PSYCH_GLOSS    glossary of terms, struct fieldnames and common variable names 


2AFC          an 2-alternative forced-choice experimental paradigm, in which
              the observer selects one of 2 stimuli per trial. Similarly 4AFC,
              8AFC, nAFC.

alpha         parameter of the underlying psychometric function F. Together,
              alpha and beta determine the horizontal displacement of the
              curve, and its slope. alpha is the first element of the parameter
              vector theta.

beta          parameter of the underlying psychometric function F. Together,
              alpha and beta determine the horizontal displacement of the 
              curve, and its slope. beta is the second element of the parameter
              vector theta.

BCa           the bias-corrected accelerated method of obtaining bootstrap 
              confidence intervals. For most problems, the coverage of BCa 
              intervals can be shown to exhibit better convergence than that of
              unadjusted bootstrap percentile intervals. See Davison, AC & Hinkley,
              DV (1997): Bootstrap methods and their application; Cambridge: CUP,
              and Efron, B & Tibshirani, RJ (1993): An Introduction to the Bootstrap;
              New York: Chapman & Hall.

bootstrap     a Monte Carlo method for estimating variability. A large number
              of simulated data sets are generated from a distribution that is 
              assumed to approximate the true distribution underlying the data 
              (in our implementation, we use the maximum-likelihood fitted 
              function of form psi in order to generate data). Whatever process 
              was carried out on the data to obtain an estimate (e.g. fitting a 
              function and obtaining a threshold) is carried out on each of the 
              simulated data sets, to obtain an expected distribution of 
              estimates. 

bootstrap     the inaccuracy of a bootstrap variability estimate that arises
error         because of a discrepancy between the estimated or assumed 
              bootstrap generating function and the true distribution.

conf          short for "confidence levels" which is our imprecise shorthand
              for "the cumulative probability value corresponding to a 
              confidence interval boundary". Our default values for conf are
              [0.023, 0.159, 0.841, 0.977] because they provide confidence
              intervals whose coverage is familiar: if the variable in question
              were Gaussian, they would give us [-2, -1, +1, +2] standard
              deviations from the mean.

confLimMethod should read 'BCa', indicating that confidence limits in the 'lims'
              fields were obtained by the BCa method

corr          linear correlation coefficient

cpe           cumulative probability estimate: for any measure z, this is an
              estimate of the integral from -infinity to z of the probability
              density function for Z. For a right-tailed test, significance is
              equal to cpe. For a left-tailed test, significance = 1-cpe.

cuts          the probability levels at which thresholds or slopes are
              calculated, given in the (0, 1) range of F.

d             a vector of length K giving deviance residuals for each block.

D             deviance summary statistic ( = sum(d.^2)). This is the first
              statistical measure returned by the PSIGNIFIT engine.

dat           data set: each row is an observation. May be expressed as
              [x y n], [x r n] or [x r w].

deriv         derivative of  the attributes of interest (parameters, thresholds
              or slopes) with respect to each of the parameters (our convention is
              for columns to denote different attributes, for example thresholds at
              different cut levels, and for rows to denote different parameters). 
              Derivatives are evaluated at the maximum-likelihood estimated
              or initial parameter values. Used to calculate "lff" (see below) in the
              BCa method.

deviance      each residual is equal to the square root of the deviance
residuals     calculated for one of the data points in isolation, signed
              according to the direction of the difference between observed
              performance and model prediction. The sum of squared deviance
              residuals equals overall deviance, D.

est           initial estimate of something (parameters, thresholds, slopes).
              Usually this is the maximum-likelihood estimate from a fit, but
              sometimes the user supplies a hypothesis explicity - in which
              case est refers to the values derived from the hypothesized
              distribution.

F             underlying psychometric function. Relates stimulus intensity x to
              the probability that the psychological mechanism of interest can
              detect the stimulus, in the absence of stimulus-independent
              errors or lucky guesses. See the MATLAB function PSYCHF.

gamma         parameter of the psychometric performance function psi,
              determining the lower bound of predicted performance: psi(x) >=
              gamma for all x. Its value corresponds to predicted performance
              in the absence of a stimulus. In nAFC paradigms, gamma is usually
              fixed at the reciprocal of the number of intervals per trial. In
              yes/no paradigms, it is usually small (< 0.5). gamma is the third
              element of the parameter vector theta.

k             a vector of length K denoting the chronological index for each
              block in the data set

K             number of blocks in the data set (= length(n))

lambda        parameter of the psychometric performance function psi,
              determining the upper bound of predicted performance: psi(x) <=
              1-lambda for all x. 1-lambda is the predicted performance level
              for an arbitrarily large stimulus. lambda is typically small 
              (<0.05) because it is generally assumed that observers do not
              make stimulus-independent errors at high rates. lambda is the
              fourth element in the parameter vector theta.

ldot:         the derivative of log-likelihood, with respect to each of the 
              parameters, evaluated at the MLE, for each of the bootstrap data 
              sets. Thus ldot has R rows and four columns (one for each 
              parameter). It is used to obtain BCa confidence interval limits, 
              and is output by the PSIGNIFIT engine. 

lims          a matrix whose columns refer to different estimates and whose 
              rows correspond to different elements of conf. Each element is 
              the estimate whose cpe in the bootstrap distribution is equal to 
              the appropriate element of conf. The method used to obtain
              the confidence limits is indicated by the field
              'confLimMethod' - usually it will be the BCa method.

lff:          the least-favourable direction(s) in parameter space for 
              inference about a variable or variables. It is used to obtain BCa 
              confidence interval limits. In our format, it is a matrix with 
              one column for each variable, and four rows indicating the 
              components of the least-favourable direction in the dimensions of 
              the four parameters. A least-favourable direction vector should 
              be calculated for each parameter, threshold or slope estimate - 
              see Davison, AC & Hinkley, DV (1997): Bootstrap methods and their 
              application; Cambridge: CUP, pp206-7 and p249. 

