Abstract
The psychometric function is a summary of the relation between performance in a classification task (such as the ability to detect or discriminate between stimuli) and stimulus level [59, 176]. Stimulus level is typically a measure of magnitude of a physical stimulus along a single physical dimension such as size, distance, light or sound intensity, concentration, or frequency. We will use the terms “stimulus level and “stimulus intensity interchangeably. We gave an example of a psychometric function in Chaps. 1 and Chaps. 2, we discussed the close relationship between the psychometric function and the generalized linear model. While there is no need to use the GLM in fitting psychometric functions we will see that doing so makes it very convenient to apply advanced statistical methods to psychophysical data.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Also, I is the name of a function in R, and it is best to avoid variables with the same names as functions.
- 2.
This is the default behavior of optim. It can be made to maximize by including the argument control = list(fnscale = -1).
- 3.
However, see the mle function in the recommended package stats4 [146].
- 4.
They state, “No special statistical methods are necessary to determine which curve fits the data, since smaller and larger values of n are easily excluded by visual comparison.” Such graphical short-cuts to fitting were common (and unavoidable) before availability of the enormous computational resources of the current era.
- 5.
- 6.
H. Sun, personal communication.
- 7.
Lower-order terms are marginal to higher-order terms. For example, main effects are marginal to interactions and simpler interactions are marginal to more complex ones. It is advised to test higher-order interactions without removing marginal effects that include the same terms as the higher-order effects. Conversely, one should not test marginal effects in the presence of significant non-marginal effects.
References
Abbey, C.K., Eckstein, M.P.: Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments. J. Vis. 2, 66–78 (2002)
Ahumada, A.J.: Perceptual classification images from vernier acuity masked by noise. Perception 25 ECVP Abstract Suppl. (1996)
Ahumada, A.J.: Classification image weights and internal noise level estimation. J. Vis. 2(1), 121–131 (2002)
Ahumada, A.J., Lovell, J.: Stimulus features in signal detection. J. Acoust. Soc. Am. 49, 1751–1756 (1971)
Ahumada, A.J., Marken, R., Sandusky, A.: Time and frequency analyses of auditory signal detection. J. Acoust. Soc. Am. 57(2), 385–390 (1975)
Akaike, H.: Information theory and an extension of the maximum likelihood principle. In: Petrov, B.N., Csàki, F. (eds.) Second International Symposium on Inference Theory, pp. 267–281. Akadémia Kiadó, Budapest (1973)
Baayen, R.H., Davidson, D.J., Bates, D.M.: Mixed-effects modeling with crossed random effects for subjects and items. J. Mem. Lang. 59, 390–412 (2008)
Bates, D.: Fitting linear mixed models. R News 5, 27–30 (2005). http://www.r-project.org/doc/Rnews/Rnews_2005-1.pdf
Bates, D., Maechler, M., Bolker, B.: lme4: Linear mixed-effects models using S4 classes (2011). R package version 0.999375-42. http://CRAN.R-project.org/package=lme4. Accessed date on 2nd August 2012
Bates, D., Maechler, M., Bolker, B.: lme4.0: Linear mixed-effects models using S4 classes (2012). R package version 0.9999-1/r1692. http://R-Forge.R-project.org/projects/lme4/. Accessed date on 2nd August 2012
Bates, D.M.: lme4: Mixed-Effects Modeling with R. Springer, New York (in preparation). http://lme4.r-forge.r-project.org/book/
Bengtsson, H., Riedy, J.: R.matlab: Read and write of MAT files together with R-to-Matlab connectivity (2011). R package version 1.5.1. http://CRAN.R-project.org/package=R.matlab. Accessed date on 2nd August 2012
