RespFit {diffIRT}

Assessing diffIRT model fit for the responses using limited information goodness-of-fit testing.

Description

This function uses the procedure by Maydeu-Olivares & Joe (2005) to asses the goodness-of-fit of the responses from a diffIRT object.

Usage

RespFit(object, order=2)

Arguments

object

A diffIRT object for which the Maydeu-Olivares & Joe test needs to be conducted.

order

Integer; The order of the moments to be compared see details.

Details

RespFit is an implementation of the method outlined in Maydeu-Olivares & Joe (2005). The traditional Pearson chi-square method are sub optimal in this case because in common IRT settings, contingency tables tend to be sparse. This causes the asymptotic distribution of the traditional test statistic to depart from its theoretical distribution. In the method proposed by Maydeu-Olivares & Joe, this problem is overcome by focussing on the first r moments (specified in order) of the observed and predicted response distributions. Choosing order to be equal to the number of items will result in the traditional chi-square test statistic. Commonly order is chosen to be small (e.g., 1 or 2).

Value

Returns an object of class RespFit with entries:

Z

A matrix with predicted statistics, observed statistics, and Z-values

Mr

The test statistic.

df

Degrees of freedom.

order

Order of the test statistic.

Warning

For large numbers of items, this test becomes computationally infeasible.

Note

The degrees of freedom for the test statistic differ between the D-diffusion and Q-diffusion model as for the Q-diffusion model, a[i] and v[i] are not simultaneously identified in response data only. See Molenaar, Tuerlinckx, & van der Maas (2013) for more details.

Author(s)

Dylan Molenaar [e-mail]

References

Maydeu-Olivares, A., & Joe, H. (2005). Limited and full information estimation and testing in 2n contingency tables: A unified framework. Journal of the American Statistical Association, 100, 1009-1020.

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/.

See Also

QQdiff for model fit assessment of the response times. diffIRT for fitting diffusion IRT models. factest for estimation of factor scores (person drift rate and person boundary separation). simdiff for simulating data according to the D-diffusion or Q-diffusion IRT model.

Examples

## Not run: 
 # open extraversion data
data(extraversion)
x=extraversion[,1:10]
rt=extraversion[,11:20]
 
# fit an unconstrained D-diffusion model
res1=diffIRT(rt,x,model="D")          

# Conduct the limited-information test
RespFit(res1, 2)

## End(Not run)