Test theory without true scores?

This paper traces the course of the consequences of viewing test responses as simply providing dichotomous data concerning ordinal relations. It begins by proposing that the score matrix is best considered to be items-plus-persons by items-plus-persons, and recording the wrongs as well as the rights. This shows how an underlying order is defined, and was used to provide the basis for a tailored testing procedure. It also was used to define a number of measures of test consistency. Test items provide person dominance relations, and the relations provided by one item can be in one of three relations with a second one: redundant, contradictory, or unique. Summary statistics concerning the number of relations of each kind are easy to get and provide useful information about the test, information which is related to but different from the usual statistics. These concepts can be extended to form the basis of a test theory which is based on ordinal statistics and frequency counts and which invokes the concept of true scores only in a limited sense.1979 Psychometric Society presidential address.I want to recognize the contributions which others have made to whatever I have accomplished. First to mention here are my teachers: principally Harold Gulliksen, Ledyard Tucker, and the late Edith Jay. Second, I would like to recognize the importance of my graduate students. Tom Reynolds has been especially important in developing the ideas that I will talk about here today, but at various times, the others have made major contributions in this and other topics. I would like to express also a debt to my family, primarily my wife, Rosemary, who herself has a longterm interest in the psychometric area. Finally, I must acknowledge the financial support of the NIMH some time ago, the Office of Naval Research, until about a year ago, and of the James McKeen Cattell Fund this past year.     

Relations between approaches to studying and note-taking behaviour in lectures

Copies of notes taken during a lecture were obtained from first-year psychology students, and the relations examined between measures derived from these (the number of points recorded, the number of words written, and the number of words per point) and a number of variables measuring personality and approach to studying. Three variables were found to be related to the measures derived from the notes: older students, those scoring high on strategic learning (strategy component) and those scoring high on surface learning (motivational component), both measured by questions derived from Biggs (1979), produced longer notes and recorded more of the important points in the lecture. The results suggest that relations between approaches to studying and specific study behaviour are not straightforward and require more detailed investigation.     

Identification,Reflection, And Correlation: Problems In The Bases Of Repertory Grid Measures

Repertory grids, deriving from George Kelly's personal construct theory, have been used to provide measures of a number of personality and cognitive variables. Several of these grid measures, such as the identification index, some measures of cognitive complexity, and other indices extracted from factor analyses of grids, are based on correlations between the columns (elements) of the grid data matrix. These measures are problematic and unstable because the intercolumn correlations depend on the direction of scoring across each of the matrix rows (constructs). This direction is not guided by explicit or theoretically justified rules and appears to be arbitrary and inconsistent between researchers. Also, correlation is a poor measure of element similarity, the basis of the identification measure. The importance of the valuating aspect of construing may provide a basis for the standardization of scoring. And scoring from the valued pole of a construct may help bring stability and meaning to the correlation-based measures.     

Lexicographic order preservation and stochastic dominance

Stochastic dominance concerns conditions on outcome probabilities that are necessary and sufficient for one act to be (strictly) preferred to another according to all preference relations that share certain properties, one of which customarily is an Archimedean property sufficient to entail existence of real-valued representations. We relax this assumption to permit linear lexicographic utility of finite and known dimensionality. In some situations, levels of the lexicographic hierarchy could correspond to explicit criteria or attributes. In our model, subjective probabilities emerge as matrix premultipliers of the outcome utility vectors. We thus obtain matrix probability generalizations of the familiar cumulative probability conditions for stochastic dominance.     

Physical attractiveness in preschoolers: Relationships with power, status, aggression and social skills

Several lines of theory and research suggest that power (e.g., social dominance) and status (e.g., social prominence and positive peer regard) are enjoyed by those blessed with good looks. The present work addresses the relations among physical attractiveness, power, status, and aggression from a resource control theoretic perspective that suggests that group members find power holders physically attractive, even if they are aggressive. Teacher ratings of physical attractiveness, social dominance, peer reception, aggression, and social skills were collected on 153 preschoolers (3-6 years) from a Midwestern city. Positive peer regard was derived via sociometric nominations. Raters unfamiliar with the children assessed their physical attractiveness from photographs. Results show that teachers' perceptions of physical attractiveness are a function of power, status, and social skills. Additionally, teachers rated aggressive children who employ both prosocial and coercive strategies of resource control (bistrategic controllers) to be among the most physically attractive. These relations did not emerge for raters unbiased by children's behavior. Results suggest social dominance achieved via prosocial means begets attractiveness ratings, even if accompanied by high levels of aggression. The implications for intervention are discussed.     

