响应面分析是一种以多项式回归为基础,探究2个或多个预测变量与1个结果变量之间非线性关系的统计分析方法。与差异分数法相比,响应面分析在探究一致性问题方面具有明显的优势。依据其数学原理,二阶响应面分析对一致性假设有如下检验流程。通过检验第一主轴与一致线的匹配性、不一致线对应截面曲线的倒“U”型形态且顶点在原点处,验证广义一致性假设。进一步结合一致线截面曲线的形态检验严格一致性假设、上升岭假设等其他情况。R语言中的RSA包能够实现模型拟合、参数估计及三维可视化等功能,为研究中的实际分析提供了全面且便捷的操作流程。尽管当前响应面分析在使用上面临一些误区和挑战,但其在理论假设检验和结果可视化等方面优势显著,在众多研究领域发挥了关键作用。
Response surface analysis (RSA) is a statistical analysis method based on polynomial regression used to examine nonlinear relationships between two or more predictor variables and one outcome variable. Compared with the difference score method, RSA has distinct advantages in exploring the congruence problem. According to its mathematical principles, quadratic RSA follows a specific testing procedure for the congruence assumption. The generalized congruence assumption is verified by testing the matching between the first principal axis (FPA) and the line of congruence (LOC), and whether the inverted "U" shape, with the vertex at the origin, of the corresponding cross-sectional curve of the line of incongruence (LOIC) was exhibited. Furthermore, the morphological test of the LOC cross-section curve is carried out to test the strict congruence assumption, the rising ridge assumption, and other related conditions. The RSA package in R language enables model fitting, parameter estimation, and 3D visualization, providing a comprehensive and simple operation process for practical application in research. Although there are some misunderstandings and challenges in the use of RSA, it has significant advantages in hypothesis testing and result visualization and plays a key role in a wide range of research fields.
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