Subjects' simplification of rules for estimating money saved when buying a specified quantity of a cheaper product compared with a more expensive one

Abstract.— Estimates of money saved, when buying a specified quantity of flowers of a cheaper kind compared with a more expensive kind, were collected from two different groups, for different quantities and combinations of prices. One group gave their estimates in 13 sec, and the other in 15 sec. The data were analysed according to four different models, all consisting of a multiplicative combination of two components, one related to the quantity to be bought and the other to the combination of prices. The estimates of both groups showed systematic deviation from the correct savings, and the estimates of the groups were best described by one simple and one more complex model respectively.     

Cognitive procedures for correcting proxy‐response biases in surveys

To reduce survey costs, major surveys rely on self‐ and proxy‐responses. The use of proxies can reduce data quality introducing biases in the survey estimates. This paper identifies one source of systematic differences between self‐ and proxy‐reports: proxies' higher reliance on inferences. Using data from the National Health Interview Survey on Disability (NHIS‐D), proxy‐response biases were modelled by independently collected measures of cognitive inferences. Conditional likelihood judgements about a number of disabilities (e.g. likelihood that a person has a disability given another disability) predicted the conditional disability reports for proxy‐ but not for self‐respondents (e.g. the proportion of respondents who reported difficulty learning after reporting difficulty communicating). A model of self/proxy differences was estimated on data from the 1994 NHIS‐D and tested against 1995 data. The correlation between predicted and actual differences was 0.76. The correlation between predicted and actual proxy‐reports was 0.95. Such research can be used to estimate and correct for systematic proxy‐response biases. Copyright © 2002 John Wiley & Sons, Ltd.     

A clusterwise simultaneous component method for capturing within‐cluster differences in component variances and correlations

This paper presents a clusterwise simultaneous component analysis for tracing structural differences and similarities between data of different groups of subjects. This model partitions the groups into a number of clusters according to the covariance structure of the data of each group and performs a simultaneous component analysis with invariant pattern restrictions (SCA‐P) for each cluster. These restrictions imply that the model allows for between‐group differences in the variances and the correlations of the cluster‐specific components. As such, clusterwise SCA‐P is more flexible than the earlier proposed clusterwise SCA‐ECP model, which imposed equal average cross‐products constraints on the component scores of the groups that belong to the same cluster. Using clusterwise SCA‐P, a finer‐grained, yet parsimonious picture of the group differences and similarities can be obtained. An algorithm for fitting clusterwise SCA‐P solutions is presented and its performance is evaluated by means of a simulation study. The value of the model for empirical research is illustrated with data from psychiatric diagnosis research.     

On the handling of heavy bias in a self-paced task

Following an earlier observation that systematic variations in performance on a task with heavy frequency imbalance was correlated with fluctuations in the amount of bias in the input programme, an experiment was carried out to establish the roles of long and short term sampling. Two groups of subjects were trained on a self-paced, five-choice task. One group's input had an average of 68 per cent. bias on one source, the other had 44 per cent. on the same source. Analysis of data was carried out on three levels of local bias for each condition, one level being identical for both conditions. It was found that responses to the biased stimuli were determined by the average bias in each input sequence and not by moment to moment variations in that bias. The effect observed originally can therefore be accounted for in terms of a relatively simple additive model which includes the “repetition effect” first described by Bertelson.     

How to detect which variables are causing differences in component structure among different groups

When comparing the component structures of a multitude of variables across different groups, the conclusion often is that the component structures are very similar in general and differ in a few variables only. Detecting such “outlying variables” is substantively interesting. Conversely, it can help to determine what is common across the groups. This article proposes and evaluates two formal detection heuristics to determine which variables are outlying, in a systematic and objective way. The heuristics are based on clusterwise simultaneous component analysis, which was recently presented as a useful tool for capturing the similarities and differences in component structures across groups. The heuristics are evaluated in a simulation study and illustrated using cross-cultural data on values.     

A theory of variability discrimination: Finding differences

Visual variability discrimination requires an observer to categorize collections of items on the basis of the variability in the collection; such discriminations may be vital to the adaptive actions of both humans and other animals. We present a theory of visual variability discrimination that aggregates localized differences between nearby items, and we compare this finding differences model with a previously proposed positional entropy model across several data sets involving both people and pigeons. We supplement those previously published data sets with four new experiments, three of which involve arrays comprising items entailing systematic, quantitative differences. Although both theories provide strong and similar fits of the published data sets, only the finding differences model is applicable to investigations involving quantitative item differences, providing excellent fits in these new experiments.     

