Influential observations in principal factor analysis

We propose a method for detecting influential observations in iterative principal factor analysis. For this purpose we derive the influence functionsI(x; LL ^T ) andI(x; ) for the common variance matrixT =LL ^T and the unique variance matrix , respectively, in the common factor decomposition =LL ^T + . A numerical example is given for illustration.The authors are grateful to Tomoyuki Tarumi and Atsuhiro Hayashi for their kind permission to use their software Seto/B for drawing Figures 1 and 2 and to anonymous reviewers for comments on the paper.     

Robust interactive decision-analysis (RID): Behavioral results and implications

We have proposed a novel interactive procedure for performing decision analysis, called Robust Interactive Decision Analysis (RID), which permits a decision maker (DM) to voluntarily and interactively express strong (viz, sure) binary preferences for actions, partial decision functions, and full decision functions, and only imprecise probability and utility function assessments. These serve as INPUTS TO operators to prune the state probability space and decision space until an optimal choice strategy is obtained. The viability of the RID approach depends on a DM's ability to provide such information consistently and meaningfully. On a limited scale we experimentally investigate the behavioral implications of the RID method in order to ascertain its potential operational feasibility and viability. More specifically, we examine whether a DM can (1) express strong preferences between pairs of vectors of unconditional and conditional payoffs or utilities consistently; (2) provide imprecise (ordinal and interval) state probabilities that are individually as well as mutually consistent with the state probabilities imputed from the expressed strong preferences. The results show that a DM can provide strong individually and mutually consistent preference and ordinal probability information. Moreover, most individuals also appear to be able to provide interval probabilities that are individually and mutually consistent with their strong preference inputs. However, the several violations observed, our small sample size, and the limited scope of our investigation suggest that further experimentation is needed to determine whether and/or how such inputs should be elicited. Overall, the results indicate that the RID method is behaviorally viable.     

Conceptualizations of valence and instrumentality: A fourfold model

Within the framework of valence-instrumentality (VI) theory, a fourfold model is developed to predict the contribution which is made by one outcome of an alternative to the valence of that alternative. The proposed model uses four subjective conditional probabilities which are based on the presence and absence of an alternative, and on the occurrence and nonoccurrence of an outcome. Valence is defined as the difference between the attractiveness values of the occurrence of an alternative (or an outcome) and the nonoccurrence of an alternative (or an outcome). Also, differences between subjective probabilities replace instrumentalities. Alternative valence-instrumentality formulations are analyzed in relation to the proposed fourfold model. The proposed model can be understood as a consistent application of Vroom's model (1964, Work and motivation, New York: Wiley), while other models are judged to be relatively deficient. The fourfold model, in combination with a matrix formulation of expectancy concepts, addresses a number of criticisms of VI theory and makes possible a test of the theory within the limits of its own assumptions.     

Expectations,procedural justice,and alternative reactions to being deprived of a desired outcome

People often find that they do not have some positive outcome they once expected to obtain, while others around them have attained that outcome. Two experiments were conducted to assess how four possible responses to such a situation are affected by procedural justice (i.e., the fairness of the procedures by which the object was denied) and by one's expectations about obtaining the outcome in the future. The four possible responses examined were anger responses, achievement strivings, devaluation of the object (X), and self-deprecation. A repeated-measures analysis revealed that the dependent variables were differentially affected in Study 1, but less so in Study 2. Analyses further revealed effects of procedural justice, such that unfair procedures led to more anger, lower achievement strivings, greater devaluation of X, and (in Study 1 only) marginally less self-deprecation. Expectations had only a marginal affect on achievement strivings in Study 1, and an effect on self-deprecation in Study 2, with higher expectations leading to lower achievement strivings and less self-deprecation, respectively. Procedural justice and expectations interacted to affect subjects' derogation of the agent who deprived them (Study 1) and their devaluation of X (Study 2). Implications for future research and for theoretical development are discussed.     

The relation between classroom social status and classmate likability,compromising skill,temperament, and neighborhood social interactions

Classmate likeability, compromising skill, and temperament (n = 135) and after-school patterns of social interaction (n = 101) were examined for third through seventh grade children who were identified by a binomial probability model as popular, rejected, neglected, or average in the classroom setting. Significant effects were obtained for each type of score. Compared to the other social status groups, popular children were the best liked and rejected children were the least liked; neglected and average children fell between these two extremes. Popular children had higher compromising scores than either rejected or average children, and neglected children had higher scores than rejected children. Compared to average children, rejected children had higher attention and rhythmicity temperament scores. Finally, popular and average children had more neighborhood friends than either rejected or average children, and meglected children had more younger neighborhood friends than did average children. Results are discussed in terms of models of peer social status.     

