dodSim {sensR}

Simulate data from the Degree-of-Difference model

Description

Simulate data from the Degree-of-Difference model for a given value of d-prime. The boundary parameters can either be specified by the user, or be chosen automatically so as to 1) maximize the likelihood ratio statistic, 2) ensure responses in each category is equally probable across same-pairs and different-pairs or 3) minimize the standard error of d-prime.

Usage

dodSim(d.prime, ncat=4, sample.size = c(100, 100),
       method.tau = c("equi.prob", "LR.max", "se.min", "user.defined"),
       tau = NULL, d.prime0 = 0, ...)

Arguments

d.prime

the value of d-prime.

ncat

the number of response categories.

sample.size

the sample size for same-pairs and different-pairs. The sample size can be a scalar number in which case the sample sizes for both same-pairs and different-pairs are taken to equal that number.

method.tau

the method with which to choose the boundary parameters. If "user.defined", the user has to specify the tau argument, otherwise the set of boundary parameters are chosen automatically (see the Details section below).

tau

if method.tau = "user.defined" the set of boundary parameters, otherwise not used.

d.prime0

if method.tau = "LR.max" the value of d-prime under the null hypothesis, otherwise not used.

...

passed on to optimal_tau.

Details

In principle both d-prime and all boundary parameters have to be specified in order to be able to simulate from the DOD model. However, since it can be difficult to decide which boundary parameters to use for simulation, dodSim offers ways to choose these parameters automatically according to the following three criteria:

equi.prob

the boundary parameters are chosen such that responses in each category are equally probable across same-pairs and different-pairs.

LR.max

the boundary parameters are chosen such that the likelihood ratio statistic for the test of d-prime is maximized. This choice maximizes the power of the likelihood ratio test and is in a sense an optimal choice of boundary parameters.

se.min

the boundary parameters are chosen such that the standard error of d-prime is minimized. This method also maximizes the power of the Wald test of d-prime when the null hypothesis is no-difference (d-prime = 0). This method can be numerical unstable for small and large d-prime values (approximately d.prime < 0.5 and d.prime > 5).

Experience shows that the asymptotic properties of the DOD model are not too sensitive to the choice of boundary parameters: power, standard error of d-prime and confidence intervals seem to be fairly constant irrespectively which of the above three criteria are used to choose the boundary parameters.

Value

A 2-by-ncat matrix of counts with same-pairs in the first row and different-pairs in the second row. First/last column corresponds to "same"/"different" on the response scale.

Author(s)

Rune Haubo B Christensen

See Also

dod, dod_fit, dodControl, optimal_tau, dodPwr

Examples

## Simulate data from the DOD model with the equi.prob method:
set.seed(125)
(Data <- dodSim(d.prime=1, sample.size=100, method.tau="equi.prob"))

## Simulate data that maximizes the likelihood ratio statistic:
set.seed(125)
dodSim(d.prime=1, sample.size=100, method.tau="LR.max")

## Simulate with user-defined values for the boundary parameters:
dodSim(d.prime=1.5, sample.size=c(100, 100),
       method.tau="user.defined", tau=1:4)

## Simulate using different sample sizes for same-pairs and
## different-pairs:
dodSim(d.prime=1, ncat=3, sample.size=c(75, 125),
       method.tau="se.min")