Processing strategy moderates the cultivation effect

This study tested the hypothesis that processing strategy moderates the effect of television viewing on social perceptions (cultivation effect). One hundred twenty‐two male and female students provided estimates of the prevalence of crime, occupations, affluence, and marital discord under one of three conditions. Some participants were induced to process heuristically (heuristic group) through instructions to provide their estimates spontaneously with little elaboration. Other participants were induced to process systematically (systematic group) through an accuracy motivation/task importance manipulation. A third (control) group received instructions to simply answer the questions. The results indicated that processing strategy moderated the cultivation effect such that cultivation effects were noted in the heuristic and control groups but not in the systematic group. These results are consistent with the notion that the cultivation effect can be explained in part as the result of heuristic processing through lack of source discounting, and they provide support for the heuristic processing model of cultivation effects.     

On the importance of distinguishing between within- and between-subject effects in intransitive intertemporal choice

Most probabilistic paired comparison models treat inconsistent choices as caused by independent and random errors in the pairwise judgments. In this paper, we argue that this assumption is too restrictive for the analysis of paired comparison data obtained from multiple judges when transitivity violations are systematic. We present a new framework that contains the random error assumption as a special case but also allows for systematic changes in an option's utility assessments over the pairwise comparisons. Accounting for both between- and within-judge sources of variability, we demonstrate in an application on intertemporal choice that the proposed framework can capture systematic transitivity violations as well as individual taste differences.     

Beta-MPT: Multinomial processing tree models for addressing individual differences

Traditionally, multinomial processing tree (MPT) models are applied to groups of homogeneous participants, where all participants within a group are assumed to have identical MPT model parameter values. This assumption is unreasonable when MPT models are used for clinical assessment, and it often may be suspect for applications to ordinary psychological experiments. One method for dealing with parameter variability is to incorporate random effects assumptions into a model. This is achieved by assuming that participants’ parameters are drawn independently from some specified multivariate hyperdistribution. In this paper we explore the assumption that the hyperdistribution consists of independent beta distributions, one for each MPT model parameter. These beta-MPT models are ‘hierarchical models’, and their statistical inference is different from the usual approaches based on data aggregated over participants. The paper provides both classical (frequentist) and hierarchical Bayesian approaches to statistical inference for beta-MPT models. In simple cases the likelihood function can be obtained analytically; however, for more complex cases, Markov Chain Monte Carlo algorithms are constructed to assist both approaches to inference. Examples based on clinical assessment studies are provided to demonstrate the advantages of hierarchical MPT models over aggregate analysis in the presence of individual differences.     

Words high and low in pleasantness as rated by male and female college students

No catalog of words currently available contains normative data for large numbers of words rated low or high in affect. A preliminary sample of 1,545 words was rated for pleasantness by 26–33 college students. Of these words, 274 were selected on the basis of their high or low ratings. These words, along with 125 others (Rubin, 1981), were then rated by additional groups of 62–76 college students on 5-point rating scales for the dimensions of pleasantness, imagery, and familiarity. The resulting mean ratings were highly correlated with the ratings obtained by other investigators using some of the same words. However, systematic differences in the ratings were found for male versus female raters. Females tended to use more extreme ratings than did males when rating words on the pleasantness scale. Also, females tended to rate words higher on the imagery and familiarity scales. Whether these sex differences in ratings represent cognitive differences between the sexes or merely differences in response style is a question that can be determined only by further research.     

Mapping and correcting the influence of gaze position on pupil size measurements

Pupil size is correlated with a wide variety of important cognitive variables and is increasingly being used by cognitive scientists. Pupil data can be recorded inexpensively and non-invasively by many commonly used video-based eye-tracking cameras. Despite the relative ease of data collection and increasing prevalence of pupil data in the cognitive literature, researchers often underestimate the methodological challenges associated with controlling for confounds that can result in misinterpretation of their data. One serious confound that is often not properly controlled is pupil foreshortening error (PFE)—the foreshortening of the pupil image as the eye rotates away from the camera. Here we systematically map PFE using an artificial eye model and then apply a geometric model correction. Three artificial eyes with different fixed pupil sizes were used to systematically measure changes in pupil size as a function of gaze position with a desktop EyeLink 1000 tracker. A grid-based map of pupil measurements was recorded with each artificial eye across three experimental layouts of the eye-tracking camera and display. Large, systematic deviations in pupil size were observed across all nine maps. The measured PFE was corrected by a geometric model that expressed the foreshortening of the pupil area as a function of the cosine of the angle between the eye-to-camera axis and the eye-to-stimulus axis. The model reduced the root mean squared error of pupil measurements by 82.5 % when the model parameters were pre-set to the physical layout dimensions, and by 97.5 % when they were optimized to fit the empirical error surface.     

