A Confirmatory Factor Analytic Study Examining the Dimensionality of Educational Achievement Tests

It is important to check the fundamental assumption of most popular Item Response Theory models, unidimensionality. However, it is hard for educational and psychological tests to be strictly unidimensional. The tests studied in this paper are from a standardized high-stake testing program. They feature potential multidimensionality by presenting various item types and item sets. Confirmatory factor analyses with one-factor and bifactor models, and based on both linear structural equation modeling approach and nonlinear IRT approach were conducted. The competing models were compared and the implications of the bifactor model for checking essential unidimensionality were discussed.

Fast Algorithms Using Minimal Data Structures for Common Topological Relationships in Large, Irregularly-spaced Topographic Data Sets

Digital terrain models (DTM) typically contain large numbers of postings, from hundreds of thousands to billions. Many algorithms that run on DTMs require topological knowledge of the postings, such as finding nearest neighbors, finding the posting closest to a chosen location, etc. If the postings are arranged irregu- larly, topological information is costly to compute and to store. This paper offers a practical approach to organizing and searching irregularly-space data sets by presenting a collection of efficient algorithms (O(N),O(lgN)) that compute important topological relationships with only a simple supporting data structure. These relationships include finding the postings within a window, locating the posting nearest a point of interest, finding the neighborhood of postings nearest a point of interest, and ordering the neighborhood counter-clockwise. These algorithms depend only on two sorted arrays of two-element tuples, holding a planimetric coordinate and an integer identification number indicating which posting the coordinate belongs to. There is one array for each planimetric coordinate (eastings and northings). These two arrays cost minimal overhead to create and store but permit the data to remain arranged irregularly.