Hoben Thomas

Almost nonparametric inference for repeated measures in mixture models

We consider ways to estimate the mixing proportions in a finite mixture distribution or to estimate the number of components of the mixture distribution without making parametric assumptions about the component distributions. We require a vector of observations on each subject. This vector is mapped into a vector of 0s and 1s and summed. The resulting distribution of sums can be modelled as a mixture of binomials. We then work with the binomial mixture. The efficiency and robustness of this method are compared with the strategy of assuming multivariate normal mixtures when, typically, the true underlying mixture distribution is different. It is shown that in many cases the approach based on simple binomial mixtures is superior.

Sex differences in speed of mental rotation and the X-linked genetic hypothesis ☆

Abstract Response times to a mental rotation task from 12 studies involving 505 adults were used to evaluate hypotheses concerning sex differences derived from an X-linked genetic model. The model assumes task facilitation in speed of mental rotation is mediated by a recessive gene. Four of five hypotheses derived from the model were confirmed in the results.

A theory of high mathematical aptitude

Abstract Talent searches identifying mathematically able junior high school youth have shown, on a number of summary statistics, remarkably consistent sex differences on mathematical aptitude test scores. To date no theory has been presented which can account for the data. A model is proposed which assumes there is a sex-linked gene which facilitates high mathematical test score performance. The model accounts for the ordered data relations.

Examining individual differences in infants’ habituation patterns using objective quantitative techniques

The assessment of individual differences in infant habituation patterns is important for answering basic questions about continuity in cognitive development. Nevertheless, there are flaws with existing methods for determining relevant parameters of the cognitive processes associated with habituation. In this paper, a more rigorous, model-based alternative approach is illustrated. The approach demonstrates how the habituation data of individual infants may be fit by specific functions, how habituation may be distinguished from random responding, and how the parameter estimates of individual infants’ habituation functions might be analyzed for meaningful subgroups or clusters. The model-based approach provides novel insights about individual subgroups when applied to a real habituation data set and thereby demonstrates the feasibility and utility of the techniques advocated.

A theory explaining sex differences in high mathematical ability has been around for some time

of the original article: Several hundred thousand intellectually talented 12to 13-year-olds have been tested nationwide over the past 16 years with the mathematics and verbal sections of the Scholastic Aptitude Test (SAT). Although no sex differences in verbal ability have been found, there have been consistent sex differences favoring males in mathematical reasoning ability, as measured by the mathematics section of the SAT (SAT-M). These differences are most pronounced at the highest levels of mathematical reasoning, they are stable over time, and they are observed in other countries as well. The sex difference in mathematical reasoning ability can predict subsequent sex differences in achievement in mathematics and science and is therefore of practical importance. To date a primarily environmental explanation for the difference in ability has not received support from the numerous studies conducted over many years by the staff of Study of Mathematically Precocious Youth (SMPY) and others. We have studied some of the classical environmental hypotheses: attitudes toward mathematics, perceived usefulness of mathematics, confidence, expectations/encouragement from parents and others, sex-typing, and differential course-taking. In addition, several physiological correlates of extremely high mathematical reasoning ability have been identified (left-handedness, allergies, myopia, and perhaps bilateral representation of cognitive functions and prenatal hormonal exposure). It is therefore proposed that the sex difference in SAT-M scores among intellectually talented students, which may be related to greater male variability, results from both environmental and biological factors. A theory explaining sex differences in high mathematical ability has been around for some time

A test of the X-linked genetic hypothesis for sex differences on Piaget's water-level task

Abstract Data from seven studies involving 849 high school and college students were used to test the recessive X-linked genetic model prediction that the square of the proportion of men who perform accurately on the water-level task is equal to the proportion of women who perform accurately. Goodness-of-fit tests showed that this prediction was confirmed for each sample. A model with a single estimate of gene frequency accounted for all the data when a classification error parameter was incorporated into the X-linked model. In both models the gene frequency parameter was about 2 3 .

Competency Criteria and the Class Inclusion Task: Modeling Judgments and Justifications.

Preschool age childrens class inclusion task responses were modeled as mixtures of different probability distributions. The main idea: Different response strategies are equivalent to different probability distributions. A child displays cognitive strategy s if P (child uses strategy s, given the childs observed score X = x) = p(s) is the most probable strategy. The general approach is widely applicable to many settings. Both judgment and justification questions were asked. Judgment response strategies identified were subclass comparison, guessing, and inclusion logic. Childrens justifications lagged their judgments in development. Although justification responses may be useful, C. J. Brainerd was largely correct: If a single response variable is to be selected, a judgments variable is likely the preferable one. But the process must be modeled to identify cognitive strategies, as B. Hodkin has demonstrated.

Individual Differences and Development in Water-Level Task Performance.

Abstract Data from 23 samples of subjects aged 6.5 years to college age were modeled by a binomial mixture distribution which allows for individual differences in probability of successful task performance. At almost every age and for each sex there are two kinds of performers: those with a high probability of task success (accurate performers) and those with a low probability of task success (inaccurate performers). Age-related improvement of performance is not a consequence of children becoming gradually more accurate in task performance. Improvement is due largely to the increasing proportions of subjects that become accurate performers. Between-sex differences in performance are in evidence at all ages. The proportion of accurate performers is larger in males than in females at every age.

Prediction of childhood cognitive abilities from a set of early indicators of information processing capabilities

Childhood tests of intelligence are often composed of several different tasks or scales. In contrast to this, many studies assessing early indicators of cognitive ability include only one or two different infant paradigms. The present study employs an extended set of infant paradigms for the prediction of childhood development and intelligence. Two groups of infants (64 three- and 63 six-months olds) were tested. Subjects were retested at 24- and 32-months of age with several indicators related to developmental state, verbal skills and intelligence. Especially in the group of 6-month-olds, the analysis demonstrated that significant R(2) contributions were yielded by a set of different predictor variables. The results show that a set of predictors in contrast to single predictors leads to a substantial increase of the variance accounted for.

Habituation assessment in infancy

Infant-control habituation methodology, although serving the research community well, has never been carefully analyzed. A main use is to equate infants in their level of habituation prior to experimental manipulations in a posthabituation phase. When studied analytically and with simulation, it is found to have serious difficulties. It inadvertently recruits infants with large variations in performance while discriminating against those with less variable performance. For nonhabituating infants, its Type I error rates can approach 1. A model-based nonlinear regression framework is proposed, which, because of large individual differences in infants, takes as the unit of analysis the individual infant. It is shown to be more powerful and efficient than existing procedures and can offer practical and theoretical benefits.