Ordinal properties of subjective ratios and differences: Comment on Veit

Because nonmetric analyses of judged ratios and differences in sensory magnitude have yielded similar scales, some investigators have concluded that a single perceived relation underlies both judgment tasks. Issues rasied by this interpretation are considered in this article. Simulated data based on the assumption that subjects evaluate both perceived relations were computed for stimulus values used by Veit to investigate judgments of ratios and differences in grayness. A nonmetric analysis of both sets of simulated data in terms of a difference model yielded a solution such that each set of data was a weak monotonic transformation of the model's values, and the scale values were approximately linear with those obtained by Veit from empirical data. This result leaves open the question of whether one or two perceived relations underly the data. Ordinal properties of ratios and differences for a finite set are discussed together with their relation to systematic biases in psychophysical judgment tasks.     

Effects of subliminal stimulation on masculinity-femininity ratings of a male model

The effects of subliminal stimulation on masculinity-femininity ratings of a male model were tested for 100 male undergraduates, randomly divided into four groups and individually shown a slide of a male model. One group received no further stimulation. A second group received a subliminal flash of white light across the image of the model; a third group was presented with the subliminal message "masculine," while a fourth group was presented with the subliminal message "feminine." Subjects were asked to rate the model on a six-point scale of masculinity-femininity. The differences in ratings among groups were not significant, indicating that subliminal stimulation did not influence masculinity-femininity value-norm-anchor judgments. There were no significant differences in the reported perception of additional stimuli or the tendency to be relaxed among the four groups. However, subjects who received the "masculine" message and reported that they were more relaxed did tend to rate the model higher in masculinity.     

Procedural learning across the lifespan: A systematic review with implications for atypical development

This systematic review aimed to investigate procedural learning across the lifespan in typical and atypical development. Procedural learning is essential for the development of everyday skills, including language and communication skills. Although procedural learning efficiency has been extensively studied, there is no consensus yet on potential procedural learning changes during development and ageing. Currently, three conflicting models regarding this trajectory exist: (1) a model of age invariance; (2a) a model with a peak in young adulthood; and (2b) a model with a plateau in childhood followed by a decline. The aims of this study were (1) to investigate this debate on procedural learning across the lifespan by systematically reviewing evidence for each model from studies using the serial reaction time task; and (2) to review procedural learning in autism spectrum disorder (ASD) and specific language impairment (SLI), two developmental disorders characterized by deficits in communication skills, in the light of these models. Our findings on typical development strongly support a model of age-related changes (Model 2a or 2b) and show that mixed findings regarding the developmental trajectory during childhood can be explained by methodological differences across studies. Applying these conclusions to systematic reviews of studies of ASD and SLI makes it clear that there is a strong need for the inclusion of multiple age groups in these clinical studies to model procedural learning in atypical development. Clinical implications of the findings are discussed. Future research should focus on the role of declarative learning in both typical and atypical development.     

White South Africans' Reactions to Black Advancement: A Two-Sample Confirmatory Investigation of the Structure of Attitude Using an Analogy to the Multitrait-Multimethod Design

The tripartite (affective, conative, cognitive) theory of attitude has been investigated in a number of empirical studies, with findings mostly favoring the theory. Little attention has been paid, however, to other important characteristics of attitude. One of these is multiplexity which refers to the number of separate domains into which an attitude object can be partitioned. In this study, a data design was used which made it possible to investigate trait and domain structure simultaneously. A questionnaire measuring affective, conative, and cognitive responses to three aspects of black advancement was administered to two groups of white South Africans: English speakers employed by a large private-sector company and Afrikaans speakers employed by the government. Confirmatory techniques were employed to investigate the structure of the data. Single-group analysis procedures adapted from Widaman (1985) were initially performed to establish a model satisfactory for both samples. Multi-group procedures were then performed on the two samples to investigate group differences in data structure. The structure was very similar in the two samples with the exception that domain variances were smaller in the English-speaking sample.     

