GUESSING AND THE ERROR STRUCTURE OF LEARNING-MODELS
通过结构方程模型处理测试分数数据中的猜测和题目难度问题，纠正以测试分数作为能力代理变量导致的估计偏差，为教育经济学研究者提供更准确的学习生产函数估计方法。
This paper is broadly concerned with problems associated with the use of test score data to infer the relative strength of inputs to the production of learning. It should be of interest to those employing a typical strategy of economic education research: pretesting students, applying some special educational treatment to a subset of students, and posttesting the students. By this strategy the researcher enquires whether the treated group learned more or learned more efficiently. This paper specifically addresses several concerns raised by Thomas Johnson by laying out a set of structural equations and thereby modelling the probability of answering a test item correctly and by dealing in a novel way with the hypothesis that some test questions are more difficult than others. The key structural equation of the model is the learning production function which explains student learning in terms of student aptitude and study time. Because student aptitude cannot be observed, a standard procedure has been to use the pretreatment test score as an aptitude proxy. William Becker and Salemi have pointed out that such a procedure can seriously bias estimates of the production function parameters. The approach of this paper is to model explicitly the probability distribution of the test score of a student conditional on his ability level. This approach is similar to that used to estimate models with qualitative dependent variables. But the test score model suggests a convenient approximation and a correction to least squares which together deliver consistent estimates of the structural parameters.