by Mingfeng Xue. Measurements (e.g., tests, surveys, questionnaires) are inevitably involved with various sources of errors. Among many psychometric theories, item response theory stands out for its capability of detailed analyses at the item level and its potential to reduce some of the measurement errors. This post first discussed the limitations of conventional summation and average, which give rise to the IRT models, and then introduced a basic form of the Rasch model, including expressions of the model, the assumptions underlying it, some of its advantages, and software packages. Some codes are also provided.