Transformations to additivity in measurement error models
Transformations to additivity in measurement error models
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DOI：
10.2307/2533112
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发表时间：
1997-03-01
期刊：
影响因子：
1.9
通讯作者：
Wang, N
中科院分区：
文献类型：
--
作者：
Eckert, RS;Carroll, RJ;Wang, N
在许多问题中，人们希望对响应Y和协变量X之间的关系进行建模。有时直接观察X是困难的、昂贵的，甚至是不可能的，但是我们可以观察一个更容易获得的替代变量W。到目前为止，关注的实际协变量X和替代变量W之间关系的最常见模型是W = X + U，其中变量U表示测量误差。这种附加测量误差的假设对于某些数据集可能是不合理的。我们提出了一个新的模型，即h（W）= h（X）+U，其中h（.）是从单调函数族H中选取的单调变换函数。新模型的思想是，在正确的尺度下，测量误差是加性的。我们提出了两个可能的变换族H。一个是基于选择一个转换，使样本内的平均值和标准差的复制W的不相关。第二种是基于选择转换，以便误差（U）符合预先指定的分布。所使用的变换族是参数幂变换和三次样条族。给出了几个数据实例来说明该方法。
In many problems, one wants to model the relationship between a response Y and a covariate X. Sometimes it is difficult, expensive, or even impossible to observe X directly, but one can instead observe a substitute variable W that is easier to obtain. By far, the most common model for the relationship between the actual covariate of interest X and the substitute W is W = X + U, where the variable U represents measurement error. This assumption of additive measurement error may be unreasonable for certain data sets. We propose a new model, namely h(W) = h(X) + U, where h(.) is a monotone transformation function selected from some family H of monotone functions. The idea of the new model is that, in the correct scale, measurement error is additive. We propose two possible transformation families H. One is based on selecting a transformation that makes the within-sample mean and standard deviation of replicated W's uncorrelated. The second is based on selecting the transformation so that the errors (U's) fit a prespecified distribution. Transformation families used are the parametric power transformations and a cubic spline family. Several data examples are presented to illustrate the methods.