Advertisement

Behavior Research Methods

, Volume 47, Issue 1, pp 13–26 | Cite as

A MATLAB toolbox for the efficient estimation of the psychometric function using the updated maximum-likelihood adaptive procedure

  • Yi Shen
  • Wei Dai
  • Virginia M. Richards
Article
  • 1k Downloads

Abstract

A MATLAB toolbox for the efficient estimation of the threshold, slope, and lapse rate of the psychometric function is described. The toolbox enables the efficient implementation of the updated maximum-likelihood (UML) procedure. The toolbox uses an object-oriented architecture for organizing the experimental variables and computational algorithms, which provides experimenters with flexibility in experimental design and data management. Descriptions of the UML procedure and the UML Toolbox are provided, followed by toolbox use examples. Finally, guidelines and recommendations of parameter configurations are given.

Keywords

Psychometric function Adaptive procedure 

Notes

Author note

This work was supported by NIH NIDCD Grant No. R21 DC010058, awarded to the third author. We acknowledge Sierra N. Broussard’s assistance in running several computer simulations.

Reference

  1. Brainard, D. H. (1997). The psychophysics toolbox. Spatial Vision, 10, 433–436. doi: 10.1163/156856897X00357 CrossRefPubMedGoogle Scholar
  2. Brand, T., & Kollmeier, B. (2002). Efficient adaptive procedures for threshold and concurrent slope estimates for psychophysics and speech intelligibility tests. Journal of the Acoustical Society of America, 111, 2801–2810.CrossRefPubMedGoogle Scholar
  3. Derman, C. (1957). Non-parametric up-and-down experimentation. Annals of Mathematical Statistics, 28, 795–798. doi: 10.1214/aoms/1177706895 CrossRefGoogle Scholar
  4. Durham, S. D., & Flournoy, N. (1995). Up-and-down designs I: Stationary treatment distributions. In N. Flournoy & W. F. Rosenberger (Eds.), Adaptive designs: Papers from the Joint AMS–IMS–SIAM Summer Conference held at Mt. Holyoke College, South Hadley, MA, July 1992 (pp. 139–157). Hayward, CA: Institute of Mathematical Statistics.CrossRefGoogle Scholar
  5. Emerson, P. L. (1986a). Observations on maximum likelihood and Bayesian methods of forced choice sequential threshold estimation. Perception & Psychophysics, 39, 151–153.CrossRefGoogle Scholar
  6. Emerson, P. L. (1986b). A quadrature method for Bayesian sequential threshold estimation. Perception & Psychophysics, 39, 381–383.CrossRefGoogle Scholar
  7. Fründ, I., Haenel, N. V., & Wichmann, F. A. (2011). Inference for psychometric functions in the presence of non-stationary behavior. Journal of Vision, 11(6), 16. doi: 10.1167/11.6.16 CrossRefPubMedGoogle Scholar
  8. Garcia-Perez, M. A. (1998). Forced-choice staircases with fixed step sizes: Asymptotic and small-sample properties. Vision Research, 38, 1861–1881.CrossRefPubMedGoogle Scholar
  9. Grassi, M., & Soranzo, A. (2009). MLP: A MATLAB toolbox for rapid and reliable auditory threshold estimation. Behavior Research Methods, 41, 20–28. doi: 10.3758/BRM.41.1.20 CrossRefPubMedGoogle Scholar
  10. Green, D. M. (1990). Stimulus selection in adaptive psychophysical procedures. Journal of the Acoustical Society of America, 87, 2662–2674.CrossRefPubMedGoogle Scholar
  11. Gu, X., & Green, D. M. (1994). Further studies of a maximum-likelihood yes–no procedure. Journal of the Acoustical Society of America, 96, 93–101.CrossRefPubMedGoogle Scholar
  12. Hall, J. L. (1968). Maximum-likelihood sequential procedure for estimation of psychometric functions [Abstract]. Journal of the Acoustical Society of America, 44, 370. doi: 10.1121/1.1970490 CrossRefGoogle Scholar
