THE STATISTICAL-ANALYSIS OF GENERAL PROCESSING TREE MODELS WITH THE EM ALGORITHM
THE STATISTICAL-ANALYSIS OF GENERAL PROCESSING TREE MODELS WITH THE EM ALGORITHM
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DOI：
10.1007/bf02294263
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发表时间：
1994-03-01
期刊：
影响因子：
3
通讯作者：
BATCHELDER, WH
中科院分区：
文献类型：
--
作者：
HU, X;BATCHELDER, WH
多项处理树模型假设观察到的行为类别可以由表示为树中的分支的一个或多个处理序列产生。这些模型形成了参数多项式模型的一个子类，它们为对数线性模型提供了一个实质性的替代方案。我们考虑通常的情况，其中分支概率是参数0小于或等于theta（s）小于或等于1的非负整数幂与它们的补数1 - theta（s）的乘积。EM算法的一个版本构造，具有非常强的性能。首先，E-步骤和M-步骤都是分析和计算容易，因此，可以构建一个快速的PC程序来获得大量参数的MLE。其次，得到了整个类的观测Fisher信息矩阵的封闭形式表达式。第三，证明了算法必然收敛于局部最大值，这是一个强于指数族作为一个整体的结果。第四，我们展示了该算法如何处理相当一般的假设检验模型参数的限制。第五，我们扩展算法来处理读取和Cressie功率发散家庭的拟合优度统计。本文包括一个例子来说明其中的一些结果。
Multinomial processing tree models assume that an observed behavior category can arise from one or more processing sequences represented as branches in a tree. These models form a subclass of parametric, multinomial models, and they provide a substantively motivated alternative to loglinear models. We consider the usual case where branch probabilities are products of nonnegative integer powers in the parameters, 0 less-than-or-equal-to theta(s) less-than-or-equal-to 1, and their complements, 1 - theta(s). A version of the EM algorithm is constructed that has very strong properties. First, the E-step and the M-step are both analytic and computationally easy; therefore, a fast PC program can be constructed for obtaining MLEs for large numbers of parameters. Second, a closed form expression for the observed Fisher information matrix is obtained for the entire class. Third, it is proved that the algorithm necessarily converges to a local maximum, and this is a stronger result than for the exponential family as a whole. Fourth, we show how the algorithm can handle quite general hypothesis tests concerning restrictions on the model parameters. Fifth, we extend the algorithm to handle the Read and Cressie power divergence family of goodness-of-fit statistics. The paper includes an example to illustrate some of these results.