Intelligence and fertility in the United States: 1912-1982

Results are presented for the 1st analysis of the relationship between IQ and completed fertility using a large, representative sample of the US population. Correlations are predominantly negative for cohorts born between 1894 and 1964 but are significantly more positive for cohorts whose fertility was concentrated in the baby boom years. Previous studies reporting slightly positive correlations appear to have been biased in their restriction of samples to atypical cohorts. The National Opinion Research Center (NORC), a nonprofit research organization affiliated with the University of Chicago, conducted the General Social Survey (GSS) in the US each year from 1972 to 1982, except for 1979. A combination of block quota and full probability sampling was employed. Hour-long interviews were completed with 12,120 respondents who were English-speaking, noninstitutionalized adults (18 years or older) living within the continental US. Such questions as age, place of birth, income and occupation, were asked in each interview. Other questions about attitudes on various social, political, and moral issues were rotated in different years. The unique opportunity this data set affords is an overview of the relationship between intelligence and fertility for a nationally representative sample of Americans whose major reproductive years fell between 1912 and 1982. Data were consolidated from the 4 surveys in which the vocabulary test was given (1974, 1976, 1978, and 1982). Respondents were divided into 15 birth cohorts of 5-year intervals ranging from before 1894 to 1964. Correlations between vocabulary scores and number of siblings are markedly negative across all 15 cohorts. Vocabulary sibling correlations are more negative in every cohort than vocabulary offspring correlations. Previous reports of a neutral or slightly eugenic relationship appear to be due to the nature of the samples used, in part because the cohorts chosen were atypical, and in part because they did not include nonwhites. Childless respondents averaged slightly higher scores than did those with 1 or more children, indicating that the automatic exclusion of the childless from sibling-IQ studies has not spuriously inflated negative correlations.     

Correspondence analysis used complementary to loglinear analysis

Loglinear analysis and correspondence analysis provide us with two different methods for the decomposition of contingency tables. In this paper we will show that there are cases in which these two techniques can be used complementary to each other. More specifically, we will show that often correspondence analysis can be viewed as providing a decomposition of the difference between two matrices, each following a specific loglinear model. Therefore, in these cases the correspondence analysis solution can be interpreted in terms of the difference between these loglinear models. A generalization of correspondence analysis, recently proposed by Escofier, will also be discussed. With this decomposition, which includes classical correspondence analysis as a special case, it is possible to use correspondence analysis complementary to loglinear analysis in more instances than those described for classical correspondence analysis. In this context correspondence analysis is used for the decomposition of the residuals of specific restricted loglinear models.     

Three-way metric unfolding via alternating weighted least squares

Three-way unfolding was developed by DeSarbo (1978) and reported in DeSarbo and Carroll (1980, 1981) as a new model to accommodate the analysis of two-mode three-way data (e.g., nonsymmetric proximities for stimulus objects collected over time) and three-mode, three-way data (e.g., subjects rendering preference judgments for various stimuli in different usage occasions or situations). This paper presents a revised objective function and new algorithm which attempt to prevent the common type of degenerate solutions encountered in typical unfolding analysis. We begin with an introduction of the problem and a review of three-way unfolding. The three-way unfolding model, weighted objective function, and new algorithm are presented. Monte Carlo work via a fractional factorial experimental design is described investigating the effect of several data and model factors on overall algorithm performance. Finally, three applications of the methodology are reported illustrating the flexibility and robustness of the procedure.We wish to thank the editor and reviewers for their insightful comments.     

Iterative least squares estimates of communality: Initial estimate need not affect stabilized value

A common criticism of iterative least squares estimates of communality is that method of initial estimation may influence stabilized values. As little systematic research on this topic has been performed, the criticism appears to be based on cumulated experience with empirical data sets. In the present paper, two studies are reported in which four types of initial estimate (unities, squared multiple correlations, highestr, and zeroes) and four levels of convergence criterion were employed using four widely available computer packages (BMDP, SAS, SPSS, and SOUPAC). The results suggest that initial estimates have no effect on stabilized communality estimates when a stringent criterion for convergence is used, whereas initial estimates appear to affect stabilized values employing rather gross convergence criteria. There were no differences among the four computer packages for matrices without Heywood cases.     

Parent-infant resemblance for general and specific cognitive abilities in the Colorado adoption project

Previous publications emanating from the Colorado Adoption Project have reported significant relationships between parental general cognitive ability (g) and infant Bayley MDI scores. The present study compared infant Bayley factor scores representing separable dimensions of infant cognition with parental general and specific cognitive abilities for 182 adoptive families and 164 nonadoptive families. Parent/offspring correlations between 12-month Bayley factors and parental cognitive abilities suggest only minimal relationships for both parental g and specific abilities. At 24 months, more parent/offspring resemblance was present; moreover, Bayley factors that were related to parental cognition tended to be related to parental g, not to specific abilities. The finding of significant parent/offspring relationships at 24 months between biological parents and their adopted-away infants, as well as between nonadoptive parents and their infants, suggests some genetic continuity from infancy to adulthood.