The purposes of this study are twofold. First, to investigate the construct or factorial structure of a set of Reading and Mathematics computerized adaptive tests (CAT), "Measures of Academic Progress" (MAP), given in different states at different grades and academic terms. The second purpose is to investigate the invariance of test factorial structure across different grades, academic terms and states. Because of the uniqueness of CAT data (different student receive different items), traditional factor analysis based on fixed form data is no longer practically possible at the item level. This study illustrates how to overcome the difficulty of applying factor analysis in CAT data and study results provide evidences for valid interpretation MAP tests scores across grades at different academic terms for different states. The CFA [confirmatory factor analysis] Measurement Model and the CFA Measurement Model in the Multiple Group are described in an appendix. (Contains 3 figures and 9 tables.)