Fit a Quadrilateral Dissimilarity Model
Description
Fits a Quadrilateral Dissimilarity Model to samedifferent data.
Usage
1 2 3 4 5 6  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 
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: 
optimargs 
takes additional arguments passed to 
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 ( 
coefficients 
estimated parameters. 
psi 

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
1 2 3 4 5 6 7 8 9 10 11 12 
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