On the aggregation across subjects in analyzing individual choice behavior

Authors dealing with models of individual choice behavior often point out the pitfalls of using group data to test such models. However, it is possible to derive properties of the choice behavior of the population based on these models of individual choice behavior. The present paper develops a procedure for the aggregation of choice data which takes into account individual differences. The utility of using aggregated choice data and the properties of the present procedure in comparison to other methods which utilized group data in analyzing choice behavior are discussed.     

Process traces of binary choices: Evidence for selective and adaptive decision heuristics

While previous research has shown that human decision processes adjust to the characteristics of choice situations and task demands, the present study examined whether information processing would even adapt to the characteristics of an individual choice pair. By a process tracing method it was found that the amount of inspected information systematically depended upon the particular choice pair. In order to specify the selective and adaptive information processing, criterion-dependent choice models were introduced. These models postulate that information processing continues until the accumulated amount by which one alternative is better than the other reaches or exceeds a certain criterion. These models are strongly supported by the empirical data of the present study. Deviations between model predictions and observed data are explained in terms of fluctuating feature values of the choice alternatives.     

Structural equation modeling of paired-comparison and ranking data

L. L. Thurstone's (1927) model provides a powerful framework for modeling individual differences in choice behavior. An overview of Thurstonian models for comparative data is provided, including the classical Case V and Case III models as well as more general choice models with unrestricted and factor-analytic covariance structures. A flow chart summarizes the model selection process. The authors show how to embed these models within a more familiar structural equation modeling (SEM) framework. The different special cases of Thurstone's model can be estimated with a popular SEM statistical package, including factor analysis models for paired comparisons and rankings. Only minor modifications are needed to accommodate both types of data. As a result, complex models for comparative judgments can be both estimated and tested efficiently.     

The influence of component participation and role models on goal acceptance, goal satisfaction, and performance

The present investigation examined the effects of different types of participation (choice) and role models in goal setting on goal acceptance, goal satisfaction, and performance. It was hypothesized that choice in setting a goal and a strategy to achieve the goal would positively benefit goal acceptance, performance, and goal satisfaction. In addition, it was predicted that a role model would differentially influence an individual's goal acceptance, goal satisfaction, and performance. One hundred twenty male college students working on a class scheduling task were exposed to either a high- or low-performing role model and given various amounts of choice in the goal-setting process. The results of two-way analyses of variance demonstrated that goal acceptance, goal satisfaction, and performance were highest for individuals given choice over their goal and their strategy to achieve the goal. In addition, the results demonstrated that an individual exposed to a high-performing role model outperformed and had higher goal acceptance and satisfaction than an individual exposed to a low-performing model. The results are discussed as a means for clarifying the effects of different types of choice in the goal-setting process and the importance of role-provided information in influencing an individual's performance.     

Measurement of Ability in Adaptive Learning and Assessment Systems when Learners Use On-Demand Hints

Adaptive learning and assessment systems support learners in acquiring knowledge and skills in a particular domain. The learners’ progress is monitored through them solving items matching their level and aiming at specific learning goals. Scaffolding and providing learners with hints are powerful tools in helping the learning process. One way of introducing hints is to make hint use the choice of the student. When the learner is certain of their response, they answer without hints, but if the learner is not certain or does not know how to approach the item they can request a hint. We develop measurement models for applications where such on-demand hints are available. Such models take into account that hint use may be informative of ability, but at the same time may be influenced by other individual characteristics. Two modeling strategies are considered: (1) The measurement model is based on a scoring rule for ability which includes both response accuracy and hint use. (2) The choice to use hints and response accuracy conditional on this choice are modeled jointly using Item Response Tree models. The properties of different models and their implications are discussed. An application to data from Duolingo, an adaptive language learning system, is presented. Here, the best model is the scoring-rule-based model with full credit for correct responses without hints, partial credit for correct responses with hints, and no credit for all incorrect responses. The second dimension in the model accounts for the individual differences in the tendency to use hints.     

Modeling within-subject dependencies in ordinal paired comparison data

This paper presents two probabilistic models based on the logistic and the normal distribution for the analysis of dependencies in individual paired comparison judgments. It is argued that a core assumption of latent class choice models, independence of individual decisions, may not be well-suited for the analysis of paired comparison data. Instead, the analysis and interpretation of paired comparison data may be much simplified by allowing for within-person dependencies that result from repeated evaluations of the same options in different pairs. Moreover, by relating dependencies among the individual-level responses to (in)consistencies in the judgmental process, we show that the proposed graded paired comparison models reduce to ranking models under certain conditions. Three applications are presented to illustrate the approach.This research was partially supported by NSF grant SBR-9409531. The authors are grateful to the reviewers, Alan Agresti and Herbert Hoijtink for their helpful comments on this research.     