A stochastic theory of matching processes

A theory of matching processes is developed within which serial models and parallel models based on within-stage independent intercompletion times are defined. These models are then specialized to a class of processes possessing exponential intercompletion time densities and equivalence properties of parallel and serial models within this class are investigated. Nonequivalence theorems are proved that designate possible differences in “same” (+) and different (?) matching rates as important in testing parallel and serial models. An experimental paradigm is then derived with the property that if + rates are different from — rates, and if processing is self-terminating, then the parallel and serial models are distinguishable at the level of mean reaction times. The serial class of models that is tested by this paradigm includes a large number of stochastic distributions whose central assumption is additivity of element processing times. The corresponding parallel class of models is currently limited to those assuming exponential intercompletion times. A numerical example and an example of non-parametric relations predicted by the serial or parallel models are given. Some advantages and limitations of the present treatment are discussed.     

Motor response inhibition and execution in the stop-signal task: development and relation to ADHD behaviors.

The main aim of this study was to investigate the developmental course of motor response inhibition and execution as measured by the stop-signal task in a population-based sample of 525 4- to 12-year-olds. A further aspiration of the study was to enhance the limited knowledge on how the various stop-signal measures relate to ADHD behaviors in a normal sample. We also wanted to contribute to the theoretical understanding of the various stop-signal measures by examining the relations between the stop-signal measures and performance on tasks reflecting other aspects of response inhibition and execution. Our results showed that the ability to inhibit as well as to execute a motor response as measured by the stop-signal task improved with age during childhood. Of specific interest are the findings suggesting that this task captures the development of motor response inhibition in the late preschool years (age 5 years). Both of the inhibition measures derived from the stop-signal task (i.e., SSRT and probability of inhibition) related significantly to teacher ratings of inattention as well as to performance on tasks tapping other aspects of inhibition. The data provided by this study have thus contributed to the scarce knowledge on early development of motor response inhibition, as well as suggested that the stop-signal task may be a valuable tool for capturing deficient motor response inhibition in ADHD behaviors in normal samples.     

Factor analysis of variability measures in eight independent samples of children and adults

Variability in strategy use has been measured and conceptualized in several ways. The present study sought to determine whether a sample of variability measures could be reduced to a smaller number of factors that the individual measures had in common. Factor analysis of five commonly used variability measures was performed separately on data from eight independent samples of children and adults. The results revealed that the variability measures could be reduced to one of two general types of variability: strategy diversity, which refers to the sheer number of strategies used, and strategy change, which refers to the number of trial-by-trial changes in strategy use. Support for this two-factor model of variability was found for all samples of children and adults. Moreover, each type of variability had distinctive relations with cognitive performance that varied with age. In general, strategy diversity was positively related to recall for children but not adults, whereas strategy change was negatively related to recall for adults but not children. Based on this evidence, three recommendations for researchers studying strategy variability are described.     

Hidden talents in harsh conditions? A preregistered study of memory and reasoning about social dominance

Although growing up in stressful conditions can undermine mental abilities, people in harsh environments may develop intact, or even enhanced, social and cognitive abilities for solving problems in high‐adversity contexts (i.e. ‘hidden talents’). We examine whether childhood and current exposure to violence are associated with memory (number of learning rounds needed to memorize relations between items) and reasoning performance (accuracy in deducing a novel relation) on transitive inference tasks involving both violence‐relevant and violence‐neutral social information (social dominance vs. chronological age). We hypothesized that individuals who had more exposure to violence would perform better than individuals with less exposure on the social dominance task. We tested this hypothesis in a preregistered study in 100 Dutch college students and 99 Dutch community participants. We found that more exposure to violence was associated with lower overall memory performance, but not with reasoning performance. However, the main effects of current (but not childhood) exposure to violence on memory were qualified by significant interaction effects. More current exposure to neighborhood violence was associated with worse memory for age relations, but not with memory for dominance relations. By contrast, more current personal involvement in violence was associated with better memory for dominance relations, but not with memory for age relations. These results suggest incomplete transfer of learning and memory abilities across contents. This pattern of results, which supports a combination of deficits and ‘hidden talents,’ is striking in relation to the broader developmental literature, which has nearly exclusively reported deficits in people from harsh conditions. A video abstract of this article can be viewed at: https://youtu.be/e4ePmSzZsuc .     