Bernstein, S.N.: Sur l’ordre de la meilleure approximation des fonctions continues par les polynômes de degré donné. Mémoires de l’ Académie Royale de Belgique 4, 1–104 (1912)
Bishop, Y.M.M., Fienberg, S.E., Holland, P.W.: Discrete Multivariate Analysis: Theory and Practice. MIT, Cambridge (1975)
Block, H.D., Marschak, J.: Random orderings and stochastic theories of responses. In: Olkin, I., Ghurye, S., Hoeffding, W., Madow, W., Mann, H. (eds.) Contributions to Probability and Statistics, pp. 38–45. Stanford University Press, Stanford (1960)
Boeck, P.D., Wilson, M. (eds.): Explanatory Item Response Models: A Generalized Linear and Nonlinear Approach. Springer, New York (2004)
Boring, E.G.: Sensation and Perception in the History of Experimental Psychology. Irvington Publishers, Inc., New York (1942)
Bouet, R., Knoblauch, K.: Perceptual classification of chromatic modulation. Vis. Neurosci. 21, 283–289 (2004)
Bracewell, R.N.: The Fourier Transform and its Applications, 3rd edn. McGraw-Hill, New York (2000)
Bratley, P., Fox, B.L., Schrage, L.E.: A Guide to Simulation. Springer, New York (1983)
Brindley, G.S.: Two more visual theorems. Q. J. Exp. Psychol. 12, 110–112 (1960)
Britten, K.H., Shadlen, M.N., Newsome, W.T., Movshon, J.A.: The analysis of visual motion: A comparison of neuronal and psychophysical performance. J. Neurosci. 12(12), 4745–4765 (1992)
Broström, G., Holmberg, H.: glmmML: Generalized linear models with clustering (2011). R package version 0.82-1. http://CRAN.R-project.org/package=glmmML. Accessed date on 2nd August 2012
Burnham, K.P., Anderson, D.R.: Model Selection and Inference: A Practical Information-Theoretic Approach. Springer, New York (1998)
Canty, A., Ripley, B.D.: boot: Bootstrap R (S-Plus) Functions (2012). R package version 1.3-5
Carney, T., Tyler, C.W., Watson, A.B., Makous, W., Beutte, B., Chen, C.C., Norcia, A.M., Klein, S.A.: Modelfest: Year one results and plans for future years. In: Rogowitz, B.E., Pappas, T.N. (eds.) Proceedings of SPIE: Human vision and electronic imaging V, vol. 3959, pp. 140–151. SPIE, Bellingham (2000)
Carroll, L.: Through the Looking Glass and Ahat Alice Found There. Macmillan, Bassingstoke (1871)
Chambers, J.M., Hastie, T.J. (eds.): Statistical Models in S. Chapman and Hall/CRC, Boca Raton (1992)
Charrier, C., Maloney, L.T., Cherifi, H., Knoblauch, K.: Maximum likelihood difference scaling of image quality in compression-degraded images. J. Opt. Soc. Am. A 24, 3418–3426 (2007)
Chauvin, A., Worsley, K., Schyns, P., Arguin, M., Gosselin, F.: Accurate statistical tests for smooth classification images. J. Vis. 5, 659–667 (2005)
Christensen, R.H.B.: ordinal—regression models for ordinal data (2010). R package version 2011.09-14. http://www.cran.r-project.org/package=ordinal/. Accessed date on 2nd August 2012
Christensen, R.H.B., Brockhoff, P.B.: sensR—an R-package for sensory discrimination (2011). R package version 1.2-13. http://www.cran.r-project.org/package=sensR/. Accessed date on 2nd August 2012
Christensen, R.H.B., Hansen, M.K.: binomTools: Performing diagnostics on binomial regression models (2011). R package version 1.0-1. http://CRAN.R-project.org/package=binomTools. Accessed date on 2nd August 2012
Chung, K.L., Aitsahlia, F.: Elementary Probability Theory, 4th edn. Springer, New York (2006)
Clark, H.H.: The language-as-fixed-effect fallacy: A critique of language statistics in psychological research. J. Verbal Learn. Verbal Behav. 12, 355–359 (1973)
Cleveland, W.S., Diaconis, P., McGill, R.: Variables on scatterplots look more highly correlated when the scales are increased. Science 216, 1138–1141 (1982)
Cleveland, W.S., McGill, R.: Graphical perception: Theory, experimentation and application to the development of graphical methods. J. Am. Stat. Assoc. 79, 531–554 (1984)
Cleveland, W.S., McGill, R.: The many faces of a scatterplot. J. Am. Stat. Assoc. 79, 807–822 (1984)
