Fitting Psychometric Models with Methods Based on Automatic Differentiation

Quantitative psychology is concerned with the development and application of mathematical models in the behavioral sciences. Over time, models have become more complex, a consequence of the increasing complexity of research designs and experimental data, which is also a consequence of the utility of mathematical models in the science. As models have become more elaborate, the problems of estimating them have become increasingly challenging. This paper gives an introduction to a computing tool called automatic differentiation that is useful in calculating derivatives needed to estimate a model. As its name implies, automatic differentiation works in a routine way to produce derivatives accurately and quickly. Because so many features of model development require derivatives, the method has considerable potential in psychometric work. This paper reviews several examples to demonstrate how the methodology can be applied. From the Presidential Address delivered at the 70th Annual Meeting of the Psychometric Society, Tilburg University, The Netherlands, July 5–8, 2005.     

Effets de la pression temporelle sur les estimations de durées

This study aims at examining the effects of time pressure on adults’ time estimation. Participants had to solve mazes under two conditions of time pressure (with/without). After each maze, they had to estimate the time elapsed since the beginning of maze solving. Results show that under time pressure, participants 1) overestimated the duration of maze solving and 2) were less variable in their time estimation, in comparison to the condition without time pressure. These results are discussed in the framework of temporal information processing model.     

The impact of job demands,climate, and optimism on well-being and distress at work: What are the mediating effects of basic psychological need satisfaction?

IntroductionPsychological health at work, a multidimensional concept grasped by the absence of negative states and by the presence of positive states, is here approximated in terms of distress and well-being.ObjectiveThis study was aimed at examining the extent to which job demands, individual resources (optimism), and organizational resources (climate) are linked to well-being and distress at work. We looked at whether these links are mediated in satisfaction of the three basic psychological needs posited in self-determination theory (competence, relatedness, and autonomy).MethodThe participants were 298 French elementary, middle, and high school teachers who were asked to answer a questionnaire. The data was analyzed using Hayes and Preacher's method for testing multiple mediations.ResultsSatisfaction of the psychological needs for competence and relatedness fully mediated the links between job climate and psychological health at work (well-being and distress). Optimism turned out to be an important factor of health, not only because it had a strong impact on well-being and distress, but also because its effects were partially mediated by satisfaction of the need for competence.ConclusionThe present results confirm the relevance of the variables used to predict psychological health (particularly optimism). Job demands directly affected well-being and distress levels. The climate — by way of satisfaction of the need for competence and for relatedness — plays a critical role in matters of occupational health.     

The effect of different methods to construct non-symbolic stimuli in numerosity estimation and comparison

Numerosity estimation and comparison tasks are often used to measure the acuity of the approximate number system (ANS), a mechanism which allows extracting numerosity from an array of dots independently from several visual cues (e.g. area extended by the dots). This idea is supported by studies showing that numerosity can be processed while these visual cues are controlled for. Different methods to construct dot arrays while controlling their visual cues have been proposed in the past. In this paper, these methods were contrasted in an estimation and a comparison task. The way of constructing the dot arrays had little impact on estimation. In contrast, in the comparison task, participants' performance was significantly influenced by the method that was used to construct the arrays of dots, indicating better performance when the visual cues of the dot arrays (partly) co-varied with numerosity. The present study therefore shows that estimates of ANS acuity derived from comparison tasks are inconsistent and dependent on how the stimuli are constructed. This makes it difficult to compare studies which utilised different methods to construct the dot arrays in numerosity comparison tasks. In addition, these results question the currently held view of the ANS as capable of robustly extracting numerosity independently from visual cues.     

Measured and self-estimated trait emotional intelligence in a UK sample of managers

Trait emotional intelligence (EI) was measured and self-estimated in a UK sample of 128 managers (52.3% female), recruited at a professional services firm. Participants’ measured scores were compared to standardization sample data and gender differences in measured and estimated scores, as well as in estimation bias and accuracy were examined. As hypothesized, managers’ global trait EI scores were significantly higher than those of the normative sample of the measure used, although the scores of female participants were largely responsible for this difference. Gender-specific hypotheses were confirmed for measured scores (differences only hypothesized at the factor level) and estimation accuracy (males estimating their trait EI more accurately), but not for estimated scores (female participants had higher estimates, but the opposite was hypothesized). Further, female managers showed signs of estimation bias.     