Individual solution processes while solving addition and multiplication math facts in adults

Contrary to predictions of current solution process models, adults used a variety of procedures other than retrieval to solve addition and multiplication math facts. Predictors assumed to capture retrieval processes posited by such models did account for a substantial proportion of variance in averaged retrieval solution times. But most of the variance in individual participants' retrieval times remained unaccounted for. Cross-operation associations in patterns of strategy use and retrieval latencies were obtained. Adults with stronger higher level math achievement were more likely to use retrieval, solved math facts faster and less variably, and executed retrieval processes posited by current solution process models faster than participants with less math attainment. The results are explained within the context of the adaptive strategy choice model.     

A marginal maximum likelihood method for the vector threshold model to analyze dichotomous choice data

Abstract: At least two types of models, the vector model and the unfolding model can be used for the analysis of dichotomous choice data taken from, for example, the pick any/ n method. The previous vector threshold models have a difficulty with estimation of the nuisance parameters such as the individual vectors and thresholds. This paper proposes a new probabilistic vector threshold model, where, unlike the former vector models, the angle that defines an individual vector is a random variable, and where the marginal maximum likelihood estimation method using the expectation-maximization algorithm is adopted to avoid incidental parameters. The paper also attempts to discuss which of the two models is more appropriate to account for dichotomous choice data. Two sets of dichotomous choice data are analyzed by the model.     

Improving the quality of careers guidance: Towards an understanding of the development of personal models

The process by which careers officers develop personal models of guidance through the interaction of theoretical knowledge with their experiences of training and practice is examined. Semi-structured interviews were conducted with 11 careers officers. Questions were asked about the training and development of careers officers in the practice of careers guidance and counselling with young people. The responses are considered in relation to theories of careers choice, careers counselling and guidance, models of counselling, and the supervisory role in the development of individual practice. Some recommendations are made for improvements to training and supervision for careers guidance.     

The Role of Independence and Stationarity in Probabilistic Models of Binary Choice

After more then 50 years of probabilistic choice modeling in economics, marketing, political science, psychology, and related disciplines, theoretical and computational advances give scholars access to a sophisticated array of modeling and inference resources. We review some important, but perhaps often overlooked, properties of major classes of probabilistic choice models. For within‐respondent applications, we discuss which models require repeated choices by an individual to be independent and response probabilities to be stationary. We show how some model classes, but not others, are invariant over variable preferences, variable utilities, or variable choice probabilities. These models, but not others, accommodate pooling of responses or averaging of choice proportions within participant when underlying parameters vary across observations. These, but not others, permit pooling/averaging across respondents in the presence of individual differences. We also review the role of independence and stationarity in statistical inference, including for probabilistic choice models that, themselves, do not require those properties. Copyright © 2017 John Wiley & Sons, Ltd.     

Alphabetic confusion: A test of models for individuals

An earlier article reported extensive analyses of confusion data compiled from group averages (Townsend, 1971). The present study provided for essentially the same analyses with different long-term data obtained with two individuals, the primary intent being to examine the ability of recognition and scaling models to explain data at the individual level (which the recognition models purport to describe) and to compare the confusion characteristics of the English uppercase alphabet between the two Ss and between the individual Ss and the group-averaged data. The choice and overlap models were superior to the all-or-none model in predicting the empirical confusion matrices and tended to explain the data structure in a similar manner. Multidimensional scaling analysis again supported a Euclidean metric and suggested four or five underlying stimulus dimensions. However, as before, there were no overriding intuitively appealing psychological dimensions corresponding to these, and possible reasons are discussed. The choice and overlap models appeared to fit as well or better at the individual level than at the group level and the all-or-none model to fit worse. In the present study, probability correct was fit even better by the all-or-none model than in the group study and replicated the result of being better here than the overlap and choice models. Individuals and the group were consistent in their sensory confusions as represented by similarity parameters in the choice and overlap models but differed in their response biases. A simple measure of physical similarity explained 50% of the variance of the similarity structure in the confusion data.     

