CONTEMPORARY EVOLUTIONARY THEORY AS A NEW HEURISTIC MODEL FOR THE SOCIOSCIENTIFIC METHOD IN BIBLICAL STUDIES

Abstract. Notions of uniform and gradual evolution have been replaced in some circles by biological and paleontological models that postulate that periods of rapid change punctuate long periods of evolutionary stasis. This new theory, called punctuated equilibria (or PE for short), may have implications for paradigms in scholarly disciplines other than the sciences. Whereas old evolutionary models exerted great influence upon historians, sociologists, anthropologists, and students of religion for more than a century, the new model may provide heuristic paradigms for research that correlate more adequately with the current observations of scholars. We therefore provide suggestions for deployment of this new scientific paradigm in history and anthropology. In particular, this model can explain the rise of the Israelite state and the religious ethos in the Hebrew Bible, two major concerns of today's socioscientific study of biblical materials. Thus the possibility of an overarching paradigm for the social sciences is entertained.     

The robustness of the usual correction for restriction in range due to explicit selection

Corrections for restriction in range due to explicit selection assume the linearity of regression and homoscedastic array variances. This paper develops a theoretical framework in which the effects of some common forms of violation of these assumptions on the estimation of the unrestricted correlation can be investigated. Simple expressions are derived for both the restricted and corrected correlations in terms of the target (unrestricted) correlation in these situations.The author is grateful to D. Holt, C. J. Skinner and T. M. F. Smith (all University of Southampton) for their helpful comments. Research was initially supported by grant No. HR7152 from the Economic and Social Research Council.     

Ignorance or integration: the cognitive processes underlying choice behavior

The fast‐and‐frugal heuristic framework assumes noncompensatory tools for human preferences (i.e., priority heuristic) and inferences (i.e., take the best heuristic). According to this framework, these heuristics predict choice behavior as well as model the cognitive processes underlying such behavior. The current paper presents two studies that juxtapose predictions derived from these two simple heuristics with alternative predictions derived from compensatory principles. Dependent measures that included reaction time, choice pattern, confidence level, and accuracy were better predicted by compensatory indices than by noncompensatory indices. These findings suggest that people do not rely on limited arguments only, but tend to integrate all acquired information into their choice processes. This tendency was replicated even when the experimental task facilitated the use of noncompensatory principles. We argue that the fast and frugal heuristics can predict the final outcome only under certain conditions, but even in these particular situations they are not applicable to the processes underlying choice behavior. An integrative model for choice behavior is proposed that better represents the data. Copyright © 2009 John Wiley & Sons, Ltd.     

The source of the truth bias: Heuristic processing?

People believe others are telling the truth more often than they actually are; this is called the truth bias. Surprisingly, when a speaker is judged at multiple points across their statement the truth bias declines. Previous claims argue this is evidence of a shift from (biased) heuristic processing to (reasoned) analytical processing. In four experiments we contrast the heuristic‐analytic model (HAM) with alternative accounts. In Experiment 1, the decrease in truth responding was not the result of speakers appearing more deceptive, but was instead attributable to the rater's processing style. Yet contrary to HAMs, across three experiments we found the decline in bias was not related to the amount of processing time available (Experiments 1–3) or the communication channel (Experiment 2). In Experiment 4 we found support for a new account: that the bias reflects whether raters perceive the statement to be internally consistent.     

Interpreting degenerate solutions in unfolding by use of the vector model and the compensatory distance model

In this paper, we reconsider the merits of unfolding solutions based on loss functions involving a normalization on the variance per subject. In the literature, solutions based on Stress-2 are often diagnosed to be degenerate in the majority of cases. Here, the focus lies on two frequently occurring types of degeneracies. The first type typically locates some subject points far away from a compact cluster of the other points. In the second type of solution, the object points lie on a circle. In this paper, we argue that these degenerate solutions are well fitting and informative. To reveal the information, we introduce mixtures of plots based on the ideal point model of unfolding, the vector model, and on the signed distance model. In addition to a different representation, we provide a new iterative majorization algorithm to optimize the average squared correlation between the distances in the configuration and the transformed data per individual. It is shown that this approach is equivalent to minimizing Kruskal’s Stress-2.This revised article was published online in August 2005 with the PDF paginated correctly.     

Global optimality of the successive Maxbet algorithm

The Maxbet method is an alternative to the method of generalized canonical correlation analysis and of Procrustes analysis. Contrary to these methods, it does not maximize the inner products (covariances) between linear composites, but also takes their sums of squares (variances) into account. It is well-known that the Maxbet algorithm, which has been proven to converge monotonically, may converge to local maxima. The present paper discusses an eigenvalue criterion which is sufficient, but not necessary for global optimality. However, in two special cases, the eigenvalue criterion is shown to be necessary and sufficient for global optimality. The first case is when there are only two data sets involved; the second case is when the inner products between all variables involved are positive, regardless of the number of data sets.The authors are obliged to Henk Kiers for critical comments on a previous draft.     

Homogeneity analysis withk sets of variables: An alternating least squares method with optimal scaling features

Homogeneity analysis, or multiple correspondence analysis, is usually applied tok separate variables. In this paper we apply it to sets of variables by using sums within sets. The resulting technique is called OVERALS. It uses the notion of optimal scaling, with transformations that can be multiple or single. The single transformations consist of three types: nominal, ordinal, and numerical. The corresponding OVERALS computer program minimizes a least squares loss function by using an alternating least squares algorithm. Many existing linear and nonlinear multivariate analysis techniques are shown to be special cases of OVERALS. An application to data from an epidemiological survey is presented.This research was partly supported by SWOV (Institute for Road Safety Research) in Leidschendam, The Netherlands.     

A note on the unbiased estimation of the intraclass correlation

The intraclass correlation,, is a parameter featured in much psychological research. Two commonly used estimators of, the maximum likelihood and least squares estimators, are known to be negatively biased. Olkin and Pratt (1958) derived the minimum variance unbiased estimator of the intraclass correlation, but use of this estimator has apparently been impeded by the lack of a closed form solution. This note briefly reviews the unbiased estimator and gives a FORTRAN 77 subroutine to calculate it.The first author was supported by an All-University Fellowship from the University of Southern California.     

A note on Roy's largest root

The name Roy's largest root and similar names are used in practice to label two different but functionally related statistics—one proportional to anF, and the other, a squared canonical correlation. This note presents the logic that leads to the two formulations, states which statistic some popular statistical packages use, and shows the possible source of this inconsistency in the original work of Roy (1953) and Heck (1960).     

A mixture model for distributions of correlation coefficients

An old problem in personnel psychology is to characterize distributions of test validity correlation coefficients. The proposed model views histograms of correlation coefficients as observations from a mixture distribution which, for a fixed sample sizen, is a conditional mixture distributionh(r|n) = _{j j} h(r; _j ,n), whereR is the correlation coefficient, _j are population correlation coefficients and _j are the mixing weights. The associated marginal distribution ofR is regarded as the parent distribution underlying histograms of empirical correlation coefficients. Maximum likelihood estimates of the parameters _j and _j can be obtained with an EM algorithm solution and tests for the number of componentst are achieved after the (one-component) density ofR is replaced with a tractable modeling densityh(r; _j ,n). Two illustrative examples are provided.