通常我们再进行回归分析时，认为只有因变量y有测量误差，而自变量x是没有测量误差的，所以我们的回归公式中，误差项也全部来自于y。但有时候，如果x和y都存在误差，且我们也想把x的测量误差考虑在内，那么一般的模型是做不到的。Reduced Major Axis Regression便是专门针对这种问题的。Harper (2016) 对Reduced Major Axis Regression的适用场景做了很好的描述：

“The theoretical underpinnings of standard least-squares (LS) regression analysis are based on the assumption that the independent variable (often thought of as x) is measured without error as a design variable. The dependent variable (often labeled y) is modeled as having uncertainty or error. Both independent and dependent measurements may have multiple sources of error. Thus, the underlying least-squares regression assumptions can be violated. Reduced major axis (RMA) regression is specifically formulated to handle errors in both the x and y variables. It is an alternative to least squares and demonstrates the importance of understanding the assumptions underlying statistical procedures.”

     Reduced Major Axis Regression和一般的最小二乘回归的结果，有时候还是有明显区别。比如Harper (2016) 给出的案例中：

      Reduced Major Axis Regression的实际应用案例(Fraley et al. 2020)：

     在R中，lmodel2包就可以轻松完成这一分析并作图。lmodel2包地址：https://rdrr.io/cran/lmodel2/man/lmodel2.html

参考文献：

Fraley, K. M., H. J. Warburton, P. G. Jellyman, D. Kelly, and A. R. McIntosh. 2020. Do body mass and habitat factors predict trophic position in temperate stream fishes? Freshwater Science 39:405-414.

Harper, W. V. 2016. Reduced Major Axis Regression. Pages 1-6 Wiley StatsRef: Statistics Reference Online.

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