Person:
Alcalá Quintana, Rocío

First Name

Rocío

Last Name

Alcalá Quintana

URI

https://hdl.handle.net/20.500.14352/80039

Affiliation

Universidad Complutense de Madrid

Faculty / Institute

Psicología

Department

Psicobiología y Metodología en Ciencias del Comportamiento

Area

Metodología de las Ciencias del Comportamiento

Identifiers

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Search Results

Now showing 1 - 8 of 8

Bayesian adaptive estimation of arbitrary points on a psychometric function
(The British journal of mathematical and statistical psychology, 2007) García Pérez, Miguel Ángel; Alcalá Quintana, Rocío
Bayesian adaptive methods have been extensively used in psychophysics to estimate the point at which performance on a task attains arbitrary percentage levels, although the statistical properties of these estimators have never been assessed. We used simulation techniques to determine the small-sample properties of Bayesian estimators of arbitrary performance points, specifically addressing the issues of bias and precision as a function of the target percentage level. The study covered three major types of psychophysical task (yes-no detection, 2AFC discrimination and 2AFC detection) and explored the entire range of target performance levels allowed for by each task. Other factors included in the study were the form and parameters of the actual psychometric function Psi, the form and parameters of the model function M assumed in the Bayesian method, and the location of Psi within the parameter space. Our results indicate that Bayesian adaptive methods render unbiased estimators of any arbitrary point on psi only when M=Psi, and otherwise they yield bias whose magnitude can be considerable as the target level moves away from the midpoint of the range of Psi. The standard error of the estimator also increases as the target level approaches extreme values whether or not M=Psi. Contrary to widespread belief, neither the performance level at which bias is null nor that at which standard error is minimal can be predicted by the sweat factor. A closed-form expression nevertheless gives a reasonable fit to data describing the dependence of standard error on number of trials and target level, which allows determination of the number of trials that must be administered to obtain estimates with prescribed precision.
Stopping rules in Bayesian adaptive threshold estimation
(Spatial Vision, 2005) Alcalá Quintana, Rocío; García Pérez, Miguel Ángel
Threshold estimation with sequential procedures is justifiable on the surmise that the index used in the so-called dynamic stopping rule has diagnostic value for identifying when an accurate estimate has been obtained. The performance of five types of Bayesian sequential procedure was compared here to that of an analogous fixed-length procedure. Indices for use in sequential procedures were: (1) the width of the Bayesian probability interval, (2) the posterior standard deviation, (3) the absolute change, (4) the average change, and (5) the number of sign fluctuations. A simulation study was carried out to evaluate which index renders estimates with less bias and smaller standard error at lower cost (i.e. lower average number of trials to completion), in both yes–no and two-alternative forced-choice (2AFC) tasks. We also considered the effect of the form and parameters of the psychometric function and its similarity with themodel function assumed in the procedure. Our results show that sequential procedures do not outperform fixed-length procedures in yes–no tasks. However, in 2AFC tasks, sequential procedures not based on sign fluctuations all yield minimally better estimates than fixed-length procedures, although most of the improvement occurs with short runs that render undependable estimates and the differences vanish when the procedures run for a number of trials (around 70) that ensures dependability. Thus, none of the indices considered here (some of which are widespread) has the diagnostic value that would justify its use. In addition, difficulties of implementation make sequential procedures unfit as alternatives to fixed-length procedures.
Fixed vs. variable noise in 2AFC contrast discrimination: lessons from psychometric functions.
(Spatial vision, 2009) García Pérez, Miguel Ángel; Alcalá Quintana, Rocío
Recent discussion regarding whether the noise that limits 2AFC discrimination performance is fixed or variable has focused either on describing experimental methods that presumably dissociate the effects of response mean and variance or on reanalyzing a published data set with the aim of determining how to solve the question through goodness-of-fit statistics. This paper illustrates that the question cannot be solved by fitting models to data and assessing goodness-of-fit because data on detection and discrimination performance can be indistinguishably fitted by models that assume either type of noise when each is coupled with a convenient form for the transducer function. Thus, success or failure at fitting a transducer model merely illustrates the capability (or lack thereof) of some particular combination of transducer function and variance function to account for the data, but it cannot disclose the nature of the noise. We also comment on some of the issues that have been raised in recent exchange on the topic, namely, the existence of additional constraints for the models, the presence of asymmetric asymptotes, the likelihood of history-dependent noise, and the potential of certain experimental methods to dissociate the effects of response mean and variance.
The role of parametric assumptions in adaptive Bayesian estimation.
(Psychological methods, 2004) Alcalá Quintana, Rocío; García Pérez, Miguel Ángel
Variants of adaptive Bayesian procedures for estimating the 5% point on a psychometric function were studied by simulation. Bias and standard error were the criteria to evaluate performance. The results indicated a superiority of (a) uniform priors, (b) model likelihood functions that are odd symmetric about threshold and that have parameter values larger than their counterparts in the psychometric function, (c) stimulus placement at the prior mean, and (d) estimates defined as the posterior mean. Unbiasedness arises in only 10 trials, and 20 trials ensure constant standard errors. The standard error of the estimates equals 0.617 times the inverse of the square root of the number of trials. Other variants yielded bias and larger standard errors.
Sampling plans for fitting the psychometric function.
(The Spanish journal of psychology, 2005) García Pérez, Miguel A; Alcalá Quintana, Rocío