Conway, J., Eddelbuettel, D., Nishiyama, T., Prayaga, S.K., Tiffin, N.: RPostgreSQL: R interface to the PostgreSQL database system (2010). R package version 0.1-7. http://www.postgresql.org. Accessed date on 2nd August 2012
Cook, R.D., Weisberg, S.: Residuals and Influence in Regression. Chapman and Hall, London (1982)
Cornsweet, T.: Visual Perception. Academic, New York (1970)
Crozier, W.J.: On the visibility of radiation at the human fovea. J. Gen. Physiol. 34, 87–136 (1950)
Crozier, W.J., Wolf, E.: Theory and measurement of visual mechanisms. IV. On flicker with subdivided fields. J. Gen. Physiol. 27, 401–432 (1944)
Dakin, S.C., Bex, P.J.: Natural image statistics mediate brightness filling in. Proc. Biol. Sci. 1531, 2341–2348 (2003)
Dartnall, H.J.A., Bowmaker, J.K., Mollon, J.D.: Microspectrophotometry of human photoreceptors. In: Mollon, J.D., Sharpe, L.T. (eds.) Colour Vision: Physiology and Psychophysics, pp. 69–80. Academic, London (1983)
Davison, A.C., Hinkley, D.V.: Bootstrap Methods and their Applications. Cambridge University Press, Cambridge (1997). http://statwww.epfl.ch/davison/BMA/
Debreu, G.: Topological methods in cardinal utility theory. In: Arrow, K.J., Karlin, S., Suppes, P. (eds.) Mathematical Methods in the Social Sciences, pp. 16–26. Stanford University Press, Stanford (1960)
DeCarlo, L.T.: Signal detection theory and generalized linear models. Psychol. Meth. 3, 186–205 (1998)
DeCarlo, L.T.: On the statistical and theoretical basis of signal detection theory and extensions: Unequal variance, random coefficient and mixture models. J. Math. Psychol. 54, 304–313 (2010)
Delord, S., Devinck, F., Knoblauch, K.: Surface and edge in visual detection: Is filling-in necessary? J. Vis. 4, 68a (2004). http://journalofvision.org/4/8/68/
Devinck, F.: Les traitements visuels chez l’homme : stratégies de classification de la forme. Ph.D. thesis, Université Lyon 2 (2003)
Devroye, L.: Non-uniform Random Variate Generation. Springer, New York (1986)
Dobson, A.J.: An Introduction to Generalized Linear Models. Chapman and Hall, London (1990)
Edwards, A.W.F.: Likelihood, expanded edn. Johns Hopkins University Press, Baltimore (1992)
Efron, B., Tibshirani, R.J.: An Introduction to the Bootstrap. Chapman Hall, New York (1993)
Emrith, K., Chantler, M.J., Green, P.R., Maloney, L.T., Clarke, A.D.F.: Measuring perceived differences in surface texture due to changes in higher order statistics. J. Opt. Soc. Am. A 27(5), 1232–1244 (2010)
Falmagne, J.C.: Elements of Psychophysical Theory. Oxford University Press, Oxford (1985)
Faraway, J.J.: Extending Linear Models with R: Generalized Linear, Mixed Effects and Nonparametric Regression Models. Chapman and Hall/CRC, Boca Raton (2006)
Fechner, G.T.: Elemente der Psychophysik. Druck und Verlag von Breitkopfs, Leipzig (1860)
Finney, D.J.: Probit Analysis, 3rd edn. Cambridge University Press, Cambridge (1971)
Firth, D.: Bias reduction of maximum likelihood estimates. Biometrika 80, 27–38 (1993)
Fisher, R.A.: The design of experiments. In: Bennett, J.H. (ed.) Statistical Methods, Experimental Design and Scientific Inference, 9th edn. Macmillan, New York (1971)
Fleming, R.W., Jäkel, F., Maloney, L.T.: Visual perception of thick transparent materials. Psychol. Sci. 22, 812–820 (2011)
Foster, D.H., Bischof, W.F.: Bootstrap estimates of the statistical accuracy of thresholds obtained from psychometric functions. Spatial Vis. 11(1), 135–139 (1997)
Foster, D.H., Żychaluk, K.: Nonparametric estimates of biological transducer functions. IEEE Signal Process. Mag. 24, 49–58 (2007)
Fründ, I., Haenel, N.V., Wichmann, F.A.: Inference for psychometric functions in the presence of nonstationary behavior. J. Vis. 11(6), 1–19 (2011)
Genz, A., Bretz, F., Miwa, T., Mi, X., Leisch, F., Scheipl, F., Bornkamp, B., Hothorn, T.: mvtnorm: Multivariate normal and t distributions (2011). R package version 0.9-9991. http://CRAN.R-project.org/package=mvtnorm. Accessed date on 2nd August 2012
