diffIRT (version 1.5)

simdiffT: Simulate data according to the traditional diffusion model.

Description

This function simulates responses and response time data according to the traditional diffusion model for a single subject on a given number of trails. The parameters of the traditional diffusion model include: boundary separation, mean drift rate, standard deviation of drift rate, variance of the process, and ter.

Usage

simdiffT(N,a,mv,sv,ter,vp,max.iter=19999,eps=1e-15)

Arguments

N

number of trails.

a

boundary separation.

mv

mean of the normally distributed drift rates across trails.

sv

standard deviation of the normally distributed drift rate across trails.

ter

non-decision time.

vp

variance of the process, which is a scaling parameter. Default equals 1.

max.iter

Maximum number of iterations for the rejection algorithm. See Details.

eps

Convergence criterion for the rejection algorithm. See Details

Value

Returns a list with the following entries:

rt

the simulated matrix of response times

x

the simulated matrix of responses

Details

Function simdiffT is an application of the rejection algorithm outlined in Tuerlinckx et al. (2001) subject to normally distributed inter-trail variability in drift. In this algorithm, a proposal response time is sampled from an exponential distribution. This proposal is accepted as actual response time when a specific condition is satisfied (see Eq. 16 in Tuerlinckx, 2001). As this condition requires the approximation of an infinite sum, a convergence criterion needs to be specified (see the argument eps). When the condition is not satisfied, a new proposal response time is sampled. This is repeated until the proposal response time is accepted or when max.iter has been reached.

References

Molenaar, D., Tuerlinkcx, F., & van der Maas, H.L.J. (2015). Fitting Diffusion Item Response Theory Models for Responses and Response Times Using the R Package diffIRT. Journal of Statistical Software, 66(4), 1-34. URL http://www.jstatsoft.org/v66/i04/.

Tuerlinckx, F., Maris, E., Ratcliff, R., & De Boeck, P. (2001). A comparison of four methods for simulating the diffusion process. Behavior Research Methods, Instruments & Computers, 33, 443-456.

See Also

diffIRT for fitting diffusion IRT models.

Examples

## Not run: 
# 
# # simulate data accroding to the traditional diffusion model
# set.seed(1310)
# a=2
# v=1
# ter=2
# sdv=.3
# N=10000
# 
# data=simdiffT(N,a,v,sdv,ter)
# rt=data$rt
# x=data$x
# 
# # fit the traditional diffusion model (i.e., a restricted D-diffusion model, 
# # see application 3 of the paper by Molenaar et al., 2013) 
# 
# diffIRT(rt,x,model="D",constrain=c(1,2,3,0,4),start=c(rep(NA,3),0,NA)) 
# 
# # this constrained model is a traditional diffusion model
# # please note that the estimated a[i] value = 1/a
# # and that the estimated v[i] value = -v                  
# 
# ## End(Not run)