Experiencing whole type: living into the archetypal Self

Expanding on Jung’s use of the role of the superior and inferior functions, Angelo Spoto advances a new typological model based on ‘whole type’ that utilizes a typological perspective on the archetypal Self. In this new model four cognitive modes taking superior positions are developed in the first half of life and four cognitive modes taking inferior positions are encountered in the second half of life. This model indicates that type development and type dynamics take place through the holding of the tension of opposites between superior and inferior functions, helped by the transcendent function operating differently in the first and second halves of life. Specifically, in the first half of life, the transcendent function produces a tertium that moves typological development along to consolidate an ego-pattern. In the second half of life, the transcendent function takes the individual into encounters having to do with an appreciation of sacrifice, transformation, and symbol-making, as the personality advances towards a greater awareness of wholeness, by way of the inferiors.     

Sources of individual differences in fraction skills

The purpose of this investigation was to evaluate a conceptual model of relations between two kinds of mathematical knowledge (simple arithmetic and conceptual knowledge), two kinds of child characteristics (working memory and on-task related classroom behavior), and individual differences in three kinds of fraction outcomes (fraction computation, estimation, and word problems) in 105 fifth grade students. Structural equation modeling provided consistent evidence that conceptual knowledge independently contributes to individual differences in the three fraction outcomes. Simple arithmetic knowledge was uniquely related only to variability in fraction computation skills. Mathematical knowledge was found to mediate some of the contributions of both working memory and classroom behavior on variability in fraction outcomes. These supported mediating processes extend the current literature by explication of the pathways via which characteristics of children may affect individual differences in fraction outcomes.     

Children's strategies in computational estimation

We investigated strategies used to estimate answers to addition problems. Two hundred and sixteen participants (72 adults, 72 sixth graders, and 72 fourth graders) had to provide estimates of three-by-three digit addition problems (e.g., 249 + 743). The choice/no-choice method was used to obtain unbiased estimates of the performance characteristics of strategies. Results showed that (a) at all ages, the most common strategy was to round both operands down to the closest smaller decades, (b) strategy use and execution were influenced by participants' age, problem features, and relative strategy performance, and (c) age-related changes in computational estimation include changes in relative strategy use and execution, as well as in the relative influences of problem and strategy characteristics on strategy choices. Implications of these findings for understanding age-related differences in strategic aspects of computational estimation performance are discussed.     

Cognitive estimations as a measure of executive dysfunction in childhood epilepsy

Children and adolescents with epilepsy are known to demonstrate executive function deficits. Despite prior work that has shown that cognitive estimation tasks are sensitive to executive dysfunction in children, such tasks have not been studied in children with epilepsy. This is particularly important given the fact that executive tasks have heretofore shown poor ecological validity, and it has been speculated that estimation tasks may show stronger ecological validity than other executive tests. One hundred and thirteen clinically referred children and adolescents with epilepsy were included. The Biber Cognitive Estimations Test was sensitive to cognitive dysfunction, with about half showing impairments on this task in comparison to age-matched normative data; the most frequently impaired subscales were quantity estimation and time estimation. Moreover, the Biber Cognitive Estimation Test showed moderate correlations with not only overall intellectual functions and academic achievement but also other commonly administered tests of executive functions, including digit span, Trailmaking, and the Tower of London but not with the contingency naming test. Cognitive estimations were also modestly correlated with age of epilepsy onset but not other epilepsy-severity variables such as number of antiepilepsy drugs (AEDs) or seizure frequency. Unfortunately, the hypothesis that the Biber Cognitive Estimation Test would show strong ecological validity was not supported, as it showed weak relations with parent-reported executive function deficits. The significance and limitations of this investigation are discussed.     

Virtual Week: Validity and psychometric properties of a Polish adaptation

IntroductionProspective memory (PM) refers to memory for future intentions and it is essential for safe and independent living. This paper focuses on Virtual Week (VW), a measure that was developed to closely represent everyday PM tasks in an English language setting in North America and Australia.ObjectivesThe main objective of the present study is to offer the results of a Polish adaptation of VW and present the validity and psychometric properties of the adapted version.MethodThe Spearman-Brown split-half reliability coefficients and Cronbach's alphas were estimated in 77 young adults and 83 healthy older adults. To confirm the validity of the Polish VW, we analyzed whether it is sensitive to the pattern of PM deficits in the healthy elderly that is consistent with mechanisms underlying PM performance as well as theories of normal aging.ResultsThe Polish VW was found to have strong psychometric properties and be sensitive to theory- and data-based effects on PM.ConclusionThe findings strongly encourage the use of VW for experimental purposes in healthy older adults. They provide further evidence that VW has a universal appeal and may be used in non-English speaking European samples.