Gescheider., G.A.: Psychophysical scaling. Annu. Rev. Psychol. 39, 169–200 (1988)
Glass, L.: Moiré effect from random dots. Nature 223, 578–580 (1969)
GmbH, M.S.: XLConnect: Excel Connector for R (2011). R package version 0.1-5. http://CRAN.R-project.org/package=XLConnect. Accessed date on 2nd August 2012
Gold, J.M., Murray, R.F., Bennett, P.J., Sekular, A.B.: Deriving behavioural receptive fields for visually completed contours. Curr. Biol. 10, 663–666 (2000)
Green, D.M., Swets, J.A.: Signal Detection Theory and Psychophysics. Robert E. Krieger Publishing Company, Huntington (1966/1974)
Guilford, J.P.: Psychometric Methods, 2nd edn. McGraw-Hill, New York (1954)
Hadfield, J.D.: Mcmc methods for multi-response generalized linear mixed models: The MCMCglmm R package. J. Stat. Software 33(2), 1–22 (2010). http://www.jstatsoft.org/v33/i02/
Hansen, T., Gegenfurtner, K.R.: Classification images for chromatic signal detection. J. Opt. Soc. Am. A 22, 2081–2089 (2005)
Harrell, F.E.: rms: Regression modeling strategies (2011). R package version 3.3-1. http://CRAN.R-project.org/package=rms. Accessed date on 2nd August 2012
Hastie, T., Tibshirani, R.: Generalized Additive Models. Chapman and Hall, London (1990)
Hauck, W.W. Jr, Donner, A.: Wald’s test as applied to hypotheses in logit analysis. J. Am. Stat. Assoc. 72, 851–853 (1977)
Hecht, S., Shlaer, S., Pirenne, M.H.: Energy, quanta and vision. J. Gen. Physiol. 25, 819–840 (1942)
Ho, Y.X., Landy, M.S., Maloney, L.T.: Conjoint measurement of gloss and surface texture. Psychol. Sci. 19, 196–204 (2008)
James, D.A.: DBI: R Database Interface (2009). R package version 0.2.5. http://CRAN.R-project.org/package=DBI. Accessed date on 2nd August 2012
James, D.A.: RSQLite: SQLite interface for R (2011). R package version 0.10.0. http://CRAN.R-project.org/package=RSQLite. Accessed date on 2nd August 2012
James, D.A., DebRoy, S.: RMySQL: R interface to the MySQL database (2011). R package version 0.8-0. http://biostat.mc.vanderbilt.edu/RMySQL. Accessed date on 2nd August 2012
James, D.A., Luciani, J.: ROracle: Oracle database interface for R (2007). R package version 0.5-9. http://www.omegahat.org. Accessed date on 2nd August 2012
Johnson, N.L., Kemp, A.W., Kotz, S.: Univariate Discrete Distributions. Wiley, New York (2005)
Johnson, N.L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions, vol. 1. Wiley, New York (1994)
Johnson, N.L., Kotz, S., Balakrishnan, N.: Continuous Univariate Distributions, vol. 2. Wiley, New York (1995)
Keppel, G.: Design & Analysis: A Researcher’s Handbook, 2nd edn. Prentice-Hall, Englewood Cliffs (1982)
Kienzle, W., Franz, M.O., Scholkopf, B., Wichmann, F.A.: Center-surround patterns emerge as optimal predictors for human saccade targets. J. Vis. 9, 1–15 (2009)
Kienzle, W., Wichmann, F.A., Schölkopf, B., Franz, M.O.: A nonparametric approach to bottom-up visual saliency. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems 19: Proceedings of the 2006 Conference, pp. 689–696. MIT, Cambridge (2007)
Kingdom, F.A.A., Prins, N.: Psychophysics: A Practical Introduction. Academic, New York (2009)
Kleiber, C., Zeileis, A.: Applied Econometrics with R. Springer, New York (2008). http://CRAN.R-project.org/package=AER
Klein, S.A.: Measuring, estimating, and understanding the psychometric function: A commentary. Percept. Psychophys. 63, 1421–1455 (2001)
Knoblauch, K.: psyphy: Functions for analyzing psychophysical data in R (2012). R package version 0.1-7. http://cran.r-project.org/web/packages/psyphy
Knoblauch, K., Maloney, L.T.: Estimating classification images with generalized linear and additive models. J. Vis. 8, 1–19 (2008)
Knoblauch, K., Maloney, L.T.: MLDS: Maximum likelihood difference scaling in R. J. Stat. Software 25, 1–26 (2008). http://www.jstatsoft.org/v25/i02
