Sensitivity of the linear logistic test model to misspecification of the weight matrix

Abstract

Under the linear logistic test model, a weight is assigned to each cognitive operation used to respond to an item. The allocation of these weights is open to misspecification that can result in faulty estimates of the basic parameters. The effect on root mean squares (RMSs) of the difference between the parameter estimates obtained under misspecification conditions and those obtained under correct specification conditions was examined. Six levels of misspecification and four sample sizes were used. Even a small number of errors in the weight specifications resulted in large RMS values. However, weight matrices with a high proportion of nonzero elements tended to yield RMSs that were approximately half as large as those with a small number of nonzero elements. Although sample size had some effect on the RMS values, it was quite small compared to that due to the level of misspecification of the weights. The results suggest that because specifying the elements in the weight matrix is a subjective process, it must be done with great care. Index terms: error rates, linear logistic test model, misspecification, parameter estimation, weight matrix.