Modelling non‐normal data: The relationship between the skew‐normal factor model and the quadratic factor model

Maximum likelihood estimation of the linear factor model for continuous items assumes normally distributed item scores. We consider deviations from normality by means of a skew‐normally distributed factor model or a quadratic factor model. We show that the item distributions under a skew‐normal factor are equivalent to those under a quadratic model up to third‐order moments. The reverse only holds if the quadratic loadings are equal to each other and within certain bounds. We illustrate that observed data which follow any skew‐normal factor model can be so well approximated with the quadratic factor model that the models are empirically indistinguishable, and that the reverse does not hold in general. The choice between the two models to account for deviations of normality is illustrated by an empirical example from clinical psychology.     

港口门机事故驾驶员与非事故驾驶员身心素质比较

采用ＹＧ人格测验量表、团体智力筛选测验量表、复杂划消测验、双手调节器及深度知觉仪对港口门机事故驾驶员和非事故驾驶员所进行的研究表明：两组门机驾驶员在１２项人格特征以及智力、选择反应能力上未显示出显著性差异;事故组门机驾驶员双手协调及注意分配能力和深度知觉能力明显低于非事故组门机驾驶员;技能水平与事故之间存在显著的正相关．     

The effect of reinforcement differences on choice and response distribution during stimulus compounding

In Experiments I and II, rats were trained to respond on one lever during light and another during tone. The absence of tone and light controlled response cessation. In the multiple schedule of Experiment I, all reinforcements were received for responding in tone or light; in the chain schedule of Experiment II, all reinforcements were received in no tone + no light for not responding. Experiment I subjects, for which tone and light were associated with response and reinforcement increase, responded significantly more to tone-plus-light than to tone or light alone (additive summation). Experiment II subjects, for which tone and light were associated with response increase and reinforcement decrease, responded comparably to tone, light, and tone + light. Thus, additive summation was observed when stimulus-response and stimulus-reinforcer associations in tone and light were both positive, but not when they were conflicting. All subjects in both experiments responded predominantly on the light-correlated lever during tone + light, even when light intensity was reduced in testing. Furthermore, when a light was presented to a subject engaged in tone-associated responding, all subjects immediately switched the locus of responding to the light-correlated lever. No change in locus occurred when a tone was presented to a subject engaged in light-associated responding, irrespective of the stimulus-reinforcer association conditioned to tone. The light-lever preference in tone + light indicates that the heightened responding observed in Experiment I was not the summation of tone-associated behavior with light-associated behavior. Rather, it appears to be the result of a facilitation of one operant (light-associated responding) by the reinforcement-associated cue for the other.     

An application of order restricted inference methodology to a problem in psychiatry

Using data which reflects upon the genetic makeup of patients, Cadoret, Woolson and Winokur (1977) test two theories regarding the genetic makeup of patients suffering from unipolar affective disorder. This hypothesis test is a good example of a problem in order restricted inference. Using some recently developed techniques in order restricted inference we analyze these data and compare the analyses.This research was sponsored by the Office of Naval Research under contract N00014-80-C-0321.     

A still further note on freeman's measure of association

This article demonstrates that Freeman's theta, a measure of association between a nominal variable and an ordinal variable, has a sampling distribution identical with the sampling distribution of Mann-Whitney'sU.     

Allowing for infeasible pairings in the matching paradigm

The objective of research in the matching paradigm is to determine whether a one-to-one pairing configuration between objects in two arrays contains more pairings of a particular kind than expected under the null hypothesis. The presence of infeasible pairings, that is, of particular pairings which can not possibly take place, has the effect of altering the null distribution that would otherwise obtain. To enable researchers to determine the appropriate null distribution, a generalization of classical rook methodology is developed which can accommodate infeasible pairings in the matching paradigm.     

An invariant relation between changing over and reinforcement

Although concurrent schedules may arrange reinforcers irregularly, relatively large numbers of reinforcers are obtained when an animal changes from one schedule to the other. This paper proposes a quantitative relation that predicts the proportion of reinforcers obtained when an animal is working on a schedule and the proportion when the animal changes over to a schedule. Basically the relation states that the number of reinforcers obtained while an animal works on a schedule varies directly with the relative amount of time spent working on that schedule; and the number of reinforcers obtained when an animal changes to a schedule varies directly with the relative amount of time spent on the alternate schedule. An important aspect of this relation is that when relative reinforcement rates are less than .50, more reinforcers are obtained just after an animal changes to a schedule than at all other times when this schedule is engaged. Data obtained both from a stat-bird and a live pigeon were in close agreement with the quantitative predictions. The relation between changing over and reinforcement held across several procedural changes that included changes in relative reinforcement rate, changes from independent to interdependent scheduling procedures, and changes in the variable-interval reinforcement distributions. The results are discussed in terms of the effects of the local distribution of reinforcement on responding. The local reinforcement distribution can affect local response rates and affects the resulting matching relation. This arrangement has implications for explanations of choice.     

A new interpretation of stochastic test models

A new look at latent trait models is proposed. The event of an item being solved by a person is related to the event that the momentary value of a person-specific random component is at least as large as the corresponding value of an item-specific random component. The Birnbaum logistic test model is shown to be generated by a bivariate extreme value distribution for the components. Some consequences of this interpretation are outlined.I am indebted to David Strauss for calling the extreme value distribution (1) to my attention in a random utility context. The paper also benefited from discussions with H. C. Micko, H. H. Schulze and K. F. Wender.     

Asymptotic distributions of the estimators of communalities in factor analysis

Asymptotic distributions of the estimators of communalities are derived for the maximum likelihood method in factor analysis. It is shown that the common practice of equating the asymptotic standard error of the communality estimate to the unique variance estimate is correct for standardized communality but not correct for unstandardized communality. In a Monte Carlo simulation the accuracy of the normal approximation to the distributions of the estimators are assessed when the sample size is 150 or 300. This study was carried out in part under the ISM Cooperative Research Program (90-ISM-CRP-9).