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.
SONG Yupeng
,
CHEN Qingqing
,
LIU Xiaowen
. The Hypothesis Testing Process of Quadratic Response Surface Analysis and Its Operational Steps in R Language[J]. Psychological Communications, 2025
, 8(2)
: 163
-173
.
DOI: 10.12100/j.issn.2096-5494.225023
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