development The attributes in the cognitive model are specified at a fine grain size in order to yield a detailed cognitive skill profile about the examinee's test performance. This necessitates many items that must be created to measure each attribute in the hierarchy. For computer-based tests, automated item generation (AIG) is a promising method for generating multiple items "on the fly" that have similar form and psychometric properties using a common template. Example of items aligned to the attributes in a hierarchy Referring back to the pictorial representation of Ratio and Algebra hierarchy, an item can be constructed to measure the skills described in each of the attributes. For example, attribute A1 includes the most basic arithmetic operation skills, such as addition, subtraction, multiplication, and division of numbers. An item that measures this skill could be the following: examinees are presented with the algebraic expression , and asked to solve for (t + u). For this item, examinees need to subtract 3 from 19 and then divide 16 by 4. Attribute A2 represents knowledge about the property of factors. An example of an item that measures this attribute is "If (p + 1)(t – 3) = 0 and p is positive, what is the value of t?” The examinee must know the property that the value of at least one factor must be zero if the product of multiple factors is zero. Once this property is recognized, the examinee would be able to recognize that because p is positive, (t – 3) must be zero to make the value of the whole expression zero, which would finally yield the value of 3 for t. To answer this item correctly, the examinee should have mastered both attributes A1 and A2. Attribute A3 represents not only knowledge of factoring (i.e., attribute A2), but also the skills of applying the rules of factoring. An example of an item that measures this attribute is “”. Only after the examinee factors the second expression into the product of the first expression would the calculation of the value of the second expression be apparent. To answer this item correctly, the examinee should have mastered attributes A1, A2, and A3. Psychometric analysis During this stage, statistical pattern recognition is used to identify the attribute combinations that the examinee is likely to possess based on the observed examinee response relative to the expected response patterns derived from the