The purpose of this study was to investigate within- and between-threshold parameter invariance for items of a fourteen-item Positive Affect Scale developed to assess positive moods (like happy, peaceful, etc.) of university students. To test whether the estimated threshold parameters were as expected (1 to 5, with increments of 1) across all the 14 items, Graded Response, Partial Credit, and Rating Scale Models were fit the response data collected from 326 students. A comparison of the model fit statistics, such as the negative 2log likelihood and chi-square values, revealed that the Graded Response Model had the best fit and that the thresholds estimates for all the items in the Positive Affective Scale were reasonably close to the expected 1 to 5 values with increments of 1. The study illustrates how polytomous response models can be used to test the psychometric quality of items with ordinal rating scales.