The use of structured learning therapy and transfer programming with disruptive adolescents in a school setting

In behavior change literature, little attention has been paid to the systematic study of variables affecting transfer of training. The present study employed a skill-training method known as Structured Learning Therapy (SLT) for the dual purpose of testing the effectiveness of this method and to identify variables that will promote transfer of training. Forty-three disruptive male adolescents were assigned to three experimental and two control conditions. One experimental group received SLT plus an additional transfer-enhancing procedure referred to as Transfer Programming (TP) which consisted of in vivo practice of treatment gains and peer reinforcement. Another group received only SLT, and a third group received only TP. One control group received only brief instructions pertaining to the nature of the skill, while the second group served as an attention control. Consistent with predictions, the results were that the two groups receiving the SLT performed significantly better than the three groups not receiving SLT on all dependent measures at posttest. These differences generally maintained at follow-up. Contrary to expectations, the implementation of TP did not prove to promote transfer of training beyond that found with SLT alone.     

Separating response‐execution bias from decision bias: Arguments for an additional parameter in Ratcliff's diffusion model

Diffusion model data analysis permits the disentangling of different processes underlying the effects of experimental manipulations. Estimates can be provided for the speed of information accumulation, for the amount of information used to draw conclusions, and for a decision bias. One parameter describes the duration of non‐decisional processes including the duration of motor‐response execution. In the default diffusion model, it is implicitly assumed that both responses are executed with the same speed. In some applications of the diffusion model, this assumption will be violated. This will lead to biased parameter estimates. Consequently, we suggest accounting explicitly for differences in the speed of response execution for both responses. Results from a simulation study illustrate that parameter estimates from the default model are biased if the speed of response execution differs between responses. A second simulation study shows that large trial numbers (N>1,000) are needed to detect whether differences in response‐execution times are based on different execution times.     

Modeling individual differences using Dirichlet processes

We introduce a Bayesian framework for modeling individual differences, in which subjects are assumed to belong to one of a potentially infinite number of groups. In this model, the groups observed in any particular data set are not viewed as a fixed set that fully explains the variation between individuals, but rather as representatives of a latent, arbitrarily rich structure. As more people are seen, and more details about the individual differences are revealed, the number of inferred groups is allowed to grow. We use the Dirichlet process—a distribution widely used in nonparametric Bayesian statistics—to define a prior for the model, allowing us to learn flexible parameter distributions without overfitting the data, or requiring the complex computations typically required for determining the dimensionality of a model. As an initial demonstration of the approach, we present three applications that analyze the individual differences in category learning, choice of publication outlets, and web-browsing behavior.     

Some deterministic models of concept identification

It is shown that deterministic models can compete effectively with stochastic models in summarizing concept identification behavior. Three groups of deterministic models are examined. Examination of individual learners' trial by trial behavior in a concept experiment shows: (1) One person exhibited behavior consistent with a Hypothesis Permutation (HP) model despite being a nonlearner who showed no evidence of improvement over a period of 24 trials. However, when all 50 persons studied in each of two treatment groups were examined, only 22 members of one group and 10 of the other showed no inconsistencies with deterministic local consistency assumptions. (2) Certain deterministic computer programs could find at least one satisfactory order for predicting all responses by 18 of the 22 consistent solvers and 6 of the 10 consistent solvers, respectively, in the two groups just mentioned. For these 24 persons, then, a less restrictive deterministic model is adequate than for the others. (3) Those 38 original members of the first treatment group who met a stringent learning criterion were compared with respect to predictions generated by stochastic and mathematized deterministic models. One deterministic model (RSS-U 9-state) is in some respects the best of the models examined, but this success is a partial reflection of estimating eight parameters from the data.     

On the relationship between sources of within- and between-group differences and measurement invariance in the common factor model

Investigating sources of within- and between-group differences and measurement invariance (MI) across groups is fundamental to any meaningful group comparison based on observed test scores. It is shown that by placing certain restrictions on the multigroup confirmatory factor model, it is possible to investigate the hypothesis that within- and between-group differences are due to the same factors. Moreover, the modeling approach clarifies that absence of measurement bias implies common sources of within- and between-group variation. It is shown how the influence of background variables can be incorporated in the model. The advantages of the modeling approach as compared with other commonly used methods for group comparisons is discussed and illustrated by means of an analysis of empirical data.