Dataset Information

Modeling Nonlinear Conditional Dependence Between Response Time and Accuracy.

ABSTRACT: The most common process variable available for analysis due to tests presented in a computerized form is response time. Psychometric models have been developed for joint modeling of response accuracy and response time in which response time is an additional source of information about ability and about the underlying response processes. While traditional models assume conditional independence between response time and accuracy given ability and speed latent variables (van der Linden, 2007), recently multiple studies (De Boeck and Partchev, 2012; Meng et al., 2015; Bolsinova et al., 2017a,b) have shown that violations of conditional independence are not rare and that there is more to learn from the conditional dependence between response time and accuracy. When it comes to conditional dependence between time and accuracy, authors typically focus on positive conditional dependence (i.e., relatively slow responses are more often correct) and negative conditional dependence (i.e., relatively fast responses are more often correct), which implies monotone conditional dependence. Moreover, most existing models specify the relationship to be linear. However, this assumption of monotone and linear conditional dependence does not necessarily hold in practice, and assuming linearity might distort the conclusions about the relationship between time and accuracy. In this paper we develop methods for exploring nonlinear conditional dependence between response time and accuracy. Three different approaches are proposed: (1) A joint model for quadratic conditional dependence is developed as an extension of the response moderation models for time and accuracy (Bolsinova et al., 2017b); (2) A joint model for multiple-category conditional dependence is developed as an extension of the fast-slow model of Partchev and De Boeck (2012); (3) An indicator-level nonparametric moderation method (Bolsinova and Molenaar, in press) is used with residual log-response time as a predictor for the item intercept and item slope. Furthermore, we propose using nonparametric moderation to evaluate the viability of the assumption of linearity of conditional dependence by performing posterior predictive checks for the linear conditional dependence model. The developed methods are illustrated using data from an educational test in which, for the majority of the items, conditional dependence is shown to be nonlinear.

SUBMITTER: Bolsinova M

PROVIDER: S-EPMC6137682 | biostudies-literature | 2018

REPOSITORIES: biostudies-literature

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Publications

Modeling Nonlinear Conditional Dependence Between Response Time and Accuracy.

Bolsinova Maria M Molenaar Dylan D

Frontiers in psychology 20180907

The most common process variable available for analysis due to tests presented in a computerized form is response time. Psychometric models have been developed for joint modeling of response accuracy and response time in which response time is an additional source of information about ability and about the underlying response processes. While traditional models assume conditional independence between response time and accuracy given ability and speed latent variables (van der Linden, 2007), rece ...[more]

PMID: 30245650

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Project description:In the study of numeracy, some hypotheses have been based on response time (RT) as a dependent variable and some on accuracy, and considerable controversy has arisen about the presence or absence of correlations between RT and accuracy, between RT or accuracy and individual differences like IQ and math ability, and between various numeracy tasks. In this article, we show that an integration of the two dependent variables is required, which we accomplish with a theory-based model of decision making. We report data from four tasks: numerosity discrimination, number discrimination, memory for two-digit numbers, and memory for three-digit numbers. Accuracy correlated across tasks, as did RTs. However, the negative correlations that might be expected between RT and accuracy were not obtained; if a subject was accurate, it did not mean that they were fast (and vice versa). When the diffusion decision-making model was applied to the data (Ratcliff, 1978), we found significant correlations across the tasks between the quality of the numeracy information (drift rate) driving the decision process and between the speed/accuracy criterion settings, suggesting that similar numeracy skills and similar speed-accuracy settings are involved in the four tasks. In the model, accuracy is related to drift rate and RT is related to speed-accuracy criteria, but drift rate and criteria are not related to each other across subjects. This provides a theoretical basis for understanding why negative correlations were not obtained between accuracy and RT. We also manipulated criteria by instructing subjects to maximize either speed or accuracy, but still found correlations between the criteria settings between and within tasks, suggesting that the settings may represent an individual trait that can be modulated but not equated across subjects. Our results demonstrate that a decision-making model may provide a way to reconcile inconsistent and sometimes contradictory results in numeracy research.

Dataset Information

Modeling Nonlinear Conditional Dependence Between Response Time and Accuracy.

Publications

Modeling Nonlinear Conditional Dependence Between Response Time and Accuracy.

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