Knoblauch, K., Maloney, L.T.: MLCM: Maximum likelihood conjoint measurement (2011). R package version 0.0-8. http://CRAN.R-project.org/package=MLCM. Accessed date on 2nd August 2012
Knoblauch, K., Maloney, L.T.: MPDiR: Data sets and scripts for Modeling Psychophysical Data in R (2012). R package version 0.1-11. http://cran.r-project.org/web/packages/MPDiR
Knoblauch, K., Vital-Durand, F., Barbur, J.: Variation of chromatic sensitivity across the life span. Vis. Res. 41, 23–36 (2001)
Knuth, D.E.: The Art of Computer Programming: Seminumerical Programming, 3rd edn. Addison-Wesley, New York (1997)
Komárek, A., Lesaffre, E.: Generalized linear mixed model with a penalized gaussian mixture as a random-effects distribution. Comput. Stat. Data Anal. 52(7), 3441–3458 (2008)
Kontsevich, L.L., Tyler, C.W.: What makes Mona Lisa smile? Vis. Res. 44, 1493–1498 (2004)
Kosmidis, I.: brglm: Bias reduction in binary-response GLMs (2007). R package version 0.5-6. http://www.ucl.ac.uk/~ucakiko/software.html. Accessed date on 2nd August 2012
Krantz, D.H., Luce, R.D., Suppes, P., Tversky, A.: Foundations of Measurement (Vol. 1): Additive and Polynomial Representations. Academic, New York (1971)
Kuss, M., Jäkel, F., Wichmann, F.A.: Bayesian inference for psychometric functions. J. Vis. 5, 478–492 (2005). http://journalofvision.org/5/5/8/
Lang, D.T.: Rcompression: In-memory decompression for GNU zip and bzip2 formats. R package version 0.93-2. http://www.omegahat.org/Rcompression. Accessed date on 2nd August 2012
Lazar, N.A.: The Statistical Analysis of Functional MRI Data. Springer, New York (2008)
Legge, G.E., Gu, Y.C., Luebker, A.: Efficiency of graphical perception. Percept. Psychophys. 46, 365–374 (1989)
Lehmann, E.L., Casella, G.: Theory of Point Estimation, 2nd edn. Springer, New York (1998)
Lemon, J: Plotrix: A package in the red light district of R. R-News 6(4), 8–12 (2010)
Levi, D.M., Klein, S.A.: Classification images for detection and position discrimination in the fovea and parafovea. J. Vis. 2(1), 46–65 (2002)
Li, Y., Baron, J.: Behavioral Research Data Analysis in R, 1st edn. Springer, New York (2011)
Lindsey, D., Brown, A.: Color naming and the phototoxic effects of sunlight on the eye. Psychol. Sci. 13, 506–512 (2002)
Lindsey, D.T., Brown, A.M., Reijnen, E., Rich, A.N., Kuzmova, Y.I., Wolfe, J.M.: Color channels, not color appearance or color categories, guide visual search for desaturated color targets. Psychol. Sci. 21, 1208–1214 (2010)
Link, S.W.: The Wave Theory of Difference and Similarity. Lawrence Erlbaum Associates, Hillsdale (1992)
Luce, R.D., Green, D.M.: Parallel psychometric functions from a set of independent detectors. Psychol. Rev. 82, 483–486 (1975)
Luce, R.D., Tukey, J.W.: Simultaneous conjoint measurement: A new scale type of fundamental measurement. J. Math. Psychol. 32, 466–473 (1964)
Macke, J.H., Wichmann, F.A.: Estimating predictive stimulus features from psychophysical data: The decision image technique applied to human faces. J. Vis. 10 (2010)
MacLeod, D.: Visual sensitivity. Annu. Rev. Psychol. 29, 613–645 (1978)
Macmillan, N.A., Creelman, C.D.: Detection Theory: A User’s Guide, 2nd edn. Lawrence Erlbaum Associates, New York (2005)
Maloney, L.T.: Confidence intervals for the parameters of psychometric functions. Percept. Psychophys. 47(2), 127–134 (1990)
Maloney, L.T., Dal Martello, M.F.: Kin recognition and the perceived facial similarity of children. J. Vis. 6, 1047–1056 (2006). http://journalofvision.org/6/10/4/
Maloney, L.T., Yang, J.N.: Maximum Likelihood difference scaling. J. Vis. 3(8), 573–585 (2003). http://www.journalofvision.org/3/8/5
Mamassian, P., Goutcher, R.: Temporal dynamics in bistable perception. J. Vis. 5, 361–375 (2005)
Mangini, M.C., Biederman, I.: Making the ineffable explicit: Estimating the information employed for face classifications. Cognit. Sci. 28, 209–226 (2004)
