Fit a Quadrilateral Dissimilarity Model

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Description

Fits a Quadrilateral Dissimilarity Model to same-different data.

Usage

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qdm(psi, start, respfun = c("logistic", "guessing", "gumbel", "gompertz",
    "weibull", "cauchy", "shepardA", "shepardAneg", "shepardB",
    "shepardBneg", "shepardD", "shepardDneg", "shepardE", "shepardEneg",
    "shepardF", "shepardFneg"), bias = 0,
    estimfun = c("minchi2", "ols", "wls"), optimizer = c("optim", "nlm"),
    optimargs = list())

Arguments

psi

data object created with psi.

start

starting values for parameter estimation.

respfun

function that describes relationship between discrimination probabilities and similarity measure, see Details.

bias

takes perceptual bias into account. Default is 0.

estimfun

method to estimate parameters, see Details.

optimizer

which optimizer should be used: nlm or optim.

optimargs

takes additional arguments passed to nlm or optim.

Details

More details about the Quadrilateral Dissimilarity Model can be found in Dzhafarov and Colonius (2006).

Via respfun, different functions can be selected to describe the relationship between discrimination probabilities and dissimilarity measure. Implemented are the logistic function (logistic), the logistic function with guessing parameter (guessing), several other functions commonly used as psychometric functions (gumbel, gompertz, weibull, cauchy), and five functions suggested by Shepard (1987) (shepardA, shepardB, shepardD, shepardE, shepardF) and their negatives (shepardAneg, shepardBneg, shepardDneg shepardEneg, shepardFneg). Default is the logistic function. Note that for some of these functions the results critically depend on the choice of the starting values.

Parameters can be estimated by using different minimizing functions available via the estimfun argument: ordinary least squares (ols), weighted least squares (wls), and minimization of Pearson's X^2 (minchi2). Default is the minimization of X^2.

Value

An object of class qdm that consists of the following components:

optimout

output of optimizer (nlm or optim).

coefficients

estimated parameters.

psi

psi object used to fit Quadrilateral Dissimilarity Model.

respfun

function used to describe relationship between discrimination probabilities and similarity measure.

bias

perceptual bias used in the model.

References

Dzhafarov, E. N., & Colonius, H. (2006). Regular Minimality: A fundamental law of discrimination. In H. Colonius & E. N. Dzhafarov (Eds.), Measurement and representation of sensations (pp. 1–46). Hillsdale, NJ: Lawrence Erlbaum Associates.

Shepard, R. N. (1987). Towards a universal law of generalization for psychological science. Science, 237, 1317–1323.

See Also

psi, predict.qdm, persp.qdm, nlm, optim.

Examples

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## prepare data
data(FMrate)
psi1 <- psi(FMrate[FMrate$id == "subj1",])

## estimate model
p.s <- c(.2, .5, .1, .5, .3, .1, .1, .1)
q1 <- qdm(psi1, start=p.s)
print(q1)

## model predictions
predict(q1)
persp(q1)