Systems factorial technology with R

Behavior Research Methods volume 46, pages307–330(2014)Cite this article

Abstract

Systems factorial technology (SFT) comprises a set of powerful nonparametric models and measures, together with a theory-driven experiment methodology termed the double factorial paradigm (DFP), for assessing the cognitive information-processing mechanisms supporting the processing of multiple sources of information in a given task (Townsend and Nozawa, Journal of Mathematical Psychology 39:321–360, 1995). We provide an overview of the model-based measures of SFT, together with a tutorial on designing a DFP experiment to take advantage of all SFT measures in a single experiment. Illustrative examples are given to highlight the breadth of applicability of these techniques across psychology. We further introduce and demonstrate a new package for performing SFT analyses using R for statistical computing.

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Notes

  1. 1.

    In other areas of cognitive modeling, architecture is used to refer to fixed properties of the cognitive system. In some cases, this may include the temporal organization of the information processing, but they are distinct concepts. Architecture in the sense of this article may vary with a participant’s strategy, especially on high-level cognitive tasks in which a participant has a fair amount of control over strategy (Fifić, Nosofsky, & Townsend, 2008; Yang, 2011; Yang, Chang, & Wu, 2012; C. T Yang, Hsu, Huang, & Yeh, 2011). Architecture in the other sense could refer to properties that we classify under other monikers, such as workload constraints on information-processing efficiency.

  2. 2.

    In many models, the amount of information required to stop processing a given source (i.e., the threshold in an information accumulator model; cf. Brown & Heathcote, 2008; Link & Heath, 1975; Ratcliff & Smith, 2004) can vary. This also falls under the general category of stopping rule. However, the SFT approach does not include the more detailed analyses involved in identifying changes in the amount of information needed for each subprocess to finish.

  3. 3.

    We do not wish to claim that participants frequently, or even ever, attend more to the task when there are multiple sources of information. We only wish to indicate that it is not entirely an unreasonable possibility.

  4. 4.

    Each of the tools in isolation is relatively weak with respect to analyzing stochastic dependence, but they are powerful when used together (Eidels et al., 2011).

  5. 5.

    The additional adjective “effective” simply means that the salience manipulation has an effect: Channel processing times should be faster when the input is high salience. Here, we mean a particularly strong type of faster, that the response times for the fast condition should stochastically dominate the response times for the slow condition: S H(t) ≤ S L(t) for all ts, with S H (t) < S L (t) S H(t) < S L(t) for at least some t.

  6. 6.

    We will cover the sft functions together with the relevant theory and definitions without detail regarding data formats; we address the formatting of data for use in sft in a later section.

  7. 7.

    The calculation of the SIC is based on the R function ecdf. Both the ecdf function and the stepfun class are included in the stats package as part of R (R Development Core Team, 2011). For details on these or any other function or class in R, we suggest the use of the help function.

  8. 8.

    Some researchers have attempted to apply bootstrapping for hypothesis testing with the SIC. However, there are problems with that approach. One can estimate pointwise confidence intervals, then check the confidence interval at each point to see whether it includes zero. If one were to conclude that the function is significantly nonzero, the type I error rate would be much higher without appropriate correction. With a large number of estimated points on the SIC, a correction based on the assumption that each test is independent (e.g., Bonferroni) would make it nearly impossible to find a significant value of the SIC. Determining the appropriate correction on the basis of the true dependencies among the points is possible, but it is more straightforward to simply treat the SIC as a function for hypothesis testing. Bootstrapping tests are possible for hypotheses about the function, but asymptotic tests (such as the Houpt and Townsend, 2010b, test) are usually (always?) more powerful. On the basis of these issues, we have decided not to include bootstrap tests for SIC and C(t) measures in either the package or this article.

  9. 9.

    For details on the hazard function and its use in cognitive psychology, see Chechile (2003).

  10. 10.

    We have not accounted for the additional time taken by nonperceptual, non-decision-related processes, such as motor movements, in this derivation. This additional time would complicate the derivation, but it has only a limited effect on the capacity coefficient predictions when the variance of the additional time contributes relatively little to the variance of the response time, which is reasonable for human data (Townsend & Honey, 2007). In particular, the extent to which the additional time changes capacity estimates scales with the variance of the base time, leading to underestimates of OR capacity (Townsend & Honey, 2007) and overestimates of AND capacity (Townsend & Eidels, 2011).

  11. 11.

    For details on the reverse hazard function and its use in cognitive psychology, see Chechile (2011).

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Acknowledgements

This work was supported by AFOSR grant 10RH07COR to the late D. W. Repperger and P. R. Havig. We would like to thank Chris Myers for his comments on an early version of the manuscript.

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Affiliations

  1. Department of Psychology, Wright State University, 3640 Colonel Glenn Highway, Dayton, OH, 45435, USA

    Joseph W. Houpt

  2. U.S. Air Force Research Laboratory, Wright-Patterson Air Force Base, Wright-Patterson AFB, OH, USA

    Leslie M. Blaha, John P. McIntire & Paul R. Havig

  3. Indiana University, Bloomington, IN, USA

    James T. Townsend

Authors
  1. Joseph W. Houpt
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  2. Leslie M. Blaha
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  3. John P. McIntire
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  4. Paul R. Havig
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  5. James T. Townsend
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Correspondence to Joseph W. Houpt.

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Houpt, J.W., Blaha, L.M., McIntire, J.P. et al. Systems factorial technology with R. Behav Res 46, 307–330 (2014). https://doi.org/10.3758/s13428-013-0377-3

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Keywords

  • Response Time Distribution
  • Stimulus Rate
  • Cumulative Hazard Function
  • Capacity Coefficient
  • Selective Influence