To provide more refined diagnostic feedback with collateral information in item response times ( RT s), this study proposed joint modelling of attributes and response speed using item responses and RT s simultaneously for cognitive diagnosis. For illustration, an extended deterministic input, noisy ‘and’ gate ( DINA ) model was proposed for joint modelling of responses and RT s. Model parameter estimation was explored using the Bayesian Markov chain Monte Carlo ( MCMC ) method. The PISA 2012 computer‐based mathematics data were analysed first. These real data estimates were treated as true values in a subsequent simulation study. A follow‐up simulation study with ideal testing conditions was conducted as well to further evaluate model parameter recovery. The results indicated that model parameters could be well recovered using the MCMC approach. Further, incorporating RT s into the DINA model would improve attribute and profile correct classification rates and result in more accurate and precise estimation of the model parameters.