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.     

Adolescent Psychopathy and the Big Five: Results from Two Samples

The present study examines the relation between psychopathy and the Big Five dimensions of personality in two samples of adolescents. Specifically, the study tests the hypothesis that the aspect of psychopathy representing selfishness, callousness, and interpersonal manipulation (Factor 1) is most strongly associated with low Agreeableness, whereas the aspect of psychopathy representing impulsivity, instability, and social deviance (Factor 2) is associated with low Agreeableness, low Conscientiousness, and high Neuroticism. Data from 13- and 16-year-old boys and their mothers from two samples of the Pittsburgh Youth Study are used to test these hypotheses. Results were consistent across age and rating source in supporting the initial hypotheses, providing support for the construct of juvenile psychopathy and the interpretation of psychopathy as a constellation of traits drawn from a general model of personality functioning.     

Academic Self-Schemas and their Self-Congruent Learning Patterns: Findings Verified with Culturally Different Samples

This paper reported two studies investigating high school students’ academic self-schemas in learning mathematics and their self-congruent learning engagement patterns. Using cluster analyses, Study 1 located two contrasting groups of students holding positive and negative self-schemas in learning mathematics among Chinese participants. MANOVA analyses showed that these two groups of Chinese schematic students differed from each other in the use of achievement goals, approaches to learning, and expected levels of performance. These findings were validated and extended in Study 2 using a culturally different sample, Australian students. Again, cluster analyses successfully classified Australian participants into positive and negative schematic clusters. It was also found that these two groups of schematic students approached learning mathematics in a self-congruent manner similar to those found in Study 1. The converging results in both studies lent empirical support to the theoretical formulation of positive and negative schematic students and the validity of using the self-schema concept to investigate motivation and learning. The differences in their learning engagement patterns were discussed in terms of students’ different academic self-schemas in learning mathematics.     

Child Maltreatment and Emergent Personality Organization: Perspectives from the Five-Factor Model

The Five-Factor Model was used to examine personality organization in 211 six-year-old children (135 maltreated and 76 nonmaltreated). Longitudinal assessments were conducted at ages 7, 8, and 9. Six-year-old maltreated children exhibited lower agreeableness, conscientiousness, and openness to experience and higher neuroticism than did nonmaltreated children. Maltreated children also were more frequently represented in less adaptive personality clusters than were their nonmaltreated counterparts. A particularly vulnerable profile occurred predominantly among maltreated children and was related to experiencing both abuse and neglect. Child maltreatment and personality clusters were related to individual differences perceived by peers. Longitudinal stability of the personality dimensions also was assessed. At age nine, evidence was found for maintenance of the organization of the personality clusters obtained at age six and for continuity of maltreated children's personality liabilities.     

“Seeing Conversion Whole”: Testing a Model of Religious Conversion

Rambo (1993) theorized that religious conversion consists of a process involving seven dimensions, labeled context, crisis, quest, encounter, interaction, commitment, and consequences. To test the Rambo model, a new measure, the 97-item Adult Religious Conversion Experiences Questionnaire (ARCEQ), was developed, revised on the basis of feedback from a focus group, and administered by mail to 110 adult volunteers who self-identified as having experienced conversion. Reliability analysis of the subscales of the ARCEQ resulted in five (crisis, quest, encounter, commitment, and consequences) meeting the criterion ( > .80). A sixth (interaction) achieved a reliability of .76 and was retained, but the seventh (context) was dropped. Principal components factor analysis with Varimax rotation produced factors labeled Redemptive Love, Zealous Dedication, Dysphoric Need, Openness to Uncertainty, Extrinsic Crisis, and Experiential Learning, which could readily be interpreted in relation to Rambo's model. Subsidiary analyses showed a number of significant correlations between demographic characteristics of the sample and differences in religious conversion experience.     

语篇理解中背景信息的激活: 情景限制的共振过程

该研究采用双人物线索语篇材料,对语篇理解中背景信息激活过程的共振模型与剧景模型进行检验。实验一发现,如果主角和配角一直同时在故事情景中成为主线索,则目标句中主角的行为可以激活那些经过屏蔽的、与这一行为相关的配角特征。在实验二中,配角只是在特征描述段落中出现,而后通过适当的描述使其在故事情景中消失,使主角成为故事的主线索,结果发现,此时目标句中主角的行为并不会激活经过屏蔽的配角的特征描述。这些结果表明,背景信息的激活虽然具有共振的特点,但共振并不是无范围限制的,而是一种情景限制下的共振。     

Are multi‐layer backpropagation networks catastrophically amnesic?

Connectionist models with a backpropagation learning rule are known to have a serious problem. Such models exhibit catastrophic interference (or forgetting) with sequential training. Having learned a set of patterns, if the model is trained on another set of patterns, its performance on the first set can dramatically deteriorate very rapidly. The present study reconsiders this issue with four simulations. The model learned arithmetic facts sequentially, but the interference was only modest with random (hence approximately orthogonal) inputs. Essentially the same result was obtained when the inputs are made less orthogonal by adding irrelevant elements. Reducing the number of hidden units did not have major effects. This study suggests that the interference problem has been somewhat overstated.     

A formal model for structuring local perceptions of environmental space

The problem of constructing computational models of space that mimic those found in human spatial reasoning is addressed. This paper extends a formal model that addressed point objects in a 2D world to include the presence of line objects and barriers. The problem consists of determining an appropriate global model for the spatial configuration given a sequence of local views or observations. A formal model is proposed based on constraint network theory. The model leads to the identification of stable regions within which perceptual information about the environment changes slowly, and zones of transition within which the perceptual information changes more quickly. A special case of transition zones is a gateway, which may be viewed as a kind of discontinuity or singularity in the model. It is expected that the model obtained will be used to mimic human mental representations of navigable outdoor environments.     

Motivating operations and terms to describe them: some further refinements

Over the past decade, behavior analysts have increasingly used the term establishing operation (EO) to refer to environmental events that influence the behavioral effects of operant consequences. Nonetheless, some elements of current terminology regarding EOs may interfere with applied behavior analysts' efforts to predict, control, describe, and understand behavior. The present paper (a) describes how the current conceptualization of the EO is in need of revision, (b) suggests alternative terms, including the generic term motivating operation (MO), and (c) provides examples of MOs and their behavioral effects using articles from the applied behavior analysis literature.