"log slope"   gradient of the psychometric function with respect to log10(x).
              This can be calculated as threshold * slope * log(10), or by
              passing the option 'log' into FINDSLOPE. See the entries for
              "threshold" and "slope".
              
m             number of points in parameter space at which simulations are
              repeated during sensitivity analysis

n             a vector of length K denoting the number of trials in each block
              of the data set

N             total number of observations in data set (= sum(n))

nAFC          see 2AFC

p             a vector of length K denoting a model's prediction for the 
              expected values of y

PA            denotes parameters

parameters    alpha, beta, gamma and lambda.

psi           psychometric performance function, relating stimulus intensity x
              to the probability of a correct or positive response. A common 
              form for predicting performance in a single psychophysical
              experiment is
                  p = psi(x; {alpha, beta, gamma, lambda}) =
                         gamma + (1 - gamma -lambda) F(x; {alpha, beta})
              See the MATLAB function PSI.

r             a vector of length K denoting the number of correct (or positive)
              responses in each block of the data set (= y ./ n).

R             number of simulations performed

r_pd          correlation coefficient between p and d (model predictions and
              signed deviance residuals). Used as a statistical check on the
              functional form of one's model, (usually psi). This is the second
              statistical measure returned by the PSIGNIFIT engine.

r_kd          correlation coefficient between k and d (chronological indices
              and signed deviance residuals) excluding those points for which
              y == 0 or y == 1. Used as a statistical check on any change in 
              the observer's performance over time (between blocks). This is 
              the third statistical measure returned by the PSIGNIFIT engine.

sensitivity   a way of examining the severity of bootstrap error. Our technique
analysis      is to re-run the bootstrap m times, with different parameter sets
              for the generating function. The m new parameter set lie on the 
(sens)        boundary of a region in alpha-beta space. The default is to take 8
              points that lie on the boundary of a joint confidence region of 
              a given coverage  in parameter space. The shape of the region
              is likelihood-based  (all points on the skin have the same deviance value 
              with respect to the original data set). The points' precise locations are
              chosen by an algorithm that uses the original bootstrap distribution of
              parameters, and aims to spread out the points' directions in the alpha/beta
              plane while exploring the extremes of variation in alpha and beta within the
              region (gamma and lambda, if they are free parameters, may be varied in
              order to accomplish this aim). At  the end of sensitivity analysis we report
              the "worst-case"  variability estimate (see "worst" below).

shape         the functional form of F: in the current implementation, this can 
              be Weibull, logistic, cumulative Gaussian, Gumbel or linear.
              
sim           matrix of simulated values: each row is a different simulation,
              and each column is a different variable.

SL            denotes slopes

slope         gradient of the psychometric function with respect to x, 
              evaluated at a particular threshold value for x. The "slope at 
              0.5" would therefore usually refer to the value of dF/dx 
              evaluated at the point at which F(x) = 0.5. Slopes can also be 
              calculated in the context of psi (so the "75% slope" would be 
              d(psi)/dx evaluated where psi(x) = 0.75). See the entry for 
              "threshold" below.

TH            denotes thresholds

theta         [alpha beta gamma lambda].

threshold     inverse of the psychometric function with respect to x.
              The "threshold at 0.5" would usually refer to F^-1(0.5). This is 
              a threshold in the context of the underlying psychometric 
              function F, which is the default measurement in FINDTHRESHOLD and
              FINDSLOPE. By passing the option 'performance' into these two
              functions, thresholds can instead be calculated in the context of
              the psychometric performance function psi. So the "75% 
              performance threshold" would be psi^-1(0.75) and the "75%
              performance slope" would be the derivative of psi at that point.
              Note, however, that the PSIGNIFIT engine can only calculate BCa
              confidence limits for "underlying" thresholds and slopes (inverse of F).

w             a vector of length K denoting the number of incorrect (or
              negative) responses in each block of the data set (= n - r).

worst-case    a matrix with the same format as "lims": for each column (i.e.
bootstrap     each variable) confidence limits are listed. For a certain 
limit         variable t (a threshold, for example), let us use t_0 to denote
              the value of t in the bootstrap generating function, and u_0 to 
(worst)       denote, say, the upper limit of a confidence interval obtained by 
              the bootstrap method. In sensitivity analysis, we perform m 
              additional bootstraps: each one has a different generating 
              function, so each one has a different initial value for t: 
              t_1.....t_m. The m bootstraps yield m estimates for the upper 
              confidence interval limit, u_1....u_m. Now, finally, we can 
              define the "worst case" bootstrap limit u_worst:
                  u_worst = t_0 + max([u_0-t_0, u_1-t_1, ......u_m-t_m])
              So, the difference between u_worst and t_0 is the same as the
              largest difference between u and t encountered during sensitivity 
              analysis.

x             a vector of length K denoting the stimulus value for each block
              in the data set.

y             a vector of length K denoting the proportion of correct responses
              for each block in the data set (= r ./ n).

yes/no        any single-interval experimental paradigm, in which the
              observer sees one stimulus per trial.


Part of the psignifit standalone distribution version 2.5.6.
Copyright (c) J.Hill 1999-2005.
Please read the LICENSE and NO WARRANTY statement in Legal.txt
mailto:psignifit@bootstrap-software.org
http://bootstrap-software.org/psignifit/
