使用嵌套Dirichlet分布分析成分间呈正相关的成分数据及其在Morris水迷宫实验中的应用
Analysis of Compositional Data with Positive Correlations among Components using a Nested Dirichlet Distribution with Application to a Morris Water Maze Experiment
AI总结：
针对Morris水迷宫实验象限停留时间占比的成分数据特性，指出现有Dirichlet分布拟合检验方法的缺陷，提出基于Dirichlet或嵌套Dirichlet分布的双样本检验法，重分析既往数据得出不同结论。
摘要：
在典型的Morris水迷宫实验中，小鼠被放置在圆形水箱中并允许自由游动，直到找到平台从而触发逃离水箱的路径。作为参考，水箱被划分为四个象限：设有逃离触发装置的目标象限、目标象限的对侧象限，以及两个相邻象限。实验可测量多个响应变量：小鼠在水箱不同象限中停留的时长、小鼠在象限间穿越的次数，或是小鼠触发逃离水箱的速度。在考量各象限内停留时长时，研究假设正常小鼠在不含逃离路径的象限中停留时间更短，而患有获得性或诱发性精神缺陷的小鼠会在水箱所有象限中停留相等的时间。显然，各象限停留时间占比之和必须为1，因此在统计学上具有相关性；但该实验的大多数数据分析都将象限停留时间视为统计独立的。近期有一篇论文提出了一种假设检验方法，涉及将此类数据拟合为Dirichlet分布。尽管相较于忽略数据成分结构的研究有所改进，但我们证明该方法存在缺陷。我们提出了一种双样本检验方法，用于检测两个独立组的成分占比差异，其中两组数据均来自Dirichlet分布或嵌套Dirichlet分布。我们使用这一新检验方法重新分析了既往研究的数据，并得出了不同的结论。
英文摘要：
In a typical Morris water maze experiment, a mouse is placed in a circular water tank and allowed to swim freely until it finds a platform, triggering a route of escape from the tank. For reference purposes, the tank is divided into four quadrants: the target quadrant where the trigger to escape resides, the opposite quadrant to the target, and two adjacent quadrants. Several response variables can be measured: the amount of time that a mouse spends in different quadrants of the water tank, the number of times the mouse crosses from one quadrant to another, or how quickly a mouse triggers an escape from the tank. When considering time within each quadrant, it is hypothesized that normal mice will spend smaller amounts of time in quadrants that do not contain the escape route, while mice with an acquired or induced mental deficiency will spend equal time in all quadrants of the tank. Clearly, proportion of time in the quadrants must sum to one and are therefore statistically dependent; however, most analyses of data from this experiment treat time in quadrants as statistically independent. A recent paper introduced a hypothesis testing method that involves fitting such data to a Dirichlet distribution. While an improvement over studies that ignore the compositional structure of the data, we show that methodology is flawed. We introduce a two-sample test to detect differences in proportion of components for two independent groups where both groups are from either a Dirichlet or nested Dirichlet distribution. This new test is used to reanalyze the data from a previous study and come to a different conclusion.
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