How Preschoolers Use Cues of Dominance to Make Sense of Their Social Environment

A series of four experiments investigated preschoolers’ abilities to make sense of dominance relations. Experiments 1 and 2 showed that as early as 3 years old, preschoolers are able to infer dominance not only from physical supremacy but also from decision power, age, and resources. Experiments 3 and 4 showed that preschoolers have expectations regarding the ways in which a dominant and a subordinate individual are likely to differ. In particular, they expect that an individual who imposes his choice on another will exhibit higher competence in games and will have more resources.     

Social cliques as mental models

The present research investigates how a mental model derived from patterns of sentiment relations (mental clique model) interacts with social background information (membership in social categories). Testing memory for a set of sentiment relations, the data support the assumption that a strongly polarizing categorization interferes with a mental clique model derived from the learning of these sentiment relations. Such interference was claimed to occur whenever sentiment implications from the social categorization would contradict information contained in the mental clique model. In line with this reasoning, balanced triads were selectively impaired in memory as opposed to relations from unbalanced triads which did not allow construction of any clique model and which were not influenced by category interference.     

A Taxonomy of Part-Whole Relations

A taxonomy of part-whole or meronymic relations is developed to explain the ordinary English-speaker's use of the term “part of” and its cognates. The resulting classification yields six types of meronymic relations: 1. component-integral object (pedal-bike), 2. member-collection (ship-fleet), 3. portion-mass (slice-pie), 4. stuff-object (steel-car), 5. feature-activity (paying-shopping), and 6. place-area (Everglades-Florida). Meronymic relations ore further distinguished from other inclusion relations, such as spatial inclusion, and class inclusion, and from several other semantic relations: attribution, attachment, and ownership. This taxonomy is then used to explain cases of apparent intransitivity in merological syllogisms, and standard form syllogisms whose premises express different inclusion relations. The data suggest that intransitivities arise due to equivocations between different types of semantic relations. These results are then explained by means of the relation element theory which accounts for the character and behavior of semantic relations in terms of more primitive relational elements. The inferential phenomena observed are then explained by means of a single principle of element matching.     

Idiodynamics Vis-à-vis Psychophysiology: An Idiodynamic Portrayal of Cardiovascular Reactivity

Idiodynamics offers a conceptual foundation upon which alternatives to the prevailing model of cardiovascular reactivity could be advanced, built upon systematic investigations of individuals. The origins of a union of idiodynamics and psychophysiology are described, accompanied by an empirical study that exemplifies this synthesis. In the study, a montage of cardiovascular measures was used to assess autonomic patterns in six subjects across a range of laboratory tasks on three occasions. Cardiovascular profiles were derived with p-technique factor analysis and then group aggregated with chain p-technique. The group pattern suggested three components: rate, contractility, and peripheral resistance. When individual profiles were compared to the group, consistencies and disparities appeared. Differences in the number of factors, percentage of variance explained, and dominance of specific components distinguished subjects from one another, leading to a hypothesis about underlying cardiovascular complexity. Idiodynamics, combined with novel methodologies, can expand the construct of reactivity beyond traditional stimulus-response conceptualizations.     

