. The biases in the exponent and standard error estimates in this model are also investigated.The research reported here was supported by grant number APA 320 to the author by the National Science and Engineering Research Council of Canada.     

Confidence regions for multidimensional scaling analysis

Techniques are developed for surrounding each of the points in a multidimensional scaling solution with a region which will contain the population point with some level of confidence. Bayesian credibility regions are also discussed. A general theorem is proven which describes the asymptotic distribution of maximum likelihood estimates subject to identifiability constraints. This theorem is applied to a number of models to display asymptotic variance-covariance matrices for coordinate estimates under different rotational constraints. A technique is described for displaying Bayesian conditional credibility regions for any sample size.The research reported here was supported by grant number APA 320 to the author by the National Research Council of Canada.     

After the attempt: maintaining the therapeutic alliance following a patient's suicide attempt

The risk of a patient's suicide is a prominent occupational hazard for psychotherapists. The precise number of patients who attempt suicide while in treatment and then resume therapy with the same therapist is not known, but this situation is a relatively common occurrence in clinical practice. Such scenarios can pose significant challenges to the reestablishment of the therapeutic trust and a workable treatment alliance. The aim of this paper is to identify the challenges facing a clinician treating a patient who resumes therapy following a serious suicide attempt, and to offer guidelines for maintaining the viability of the therapeutic alliance.     

Separate Digits tests: A brief history,a literature review,and a reexamination of the factor structure of the test of memory and learning (TOMAL)

Following a brief history of Digit Span, a review of 27 articles, selected from 76, addresses the question of whether to scale Digits Forward and Backward separately. The review begins with studies involving Digits Forward, followed in turn by studies of Digits Backward and of both subtests. Finally, the loadings of four TOMAL subtests, Digits Forward and Backward and Letters Forward and Backward, undergo examination in the context of two, three, and four factor promax solutions, with corresponding varimax solutions provided for comparison. The analysis leads to several conclusions. Though Digits Forward and Backward show similarities, they load differently in the three and four factor solutions; Digits Backward also displays a spatial element, and perhaps a transformative element, not apparent in Digits Forward. Moreover, the differences between the two measures have important neurologic and diagnostic implications.     

Form and characteristics of the cardiovascular conditional response in Rhesus monkeys

Three Rhesus monkeys restrained in primate chairs were exposed to several Pavlovian control procedures, followed by 13 sessions of cardiac conditioning under a delay paradigm. The conditional stimulus (CS) was a vertical line and the unconditional stimulus (US) was electric foot shock. Heart rate (HR) was analyzed in successive fivesecond intervals beginning five seconds before CS onset. The major finding was that the conditional response was consistently biphasic and consisted of an initial acceleration followed by deceleration toward the baseline, but rarely reaching it before onset of US. The subjects differed in magnitude of acceleration and subsequent deceleration as well as the location of the maximum rate in the CS-US interval. A breakdown of trials on the basis of the pre-CS HR revealed that the magnitude of effect was inversely related to the pre-CS rate.     

Two methods for obtaining electrocardiograms of chair-restrained monkeys

EKG’s of chair-restrained Rhesus monkeys were recorded using 1. implantation of subdermal electrodes, and 2. surface electrodes. Both procedures resulted in reliable registration of EKG’s in experiments involving both Pavlovian and instrumental conditioning and recording. The advantages and disadvantages of the methods are discussed and detailed instructions for implementation are given.     

A comparison of three simple test theory models

In very simple test theory models such as the Rasch model, a single parameter is used to represent the ability of any examinee or the difficulty of any item. Simple models such as these provide very important points of departure for more detailed modeling when a substantial amount of data are available, and are themselves of real practical value for small or even medium samples. They can also serve a normative role in test design.As an alternative to the Rasch model, or the Rasch model with a correction for guessing, a simple model is introduced which characterizes strength of response in terms of the ratio of ability and difficulty parameters rather than their difference. This model provides a natural account of guessing, and has other useful things to contribute as well. It also offers an alternative to the Rasch model with the usual correction for guessing. The three models are compared in terms of statistical properties and fits to actual data. The goal of the paper is to widen the range of minimal models available to test analysts.This research was supported by grant AP320 from the Natural Sciences and Engineering Research Council of Canada. The author is grateful for discussions with M. Abrahamowicz, I. Molenaar, D. Thissen, and H. Wainer.