A hierarchical bayesian model of human decision-making on an optimal stopping problem

We consider human performance on an optimal stopping problem where people are presented with a list of numbers independently chosen from a uniform distribution. People are told how many numbers are in the list, and how they were chosen. People are then shown the numbers one at a time, and are instructed to choose the maximum, subject to the constraint that they must choose a number at the time it is presented, and any choice below the maximum is incorrect. We present empirical evidence that suggests people use threshold-based models to make decisions, choosing the first currently maximal number that exceeds a fixed threshold for that position in the list. We then develop a hierarchical generative account of this model family, and use Bayesian methods to learn about the parameters of the generative process, making inferences about the threshold decision models people use. We discuss the interesting aspects of human performance on the task, including the lack of learning, and the presence of large individual differences, and consider the possibility of extending the modeling framework to account for individual differences. We also use the modeling results to discuss the merits of hierarchical, generative and Bayesian models of cognitive processes more generally.     

An exemplar account of the bow and set-size effects in absolute identification

The extended generalized context model for response times (K. Lamberts, 2000) was designed to account for choice proportions and response times in perceptual categorization. In this article, the hypothesis that the model also offers an account of accuracy and response times in absolute identification was investigated. The model was applied to the data from 2 absolute identification experiments and provided a good account of the bow and the set-size effects in accuracy and response time data from individual participants, including the response time distributions for individual stimuli. The model applications demonstrated that exemplar-based process models offer a viable account of absolute identification data.     

Individual differences in learning and memory: A unitary information processing approach

Recent research in the area of individual differences in learning and memory is reviewed from a cognitive perspective. Using the two-state model of memory as a framework, individual variations in attentional, short-term store, and long-term store processes are discussed. The focus is on using individual differences to evaluate nomothetic cognitive models, as well as on using cognitive models in guiding research on individual differences. Both within-individual and between-individual differences in basic processes are examined. In so doing, the importance of strategy choice is stressed using the concept of cognitive flexibility. Several promising directions, both methodological and theoretical, are noted and the value of using specific information processing models in the study of individual differences is emphasized.     

Simple matrix methods for analyzing diffusion models of choice probability, choice response time, and simple response time

Diffusion processes (e.g., Wiener process, Ornstein-Uhlenbeck process) are powerful approaches to model human information processes in a variety of psychological tasks. Lack of mathematical tractability, however, has prevented broad applications of these models to empirical data. This tutorial explains step by step, using a matrix approach, how to construct these models, how to implement them on a computer, and how to calculate the predictions made by these models. In particular, we present models for binaries choices for unidimensional and multiattribute choice alternatives; for simple reaction time tasks; and for three alternatives choice problems.     

From individual preference construction to group decisions: Framing effects and group processes

Two choice tasks known to produce framing effects in individual decisions were used to test group sensitivity to framing, relative to that of individuals, and to examine the effect of prior, individual consideration of a decision on group choice. Written post-decision reasons and pre-decision group discussions were analyzed to investigate process explanations of choices made by preexisting, naturalistic groups. For a risky choice problem, a similar framing effect was observed for groups and individuals. For an intertemporal choice task where consumption was either delayed or accelerated, naïve groups (whose members had not preconsidered the decision) showed a framing effect, less discounting in the delay frame, opposite to that observed in individuals. Predecided groups showed a non-significant effect in the other, expected direction. In all cases, process measures better explained variability in choices across conditions than frame alone. Implications for group decision research and design considerations for committee decisions are addressed.     

Integrating Cognitive Process and Descriptive Models of Attitudes and Preferences

Discrete choice experiments—selecting the best and/or worst from a set of options—are increasingly used to provide more efficient and valid measurement of attitudes or preferences than conventional methods such as Likert scales. Discrete choice data have traditionally been analyzed with random utility models that have good measurement properties but provide limited insight into cognitive processes. We extend a well‐established cognitive model, which has successfully explained both choices and response times for simple decision tasks, to complex, multi‐attribute discrete choice data. The fits, and parameters, of the extended model for two sets of choice data (involving patient preferences for dermatology appointments, and consumer attitudes toward mobile phones) agree with those of standard choice models. The extended model also accounts for choice and response time data in a perceptual judgment task designed in a manner analogous to best–worst discrete choice experiments. We conclude that several research fields might benefit from discrete choice experiments, and that the particular accumulator‐based models of decision making used in response time research can also provide process‐level instantiations for random utility models.