Plotting p against x
Plotting p against x
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绘制 p 对 x 的图
DOI：
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发表时间：
1983
期刊：
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通讯作者：
J. Copas
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文献类型：
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作者：
J. Copas
给定n个案例的数据，我们希望绘制Px对x的估计值。如果假设参数模型，那么问题当然得到了很好的发展，例如，我们有Cox（1970）的逻辑方法或拟合多项式或样条的精算方法。但在拟合这样一个模型之前，我们通常希望先把数据绘制出来，看看这样一个模型是否合理——在简单回归的类似问题中，我们把观测结果绘制在散点图上。但是对于二进制数据，散点图并没有明显的相似之处，某种程度的数据平滑似乎是不可避免的。在建议下面给出的非参数二元回归方法时，我们关注的是两种情况(a)当x是离散的，但n不足以在每个x值处获得有意义的比例，以及(b)当x是连续的，因此（本质上）数据中的x都是不同的。
Given data on n cases we wish to plot an estimate of Px against x. If a parametric model is assumed then the problem is of course well developed, for example we have the logistic methods of Cox (1970) or the actuarial methods of fitting polynomials or splines. But before fitting such a model we will usually wish to first plot the data to see if such a model is reasonable-in the analagous problem of simple regression we plot the observations on a scatter diagram. But there is no obvious analogue of the scatter diagram for binary data, and some degree of data smoothing seems inevitable. In suggesting the non-parametric binary regression method given below we are concerned with the two cases (a) when x is discrete but n is not sufficiently large for meaningful proportions to be available at each value of x, and (b) when x is continuous so that (essentially) the x's in the data are all distinct.