simdiff {diffIRT} R Documentation

## Simulate data according to the D-diffusion or Q-diffusion IRT model.

### Description

This function simulates responses and response time data according to the D-diffusion or Q-diffusion IRT model.

### Usage

simdiff(N,nit,ai=NULL,vi=NULL,gamma=NULL,theta=NULL,ter=NULL,
model="D",max.iter=19999,eps=1e-15)

### Arguments

 N number of subjects. nit number of items. ai a vector of length nit containing the true values for the item boundary separation, a[i]. vi a vector of length nit containing the true values for the item drift rate, v[i]. gamma a vector of length N containing the true values for the person boundary separation, gamma[p]. theta a vector of length N containing the true values for the person drift rate, theta[p]. ter a vector of length nit containing the true values for the item non-decision time, ter[i]. model string; Either "D" to fit the D-diffusion IRT model or "Q" to fit the Q-diffusion IRT model. max.iter maximum number of iterations for the rejection algorithm. See Details. eps convergence criterion for the rejection algorithm. See Details

### Details

Function simdiff is an extension of the rejection algorithm outlined in Tuerlinckx et al. (2001). 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 ai true values for ai[i] vi true values for vi[i] gamma true values for gamma[p] theta true values for theta[p] ter true values for ter[i]

### Author(s)

Dylan Molenaar d.molenaar@uva.nl

### References

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.