Palamedes can be used to fit Psychometric Functions (PFs) to data using a Maximum Likelihood (ML) criterion. Various forms of PF are supported (Weibull, Logistic, Gumbel, Cumulative Normal, Hyperbolic Secant). Make any combination of the PF's parameters (threshold, slope, guess rate, lapse rate) free parameters. Estimate the standard errors of free parameters using a parametric or non-parametric bootstrap. Determine Goodness-of-Fit of the fit. Palamedes can also use a Bayesian criterion to determine the best-fitting PF to your data and the standard errors of the parameters. The psychometric function fitting procedures are demonstrated in PAL_PFML_Demo, PAL_PFML_SearchGrid_Demo, PAL_PFML_lapseFit_Demo, PAL_gammaEQlambda_Demo (all use ML) and PAL_PFBA_Demo (Bayesian). All demo files are located in the PalamedesDemos folder.

Multi-condition Model Fitting

            Palamedes can also fit PFs to several conditions simultaneously while allowing flexibility in constraining the free parameters between conditions in order to define a 'model'. For example: you wish to fit separate PFs to more than one condition in your experiment but you wish to estimate a single, shared lapse rate across all conditions (and why wouldn't you?). Palamedes can do this. Another example: you wish to constrain thresholds to increase linearly with condition but you wish to fit a single shared slope to all conditions. Palamedes can do this too. With the introduction of custom-reparametrization of parameters in Palamedes version 1.1.0 you can constrain any of the PFs parameters any which way you wish (minor assembly required). Need to fix the threshold values in conditions 1, 3, and 6 to equal 1, 2, and pi respectively but have thresholds in conditions 2, 4, 5, and 7 adhere to 'threshold(condition) = a x sin(b x condition^2) where 'a' and 'b' are free parameters? We understand. Click here for an example of what you can do. Palamedes can perform a bootstrap analysis to estimate standard errors on the parameters of your custom-defined model, and determine its Goodness-of-Fit. The model fitting procedures are demonstrated in PAL_PFLR_Demo, PAL_PFLR_FourGroup_Demo, PAL_PFLR_CustomDefine_Demo, and PAL_PFML_lapseFit_Demo in the PalamedesDemos folder.

Model Comparisons

             Palamedes can statistically compare models defined across multiple conditions (see above: Multi-condition Model Fitting) to test, for example, whether thresholds differ between conditions, whether slopes differ between conditions, whether the lapse rate equals zero, etcetera, etcetera. Users savvy with the General Linear Model may use contrasts to test, for example, whether thresholds increase linearly with, say, adaptation duration or whether the data warrant a quadratic trend. Finally, Palamedes can compare models that use custom-parametrization of the parameters of a PF (for an example, click here to see the model comparison that PAL_PFLR_CustomDefine_Demo demonstrates).  The model comparison procedures are demonstrated in PAL_PFLR_Demo, PAL_PFLR_FourGroup_Demo, PAL_PFLR_CustomDefine_Demo, and PAL_PFML_apseFit_Demo in the PalamedesDemos folder.

Adaptive Procedures

            Palamedes can be used to guide stimulus selection in your experiments. Palamedes can implement up/down procedures, ‘running fit’ procedures (best PEST, QUEST), and the psi method. All offer considerable flexibility regarding the specifics. The up/down, running fit, and psi method procedures are demonstrated in PAL_AMUD_Demo, PAL_AMRF_Demo, and PAL_AMPM_Demo respectively. All are located in the PalamedesDemos folder.

Signal Detection Measures

             Palamedes can calculate d' (d-prime) and criterion values from proportion hits and false alarms, or proportion correct, (and vice versa) for a large variety of psychophysical tasks (e.g. 1AFC, 2AFC, MAFC, Same-Different, Match-to-Sample, Oddity) and under different models (Independent Observation, Differencing). The signal detection procedures are demonstrated in PAL_SDT_1AFC_DPtoPHF_demo, PAL_SDT_1AFC_PHFtoDP_Demo, PAL_SDT_DPtoPCcomparison_Demo, PAL_SDT_1AFC_PCtoDPcomparison_Demo, and PAL_SDT_DPtoPCacrossM_Demo in the PalamedesDemos folder.

Maximum Likelihood Difference Scaling

            Palamedes will derive parameter estimates describing the transducer function based on an observer’s judgments about the perceived differences between stimuli, for stimuli presented as pairs, triads or quadruples (double pairs). A bootstrap procedure may be used to determine standard errors. The maximum likelihood difference scaling procedures are demonstrated for simulated data sets in PAL_MLDS_Demo in the PalamedesDemos folder.