Because confidence in lineup responses is important in research and practice, it is important to understand how confidence relates to the cognitive processes underlying lineup responses. Here we introduce the lineup confidence model, a multinomial processing tree model for measuring confidence in lineups. The model builds on an established multinomial processing tree model that separates four cognitive processes underlying lineup responses: culprit-presence detection, culprit-absence detection, biased suspect selection, and guessing-based selection. The lineup confidence model additionally incorporates the measurement of confidence. To test the validity of the lineup confidence model, we conducted an experiment using post-response feedback as a manipulation of confidence. Responses based on detection yielded higher confidence than responses based on guessing, and responses based on biased suspect selection also yielded higher confidence than responses based on guessing. Post-response feedback selectively influenced confidence while leaving the parameters for culprit-presence detection, culprit-absence detection, biased suspect selection, and guessing-based selection unaffected. Confidence can thus be sensitively measured with the lineup confidence model without compromising measurement of the other processes.