Assessing goodness-of-fit of the queueing model of visual search to accuracy data

The queueing model of visual search proposed by Li, Schlather, and Erdfelder (in press) is a novel mathematical model that accounts for both accuracy and response time in standard visual search with interpretable parameters. One of the merits of the model is that the probabilities of correct and incorrect responses are specified as analytical functions of the experimental manipulations, namely the set size (i.e., the number of stimuli in the display) and the presence or absence of the target. As a result, the number of model parameters remains constant even if the number of set size levels increases. However, its ability to incorporate quantitative features of the experimental condition comes with the cost that tailor-made goodness of fit tests need to be developed. The application of a standard likelihood ratio test provides too conservative results because the model implies more restrictive patterns than its number of free parameters suggests. In this presentation, I show that the distribution of the commonly used likelihood ratio statistic under the null hypothesis cannot be approximated asymptotically by the chi-square distribution with degrees of freedom that equal the difference in the number of free parameters. I explain the reasons in detail and compare alternative goodness-of-fit measures based on various approaches.