Marin-Franch, I., Żychaluk, K., Foster, D.H.: modelfree: Model-free estimation of a psychometric function (2010). R package version 1.0. http://CRAN.R-project.org/package=modelfree. Accessed date on 2nd August 2012
McCullagh, P., Nelder, J.A.: Generalized Linear Models. Chapman and Hall, London (1989)
Mineault, P.J., Barthelme, S., Pack, C.C.: Improved classification images with sparse priors in a smooth basis. J. Vis. 9, 1–24 (2009)
Mood, A., Graybill, F.A., Boes., D.C.: Introduction to the Theory of Statistics, 3rd edn. McGraw-Hill, New York (1974)
Murray, R.F.: Classification images: A review. J. Vis. 11, 1–25 (2011)
Murray, R.F., Bennett, P.J., Sekuler, A.B.: Optimal methods for calculating classification images: Weighted sums. J. Vis. 2(1), 79–104 (2002)
Murrel, P.: Introduction to Data Technologies. Chapman and Hall/CRC, Boca Raton (2009)
Nandy, A.S., Tjan, B.S.: The nature of letter crowding as revealed by first- and second-order classification images. J. Vis. 7(2), 5.1–26 (2007)
Neri, P.: Estimation of nonlinear psychophysical kernels. J. Vis. 4, 82–91 (2004). http://journalofvision.org/4/2/2/
Neri, P.: How inherently noisy is human sensory processing? Psychonomic Bull. Rev. 17, 802–808 (2010)
Neri, P., Heeger, D.J.: Spatiotemporal mechanisms for detecting and identifying image features in human vision. Nat. Neurosci. 5, 812–816 (2002)
Neri, P., Parker, A.J., Blakemore, C.: Probing the human stereoscopic system with reverse correlation. Nature 401, 695–698 (1999)
Newsome, W.T., Britten, K.H., Movshon, J.A.: Neuronal correlates of a perceptual decision. Nature 341(6237), 52–54 (1989)
Obein, G., Knoblauch, K., Viénot, F.: Difference scaling of gloss: Nonlinearity, binocularity, and constancy. J. Vis. 4(9), 711–720 (2004)
Peirce, J.W.: The potential importance of saturating and supersaturating contrast response functions in visual cortex. J. Vis. 7, 13 (2007)
Pinheiro, J., Bates, D.: Mixed-Effects Models in S and S-PLUS. Springer, New York (2000)
Pinheiro, J., Bates, D., DebRoy, S., Sarkar, D., the R Development Core Team: nlme: Linear and nonlinear mixed effects models (2012). R package version 3.1-104
Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes, 3rd ed.: The Art of Scientific Computing. Cambridge University Press, Cambridge (2007)
Quick, R.: A vector-magnitude model of contrast detection. Kybernetik 16, 65–67 (1974)
R-core members, et al.: Foreign: Read data stored by Minitab, S, SAS, SPSS, Stata, Systat, dBase, …(2011). R package version 0.8-46. http://CRAN.R-project.org/package=foreign. Accessed date on 2nd August 2012
R Development Core Team: R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria (2011). ISBN 3-900051-07-0. http://www.R-project.org/. Accessed date on 2nd August 2012
Rensink, R.A., Baldridge, G.: The perception of correlation in scatterplots. Comput. Graph. Forum 29, 1203–1210 (2010)
Rhodes, G., Maloney, L.T., Turner, J., Ewing, L.: Adaptive face coding and discrimination around the average face. Vis. Res. 47, 974–989 (2007)
Ripley, B.: RODBC: ODBC Database Access (2011). R package version 1.3-3. http://CRAN.R-project.org/package=RODBC. Accessed date on 2nd August 2012
Ripley, B.D.: Pattern Recognition and Neural Networks. Cambridge University Press, Cambridge (1996)
Roberts, F.S.: Measurement Theory. Cambridge University Press, Cambridge (1985)
Ross, M.G., Cohen, A.L.: Using graphical models to infer multiple visual classification features. J. Vis. 9(3), 23.1–24 (2009)
Ross, S.M.: A First Course in Probability Theory, 8th edn. Prentice-Hall, Englewood Cliffs (2009)
Rouder, J.N., Lu, J., Sun, D., Speckman, P., Morey, R., Naveh-Benjamin, M.: Signal detection models with random participant and item effects. Psychometrika 72, 621–642 (2007)