Research on estimation of a psychometric function psi has usually focused on comparing alternative algorithms to apply to the data, rarely addressing how best to gather the data themselves (i.e., what sampling plan best deploys the affordable number of trials). Simulation methods were used here to assess the performance of several sampling plans in yes-no and forced-choice tasks, including the QUEST method and several variants of up-down staircases and of the method of constant stimuli (MOCS). We also assessed the efficacy of four parameter estimation methods. Performance comparisons were based on analyses of usability (i.e., the percentage of times that a plan yields usable data for the estimation of all the parameters of psi) and of the resultant distributions of parameter estimates. Maximum likelihood turned out to be the best parameter estimation method. As for sampling plans, QUEST never exceeded 80% usability even when 1000 trials were administered and rendered accurate estimates of threshold but misestimated the remaining parameters. MOCS and up-down staircases yielded similar and acceptable usability (above 95% with 400-500 trials) and, although neither type of plan allowed estimating all parameters with optimal precision, each type appeared well suited to estimating a distinct subset of parameters. An analysis of the causes of this differential suitability allowed designing alternative sampling plans (all based on up-down staircases) for yes-no and forced-choice tasks. These alternative plans rendered near optimal distributions of estimates for all parameters. The results just described apply when the fitted psi has the same mathematical form as the actual psi generating the data; in case of form mismatch, all parameters except threshold were generally misestimated but the relative performance of all the sampling plans remained identical. Detailed practical recommendations are given.
Empirical performance of optimal Bayesian adaptive estimation
(The Spanish journal of psychology, 2009) García Pérez, Miguel Angel; Alcalá Quintana, Rocío
Simulation studies have shown how Bayesian adaptive estimation methods should be set up for optimal performance. We assessed the extent to which these results hold up for human observers, who are more subject to failure than simulation subjects. Discrimination and detection experiments with two-alternative forced-choice (2AFC) tasks were used for that purpose. Forty estimates of the point of subjective equality (PSE, or the 50% correct point on the psychometric function for discrimination) and 32 estimates of detection threshold (the 80% correct point on the psychometric function for detection) were taken for each of four observers with the optimal Bayesian method, while data for fitting the psychometric function psi were gathered concurrently with an adaptive method of constant stimuli governed by fixed-step-size staircases. The estimated parameters of the psychometric function served as a criterion for comparison. In the discrimination task, PSEs for each observer were distributed around the independently estimated 50% correct point on psi and their variability was occasionally minimally larger than simulation results indicated it should be. In the detection task, the distribution of threshold estimates was consistently above the independently estimated 80% correct point on psi and their variability was as expected from simulations. A close analysis of these results suggests that the optimal Bayesian method is affected by growing inattention or fatigue in detection tasks (factors that are not considered in simulations), and limits the practical applicability of Bayesian estimation of detection thresholds.
A comparison of fixed-step-size and Bayesian staircases for sensory threshold estimation
(Spatial vision, 2007) Alcalá Quintana, Rocío; García Pérez, Miguel Ángel
Fixed-step-size (FSS) and Bayesian staircases are widely used methods to estimate sensory thresholds in 2AFC tasks, although a direct comparison of both types of procedure under identical conditions has not previously been reported. A simulation study and an empirical test were conducted to compare the performance of optimized Bayesian staircases with that of four optimized variants of FSS staircase differing as to up-down rule. The ultimate goal was to determine whether FSS or Bayesian staircases are the best choice in experimental psychophysics. The comparison considered the properties of the estimates (i.e. bias and standard errors) in relation to their cost (i.e. the number of trials to completion). The simulation study showed that mean estimates of Bayesian and FSS staircases are dependable when sufficient trials are given and that, in both cases, the standard deviation (SD) of the estimates decreases with number of trials, although the SD of Bayesian estimates is always lower than that of FSS estimates (and thus, Bayesian staircases are more efficient). The empirical test did not support these conclusions, as (1) neither procedure rendered estimates converging on some value, (2) standard deviations did not follow the expected pattern of decrease with number of trials, and (3) both procedures appeared to be equally efficient. Potential factors explaining the discrepancies between simulation and empirical results are commented upon and, all things considered, a sensible recommendation is for psychophysicists to run no fewer than 18 and no more than 30 reversals of an FSS staircase implementing the 1-up/3-down rule.
The transducer model for contrast detection and discrimination: formal relations, implications, and an empirical test.
(Spatial vision, 2007) García Pérez, Miguel Ángel; Alcalá Quintana, Rocío
The transducer function mu for contrast perception describes the nonlinear mapping of stimulus contrast onto an internal response. Under a signal detection theory approach, the transducer model of contrast perception states that the internal response elicited by a stimulus of contrast c is a random variable with mean mu(c). Using this approach, we derive the formal relations between the transducer function, the threshold-versus-contrast (TvC) function, and the psychometric functions for contrast detection and discrimination in 2AFC tasks. We show that the mathematical form of the TvC function is determined only by mu, and that the psychometric functions for detection and discrimination have a common mathematical form with common parameters emanating from, and only from, the transducer function mu and the form of the distribution of the internal responses. We discuss the theoretical and practical implications of these relations, which have bearings on the tenability of certain mathematical forms for the psychometric function and on the suitability of empirical approaches to model validation. We also present the results of a comprehensive test of these relations using two alternative forms of the transducer model: a three-parameter version that renders logistic psychometric functions and a five-parameter version using Foley's variant of the Naka-Rushton equation as transducer function. Our results support the validity of the formal relations implied by the general transducer model, and the two versions that were contrasted account for our data equally well.