  13. Hall, J. L. (1981). Hybrid adaptive procedures for the estimation of psychometric functions. Journal of the Acoustical Society of America, 69, 1763–1769.CrossRefPubMedGoogle Scholar
  14. Harvey, L. O., Jr. (1986). Efficient estimation of sensory thresholds. Behavior Research Methods, Instruments, & Computers, 18, 623–632.CrossRefGoogle Scholar
  15. Harvey, L. O., Jr. (1997). Efficient estimation of sensory thresholds with ML-PEST. Spatial Vision, 11, 121–128. doi: 10.1163/156856897X00159 CrossRefPubMedGoogle Scholar
  16. Kaernbach, C. (1991). Simple adaptive testing with the weighted up–down method. Perception & Psychophysics, 49, 227–229. doi: 10.3758/BF03214307 CrossRefGoogle Scholar
  17. Kaernbach, C. (2001). Slope bias of psychometric functions derived from adaptive data. Perception & Psychophysics, 63, 1389–1398.CrossRefGoogle Scholar
  18. King-Smith, P. E., Grigsby, S. S., Vingrys, A. J., Benes, S. C., & Supowit, A. (1994). Efficient and unbiased modifications of the QUEST threshold method: Theory, simulations, experimental evaluation and practical implementation. Vision Research, 34, 885–912.CrossRefPubMedGoogle Scholar
  19. King-Smith, P. E., & Rose, D. (1997). Principles of an adaptive method for measuring the slope of the psychometric function. Vision Research, 37, 1595–1604.CrossRefPubMedGoogle Scholar
  20. Klein, S. A. (2001). Measuring, estimating, and understanding the psychometric function: A commentary. Perception & Psychophysics, 63, 1421–1455.CrossRefGoogle Scholar
  21. Kontsevich, L. L., & Tyler, C. W. (1999). Bayesian adaptive estimation of psychometric slope and threshold. Vision Research, 39, 2729–2737.CrossRefPubMedGoogle Scholar
  22. Lam, C. F., Dubno, J. R., Ahlstrom, J. B., He, N. J., & Mills, J. H. (1997). Estimating parameters for psychometric functions using the four-point sampling method. Journal of the Acoustical Society of America, 102, 3697–3703.CrossRefPubMedGoogle Scholar
  23. Laming, D., & Marsh, D. (1988). Some performance tests of Quest on measurements of vibrotactile thresholds. Perception & Psychophysics, 44, 99–107.CrossRefGoogle Scholar
  24. Leek, M. R. (2001). Adaptive procedures in psychophysical research. Perception & Psychophysics, 63, 1279–1292.CrossRefGoogle Scholar
  25. Leek, M. R., Hanna, T. E., & Marshall, L. (1992). Estimation of psychometric functions from adaptive tracking procedures. Perception & Psychophysics, 51(3), 247–256.Google Scholar
  26. Levitt, H. (1971). Transformed up–down methods in psychoacoustics. Journal of the Acoustical Society of America, 49(2, Pt. 2), 467–477. doi: 10.1121/1.1912375 CrossRefPubMedGoogle Scholar
  27. Lieberman, H. R., & Pentland, A. P. (1982). Microcomputer-based estimation of psychophysical thresholds: The Best PEST. Behavior Research Methods & Instrumentation, 14, 21–25. doi: 10.3758/BF03202110 CrossRefGoogle Scholar
  28. Otto, S., & Weinzierl, S. (2009). Comparative simulations of adaptive psychometric procedures. In Jahrestagung der Deutschen Gesellschaft für Akustik (pp. 1276–1279). Rotterdam, The Netherlands: Deutsche Gesellschaft für Akustik.Google Scholar
  29. Pelli, D. G. (1997). The VideoToolbox software for visual psychophysics: Transforming numbers into movies. Spatial Vision, 10, 437–442. doi: 10.1163/156856897X00366 CrossRefPubMedGoogle Scholar
  30. Poppe, S., Benner, P., & Elze, T. (2012). A predictive approach to nonparametric inference for adaptive sequential sampling of psychophysical experiments. Journal of Mathematical Psychology, 56, 179–195.CrossRefPubMedPubMedCentralGoogle Scholar