Salsberg, D.: The Lady Tasting Tea: How Statistics Revolutionized Science in the Twentieth Century. W. H. Freeman, New York (2001)
Sarkar, D.: Lattice: Multivariate Data Visualization with R. Springer, New York (2008). http://lmdvr.r-forge.r-project.org
Schneider, B.: Individual loudness functions determined from direct comparisons of loudness intervals. Percept. Psychophys. 28, 493–503 (1980)
Schneider, B.: A technique for the nonmetric analysis of paired comparisons of psychological intervals. Psychometrika 45, 357–372 (1980)
Schneider, B., Parker, S., Stein, D.: The measurement of loudness using direct comparisons of sensory intervals. J. Math. Psychol. 11, 259–273 (1974)
Schwartz, M.: WriteXLS: Cross-platform Perl based R function to create Excel 2003 (XLS) files (2010). R package version 2.1.0. http://CRAN.R-project.org/package=WriteXLS. Accessed date on 2nd August 2012
Solomon, J.A.: Noise reveals visual mechanisms of detection and discrimination. J. Vis. 2(1), 105–120 (2002)
Spector, P.: Data Manipulation with R. Springer, New York (2008)
van Steen, G.: dataframes2xls: dataframes2xls writes data frames to xls files (2011). R package version 0.4.5. http://cran.r-project.org/web/packages/dataframes2xls. Accessed date on 2nd August 2012
Stevens, S.S.: On the theory of scales of measurement. Science 103, 677–680 (1946)
Stevens, S.S.: On the psychophysical law. Psychol. Rev. 64, 153–181 (1957)
Strasburger, H.: Converting between measures of slope of the psychometric function. Percept. Psychophys. 63, 1348–1355 (2001)
Sun, H., Lee, B., Baraas, R.: Systematic misestimation in a vernier task arising from contrast mismatch. Vis. Neurosci. 25, 365–370 (2008)
Suppes, P.: Finite equal-interval measurement structures. Theoria 38, 45–63 (1972)
Tanner, W.P., Swets, J.A.: A decision-making theory of visual detection. Psychol. Rev. 61, 401–409 (1954)
Teller, D.Y.: The forced-choice preferential looking procedure: A psychophysical technique for use with human infants. Infant Behav. Dev. 2, 135–153 (1979)
Thibault, D., Brosseau-Lachaine, O., Faubert, J., Vital-Durand, F.: Maturation of the sensitivity for luminance and contrast modulated patterns during development of normal and pathological human children. Vis. Res. 47, 1561–1569 (2007)
Thomas, J.P., Knoblauch, K.: Frequency and phase contributions to the detection of temporal luminance modulation. J. Opt. Soc. Am. A 22(10), 2257–2261 (2005)
Thurstone, L.L.: A law of comparative judgement. Psychol. Rev. 34, 273–286 (1927)
Tolhurst, D.J., Movshon, J.A., Dean, A.F.: The statistical reliability of signals in single neurons in cat and monkey visual cortex. Vis. Res. 23(8), 775–785 (1983)
Treutwein, B., Strasburger, H.: Fitting the psychometric function. Percept. Psychophys. 61(1), 87–106 (1999)
Urban, F.M.: The method of constant stimuli and its generalizations. Psychol. Rev. 17, 229–259 (1910)
Urbanek, S.: RJDBC: Provides access to databases through the JDBC interface (2011). R package version 0.2-0. http://www.rforge.net/RJDBC/. Accessed date on 2nd August 2012
Venables, W.N., Ripley, B.D.: Modern Applied Statistics with S, 4th edn. Springer, New York (2002). http://www.stats.ox.ac.uk/pub/MASS4
Victor, J.: Analyzing receptive fields, classification images and functional images: Challenges with opportunities for synergy. Nat. Neurosci. 8, 1651–1656 (2005)
Warnes, G.R.: gmodels: Various R programming tools for model fitting (2011). R package version 2.15.1. http://CRAN.R-project.org/package=gmodels. Accessed date on 2nd August 2012
Warnes, G.R., et al.: gdata: Various R programming tools for data manipulation (2010). R package version 2.8.1. http://CRAN.R-project.org/package=gdata. Accessed date on 2nd August 2012
Watson, A.: The spatial standard observer: A human vision model for display inspection. In: 353 SID Symposium Digest of Technical Papers, 37, pp. 1312–1315 (2006)