An algorithm for extracting maximum cardinality subsets with perfect dominance or anti‐Robinson structures

A common criterion for seriation of asymmetric matrices is the maximization of the dominance index, which sums the elements above the main diagonal of a reordered matrix. Similarly, a popular seriation criterion for symmetric matrices is the maximization of an anti‐Robinson gradient index, which is associated with the patterning of elements in the rows and columns of a reordered matrix. Although perfect dominance and perfect anti‐Robinson structure are rarely achievable for empirical matrices, we can often identify a sizable subset of objects for which a perfect structure is realized. We present and demonstrate an algorithm for obtaining a maximum cardinality (i.e. the largest number of objects) subset of objects such that the seriation of the proximity matrix corresponding to the subset will have perfect structure. MATLAB implementations of the algorithm are available for dominance, anti‐Robinson and strongly anti‐Robinson structures.     

Meaning dominance norms for 120 homographs

Over the past two decades, homographs have been used in psychological experiments aimed at testing a variety of theoretical issues concerning memory and language. Often, such research requires prior knowledge of the dominance relations among various meanings of the homographs. Previously available homograph meaning norms are limited because they are now more than 10 years old, and they have typically reported only the two most dominant meanings even though many homographs have three or more common meanings. This paper presents normative data on 120 homographs from a relatively large, heterogeneous sample of subjects (N = 100). Meaning dominance was assessed by having subjects write the first definition that came to mind for each homograph. Definition responses were grouped by similarity, and the resulting meaning categories were verified against dictionary meaning classifications. The number of distinct meanings varied from two to six for the homographs investigated, and frequency of response is reported for all definition categories.     

Outline of a denotative definition of aggression

Aggression is defined as generic assertiveness which includes both constructive and destructive behaviors. An attempt is then made to classify the distinctive operational settings (phenotypic situations) which trigger aggression. The classes of such settings are: 1) privation - the frustration of vital needs and the frustration due to inner conflict of needs; 2) conflict (social) - situation-specific competition and intragroup rivalry for dominance; and 3) victimization — predator-prey relations and vandalism per se. Critical questions which emerge from the definition and classification are posed.     

Producing and Recognizing Analogical Relations

Analogical reasoning is an important component of intelligent behavior, and a key test of any approach to human language and cognition. Only a limited amount of empirical work has been conducted from a behavior analytic point of view, most of that within Relational Frame Theory (RFT), which views analogy as a matter of deriving relations among relations. The present series of four studies expands previous work by exploring the applicability of this model of analogy to topography-based rather than merely selection-based responses and by extending the work into additional relations, including nonsymmetrical ones. In each of the four studies participants pretrained in contextual control over nonarbitrary stimulus relations of sameness and opposition, or of sameness, smaller than, and larger than, learned arbitrary stimulus relations in the presence of these relational cues and derived analogies involving directly trained relations and derived relations of mutual and combinatorial entailment, measured using a variety of productive and selection-based measures. In Experiment 1 participants successfully recognized analogies among stimulus networks containing same and opposite relations; in Experiment 2 analogy was successfully used to extend derived relations to pairs of novel stimuli; in Experiment 3 the procedure used in Experiment 1 was extended to nonsymmetrical comparative relations; in Experiment 4 the procedure used in Experiment 2 was extended to nonsymmetrical comparative relations. Although not every participant showed the effects predicted, overall the procedures occasioned relational responses consistent with an RFT account that have not yet been demonstrated in a behavior-analytic laboratory setting, including productive responding on the basis of analogies.     

CDAscal: An algorithm for assessing the correspondence of one or more vectors to a symmetric matrix using ordinal regression

An algorithm for assessing the correspondence of one or more attribute rating variables to a symmetric matrix of dissimilarities is presented. The algorithm is useful as an alternative to fitting property variables into a multidimensional scaling space. Rather than requiring a two step process of first deriving a multidimensional space and then fitting variables individually into the space, the algorithm directly assesses the correspondence of each variable to the symmetric matrix and permits a regression extension such that a set of variables can be considered simultaneously. The relation between the matrix and the variables is determined by evaluating pairs of pairs relations, . Though the algorithm requires only ordinal assumptions, the correspondence may be computed intervally also. Multiple ordinal regression is performed with the values derived from the matrix serving as the dependent variable and those derived from the attribute ratings serving as the independent variables. Standard multiple regression statistics forR-square,F, andt are calculated as well as measures of ordinal association between the vectors and the matrix.