Variables differentiating affective interaction in a family therapy and a control group: Father-child welfare and mother-child emergency affect

In this study of 37 pre-therapy and 23 matched control families who never sought family therapy, father-child welfare affect and mother-child emergency affect were significantly higher in the control families. Control families were found generally to express more Welfare and Emergency emotion. Affective expression between parents did not significantly differentiate the groups.This study has been supported by Grant No. MA-4510 of the Medical Research Council of Canada and was presented at the annual meeting of the Canadian Psychiatric Association, Ottawa, Ontario, Canada, September 1983. The authors wish to express their thanks to Toby Schwartz, Harriet Gold-Kaats, and Terry Tannenbaum-Dascal, who acted as coders and research assistants; Joseph Beltempo, BSc, who helped in the statistical analysis; and James Robbins, PhD, who gave much valuable advice.     

Beyond subitizing: Is estimation of numerousness a continuous process?

Evidence is presented for the existence of two forms of estimation of numerousness — in addition to subitizing. In the experiment reported here, horizontal rows of 5–8 black dots were subitized, while estimation of 33–89 differed from 10–33 in the structure of intercorrelations between estimates. A three-dimensional space generated by Smallest Space Analysis produced three subsets of intercorrelations among percent absolute errors in estimating dots: 5–8 dots, 10–21 dots, and 33–89 dots.     

Empathy in families of women with borderline personality disorder, anorexia nervosa, and a control group

This is a study of empathy in the families of 27 women with borderline personality disorder (BPD), 28 women with restricting anorexia nervosa (AN), and 27 women without a clinical diagnosis (NC). The daughters and both parents responded to the Interpersonal Reactivity Index (IRI), an instrument for assessing four dimensions of empathy. In addition, they were personally interviewed, with the Family Interview for Protectiveness and Empathy (FIPE), about the extent of empathy expressed by the parents to their daughter during her development. On the IRI, women with BPD scored highest on the immature and lowest on the mature aspects of empathy, whereas scores of AN and NC women were all within normal limits. Parents of BPDs had the lowest IRI scores, while parents of AN and NC groups were similar to each other and to criterion group scores. IRI scores of AN daughters were positively correlated with their parents' scores whereas BPDs' scores were negatively correlated with those of their parents. There were no correlations between the IRI scores of NC subjects and their parents. On the FIPE, borderline daughters and parents agreed about the relative absence of empathic parenting, whereas AN and NC daughters and parents agreed as to the presence of empathic parenting. The theoretical and clinical implications of these contrasting findings are discussed.     

THE DEVELOPMENT OF NONMETRIC SPACE ANALYSIS: A LETTER TO PROFESSOR JOHN ROSS

A series of recent studies (Cliff, 1968, 1969; Cliff, Bradley, and Girard, 1970) describe a mathematical model for the cognitive processes involved in an individual's endorsements (or nonendorsements) of personality inventory items. In this model, the inventory items are assumed to occupy positions in a multidimensional space of subjective meaning, and the probability of endorsement is assumed to be some mathematical funotion of these positions.     

A necessary and sufficient formula for matric factoring

For the purpose of extracting factors from matrices, it is proved that a certain formula is both necessary and sufficient. In factor analysis, the formula may be applied either to the correlation matrix, or directly to the score matrix (assuming the communality problem is solved). As many factors as desired can be extracted in one operation. Having such a compact formulation is useful for teaching as well as computing purposes, since it includes all techniques of factor extraction as special cases.On leave from the Israel Institute for Applied Social Research. This research was facilitated in part by a grant from the Lucius N. Littauer Foundation to the American Committee for Social Research in Israel, Inc.     

A general nonmetric technique for finding the smallest coordinate space for a configuration of points

LetA ₁,A ₂, ...,A _n be anyn objects, such as variables, categories, people, social groups, ideas, physical objects, or any other. The empirical data to be analyzed are coefficients of similarity or distance within pairs (A _i,A _i ), such as correlation coefficients, conditional probabilities or likelihoods, psychological choice or confusion, etc. It is desired to represent these data parsimoniously in a coordinate space, by calculatingm coordinates {x _ia } for eachA _i for a semi-metricd of preassigned formd _ij =d(|x _i1 -x _j1 |, |x _i2 -x _j2|, ..., |x _im -x _jm |). The dimensionalitym is sought to be as small as possible, yet satisfy the monotonicity condition thatd _ij <d _kl whenever the observed data indicate thatA _i is closer toA _j thanA _k is toA _l . Minkowski and Euclidean spaces are special metric examples ofd. A general coefficient of monotonicity is defined, whose maximization is equivalent to optimal satisfaction of the monotonicity condition, and which allows various options both for treatment of ties and for weighting error-of-fit. A general rationale for algorithm construction is derived for maximizing by gradient-guided iterations; this provides a unified mathematical solution to the basic operational problems of norming the gradient to assure proper convergence, of trading between speed and robustness against undesired stationary values, and of a rational first approximation. Distinction is made between single-phase (quadratic) and two-phase (bilinear) strategies for algorithm construction, and between hard-squeeze and soft-squeeze tactics within these strategies. Special reference is made to the rank-image and related transformational principles, as executed by current Guttman-Lingoes families of computer programs.This research was supported in part by the National Science Foundation of the United States Government, through Grant No. GS 929 to the University of Michigan.I am deeply indebted for many helpful comments on earlier drafts of this paper received from Joseph Kruskal, James Lingoes, and the managing editor.     

The test-retest reliability of qualitative data

The test-retest reliability of qualitative items, such as occur in achievement tests, attitude questionnaires, public opinion surveys, and elsewhere, requires a different technique of analysis from that of quantitative variables. Definitions appropriate to the qualitative case are made both for the reliability coefficient of an individual on an item and for the reliability coefficient of a population on the item. From but a single trial of a large population on the item, it is possible to compute alower bound to the group reliability coefficient. Two kinds of lower bounds are presented. From two experimentally independent trials of the population on the item, it is possible to compute anupper bound to the group reliability coefficient. Two upper bounds are presented. The computations for the lower and upper bounds are all very simple. Numerical examples are given.     

A generalized simplex for factor analysis

By a simplex is meant a set of statistical variables whose interrleations reveal a simple order pattern. For the case of quantitative variables, an order model was analyzed previously which allowed only for positive correlations among the variables and a limited type of gradient among the correlation coefficients. The present paper analyzes a more general model and shows how it is more appropriate to empirical data. Among the novel features emerging from the analysis are: (a) the factoring implied of the correlation matrix; (b) the use of a non-Euclidean distance function; and (c) the possible underlying psychological theories.Read at the International Congress of Psychology, Montreal, June 7–12, 1954. This research was facilitated in part by an uncommitted grant-in-aid to the writer from the Behavioral Sciences Division of the Ford Foundation.     

A Set Theory with Support for Partial Functions

Partial functions can be easily represented in set theory as certain sets of ordered pairs. However, classical set theory provides no special machinery for reasoning about partial functions. For instance, there is no direct way of handling the application of a function to an argument outside its domain as in partial logic. There is also no utilization of lambda-notation and sorts or types as in type theory. This paper introduces a version of von-Neumann-Bernays-Gödel set theory for reasoning about sets, proper classes, and partial functions represented as classes of ordered pairs. The underlying logic of the system is a partial first-order logic, so class-valued terms may be nondenoting. Functions can be specified using lambda-notation, and reasoning about the application of functions to arguments is facilitated using sorts similar to those employed in the logic of the IMPS Interactive Mathematical Proof System. The set theory is intended to serve as a foundation for mechanized mathematics systems.