Watson, A.B., Ahumada, A.J.: A standard model for foveal detection of spatial contrast. J. Vis. 5, 717–740 (2005)
Watson, A.B., Pelli, D.G.: QUEST: A Bayesian adaptive psychometric method. Percept. Psychophys. 33, 113–120 (1983)
Watson, G.A.: Approximation Theory and Numerical Methods. Wiley, New York (1980)
Westheimer, G.: The spatial grain of the perifoveal visual field. Vis. Res. 22(1), 157–162 (1982)
Wichmann, F.A., Graf, A.B.A., Simoncelli, E.P., Bülthoff, H.H., Schölkopf, B.: Machine learning applied to perception: Decision-images for gender classification. In: Saul, L.K., Weiss, Y., Bottou, L. (eds.) Advances in Neural Information Processing Systems 17, pp. 1489–1496. MIT, Cambridge (2005)
Wichmann, F.A., Hill, N.J.: The psychometric function: I. fitting, sampling and goodness of fit. Percept. Psychophys. 63, 1293–1313 (2001)
Wickens, T.D.: Elementary Signal Detection Theory. Oxford University Press, New York (2002)
Wickham, H.: ggplot2: Elegant Graphics for Data Analysis. Springer, New York (2009). http://had.co.nz/ggplot2/book
Wilkinson, G.N., Rogers, C.E.: Symbolic description of factorial models for analysis of variance. Appl. Stat. 22, 392–399 (1973)
Wilkinson, L.: The Grammar of Graphics. Springer, New York (2005)
Wilks, S.S.: The large-sample distribution of the likelihood ratio for testing composite hypotheses. Ann. Math. Stat. 9, 60–62 (1938)
Williams, J., Ramaswamy, D., Oulhaj, A.: 10 Hz flicker improves recognition memory in older people. BMC Neurosci. 7, 21 (2006)
Winer, B.J.: Statistical Principles in Experimental Design, 2nd edn. McGraw-Hill, New York (1971)
Winship, C., Mare, R.D.: Regression models with ordinal variables. Am. Soc. Rev. 49, 512–525 (1984)
Wood, S.: gamm4: Generalized additive mixed models using mgcv and lme4 (2011). R package version 0.1-3. http://CRAN.R-project.org/package=gamm4. Accessed date on 2nd August 2012
Wood, S.N.: Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC, Boca Raton (2006)
Xie, Y., Griffin, L.D.: A ‘portholes’ experiment for probing perception of small patches of natural images. Perception 36, 315 (2007)
Yang, J.N., Szeverenyi, N.M., Ts’o, D.: Neural resources associated with perceptual judgment across sensory modalities. Cerebr. Cortex 18, 38–45 (2008)
Yee, T.W.: The vgam package for categorical data analysis. J. Stat. Software 32(10), 1–34 (2010). http://www.jstatsoft.org/v32/i10
Yeshurun, Y., Carrasco, M., Maloney, L.T.: Bias and sensitivity in two-interval forced choice procedures: Tests of the difference model. Vis. Res. 48, 1837–1851 (2008)
Yovel, Y., Franz, M.O., Stilz, P., Schnitzler, H.U.: Plant classification from bat-like echolocation signals. PLoS Comput. Biol. 4, e1000032 (2008)
Yssaad-Fesselier, R., Knoblauch, K.: Modeling psychometric functions in R. Behav. Res. Meth. Instrum. Comp. 38, 28–41 (2006)
Zhaoping, L., Jingling, L.: Filling-in and suppression of visual perception from context: A Bayesian account of perceptual biases by contextual influences. PLoS Comput. Biol. 4, e14 (2008)
Zucchini, W.: An introduction to model selection. J. Math. Psychol. 44, 41–61 (2000)
Zuur, A., Ieno, E.N., Walker, N., Saveiliev, A.A., Smith, G.M.: Mixed Effects Lodels and Extensions in Ecology with R. Springer, New York (2009)
Żychaluk, K., Foster, D.H.: Model-free estimation of the psychometric function. Attention Percept. Psychophys. 71, 1414–1425 (2009)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer Science+Business Media New York
About this chapter
Cite this chapter
Knoblauch, K., Maloney, L.T. (2012). The Psychometric Function: Introduction. In: Modeling Psychophysical Data in R. Use R!, vol 32. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4475-6_4
Download citation
DOI: https://doi.org/10.1007/978-1-4614-4475-6_4
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-4474-9
Online ISBN: 978-1-4614-4475-6
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)