Univariate and Bivariate Models of Signal Detection

R code for fitting various models to signal detection to univariate and bivariate data as well as a documentation of the main functions are available.

  • The code enables one to fit SDT models of different types. At present, the following types of models are available:
    1. The univariate Gaussian SDT model (two versions);
    2. The bivariate Gaussian SDT model (cf. Wickens, 1992; Wickens & Olzak, 1992);
    3. A mixture model of different Gaussian distributions (two versions) [cf. DeCarlo, 2002; Hilford, Glanzer, Kim and DeCarlo, 2002];
    4. A hybrid model consisting of a SDT and a double high threshold component (two versions) [cf. Macho, 2002, 2004];
    5. A mixture model of two different bivariate Gaussian distributions.
    6. Various signal detection models for modeling multiple alternative forced choice (m-AFC) data with or without rating data.
    7. Signal detection models with probabilistic response functions.
  • The code enables one to fit models to arbitrary many different types of signals.
  • The method of estimation is maximum likelihood (cf., Grey & Morgan, 1972).
  • Test statistics (Chi-square statistics, AIC, BIC, CAICF, ICOMP) and model diagnostics (rank and condition number of the information and model matrix) are computed.
  • If the model is properly estimated, estimated standard errors of estimated parameters, as well as confidence intervals are computed from the observed information matrix. In addition, likelihood ratio based confidence intervals can be computed for univariate SDT models.
  • Fixed, equality, and functional constraints of arbitrary complexity may be imposed on parameters.
  • A detailed documentation of the principal functions is available. This documentation contains many working examples with fits of different to data from the literature on detection, source monitoring, and associative recognition).
  • Functions for plotting density, ROC and zROC curves are available.


  • DeCarlo, L. T. (2002). Signal detection theory with finite mixture distributions: Theoretical developments with applications to recognition memory. Psychological Review, 109, 710-721.
  • Grey, D. R., & Morgan, B. J. T. (1972). Some aspects of ROC curve-fitting: Normal and logistic models. Journal of Mathematical Psychology, 9, 128-139.
  • Hilford, A., Glanzer, M., Kim, K., & DeCarlo, L. T. (2002). Regularities of source recognition: ROC analysis. Journal of Experimental Psychology: General, 131, 494-510.
  • Macho, S. (2002). Cognitive modeling with spreadsheets. Behavior Research Methods, Instruments, & Computers, 34, 19-36.
  • Macho, S. (2004). Modeling associative recognition: A comparison of two-high-threshold, two-high-threshold signal detection, and mixture distribution models. Journal of Experimental Psychology: Learning, Memory, & Cognition, 30, 83-97.
  • Wickens, T. D. (1992). Maximum-Likelihood estimation of a multivariate Gaussian rating model with excluded data. Journal of Mathematical Psychology, 36, 213-234.
  • Wickens, T. D., & Olzak, L. A. (1992). Three views of association in concurrent detection ratings. In: F. G. Ashby (Ed.), Multidimensional models of perception and cognition (Chapter 9: pp. 229-252). Hillsdale, NJ.: Erlbaum.


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