simdiffT {diffIRT}

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

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.

Value

Returns a list with the following entries:

rt

the simulated matrix of response times

x

the simulated matrix of responses

Author(s)

Dylan Molenaar [e-mail]

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)