  31. Prins, N. (2012a). The adaptive psi method and the lapse rate. Journal of Vision, 12(9), 322. doi: 10.1167/12.9.322 CrossRefGoogle Scholar
  32. Prins, N. (2012b). The psychometric function: The lapse rate revisited. Journal of Vision, 12(6), 25. doi: 10.1167/12.6.25 CrossRefPubMedGoogle Scholar
  33. Prins, N. (2013). The psi-marginal adaptive method: How to give nuisance parameters the attention they deserve (no more, no less). Journal of Vision, 13(7), 3. doi: 10.1167/13.7.3 CrossRefPubMedGoogle Scholar
  34. Prins, N., & Kingdom, F. A. A. (2009). Palamedes: MATLAB routines for analyzing psychophysical data. www.palamedestoolbox.org
  35. Rose, R. M., Teller, D. Y., & Rendleman, P. (1970). Statistical properties of staircase estimates. Perception & Psychophysics, 8, 199–204.CrossRefGoogle Scholar
  36. Shen, Y. (2013). Comparing adaptive procedures for estimating the psychometric function for an auditory gap detection task. Attention, Perception, & Psychophysics, 75, 771–780. doi: 10.3758/s13414-013-0438-9 CrossRefGoogle Scholar
  37. Shen, Y., & Richards, V. M. (2012). A maximum-likelihood procedure for estimating psychometric functions: Thresholds, slopes, and lapses of attention. Journal of the Acoustical Society of America, 132, 957–967.CrossRefPubMedPubMedCentralGoogle Scholar
  38. Taylor, M. M. (1971). On the efficiency of psychophysical measurement. Journal of the Acoustical Society of America, 49, 505–508.CrossRefPubMedGoogle Scholar
  39. Taylor, M. M., & Creelman, C. D. (1967). PEST: Efficient estimates on probability functions. Journal of the Acoustical Society of America, 41, 782–787.CrossRefGoogle Scholar
  40. Treutwein, B. (1995). Adaptive psychophysical procedures. Vision Research, 17, 2503–2522.CrossRefGoogle Scholar
  41. Treutwein, B. (1997). YAAP: Yet another adaptive procedure. Spatial Vision, 11, 129–134.PubMedGoogle Scholar
  42. Treutwein, B., & Strasburger, H. (1999). Fitting the psychometric function. Perception & Psychophysics, 61, 87–106.CrossRefGoogle Scholar
  43. Urban, F. M. (1910). The method of constant stimuli and its generalizations. Psychological Review, 17, 229–259.CrossRefGoogle Scholar
  44. Watson, A. B., & Pelli, D. (1983). QUEST: A Bayesian adaptive psychometric method. Perception & Psychophysics, 33, 113–120. doi: 10.3758/BF03202828 CrossRefGoogle Scholar
  45. Watson, A. B., & Solomon, J. A. (1998). Psychophysica: Mathematica notebooks for psychophysical experiments. Spatial Vision, 10, 447–466.CrossRefGoogle Scholar
  46. Wetherill, G. B., & Levitt, H. (1965). Sequential estimation of points on a psychometric function. British Journal of Mathematical and Statistical Psychology, 18, 1–10.CrossRefPubMedGoogle Scholar
  47. Wichmann, F. A., & Hill, N. J. (2001a). The psychometric function: I. Fitting, sampling, and goodness of fit. Perception & Psychophysics, 63, 1297–1313. doi: 10.3758/BF03194544 Google Scholar
  48. Wichmann, F. A., & Hill, N. J. (2001b). The psychometric function: II. Bootstrap-based confidence intervals and sampling. Perception & Psychophysics, 63, 1314–1329. doi: 10.3758/BF03194545 CrossRefGoogle Scholar
  49. Zchaluk, K., & Foster, D. H. (2009). Model-free estimation of the psychometric function. Attention, Perception, & Psychophysics, 71, 1414–1425. doi: 10.3758/APP.71.6.1414 CrossRefGoogle Scholar

Copyright information

© Psychonomic Society, Inc. 2014

Authors and Affiliations

  1. 1.Department of Cognitive SciencesUniversity of CaliforniaIrvineUSA
  2. 2.Department of Computer ScienceUniversity of CaliforniaIrvineUSA

Personalised recommendations