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   2011, Vol. 43 Issue (12) : 1454-1461     DOI:
On the Use of Polynomial Regression in Congruence Research: Application and Analysis
TANG Jie;LIN Zhi-Yang;MO Li
(School of Economics, Fujian Normal University, Fuzhou 350108, China)
(School of Management, Xiamen University, Xiamen 361005, China)
(School of Journalism and Communication, Xiamen University, Xiamen 361005, China)
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Abstract  For decades, the study of congruence in organizational research has relied on difference scores, which induces numerous methodological problems in presenting congruence, such as covered relations, reduced reliability and validity. Unfortunately, this method is still used dominantly in domestic researches due to few available alternatives. The method of polynomial regression is introduced in this research to directly test relationships among two component measures of difference scores and dependent variables, and also the advantages of polynomial regression over difference scores in expressing congruence are discussed and verified.
Then, from the aspects of foundation points, theoretical derivations, analytical procedures and hypothesis tests, the framework of polynomial regression equations coupling with response surface analysis for congruence researches are modified. Three key features of surface are concerned for analysis. The first is stationary point, which corresponds to the overall minimum, maximum, or saddle point of the surface. The second is principal axes of the surface, two of which intersect at the stationary point. The upward or downward curvature of surface, depending on the shape of surface (convex or concave), is greatest along one of the principal axes and least along the other. The third feature is the slope of the surface along two principle axes, Y = X and Y = -X lines. Formulas expressing these key features can be derived from coefficients of polynomial regression equations, based on which, this general framework clarifies how coefficients from equations can be used to comprehensively describe surface and test hypotheses. Moreover, the framework permits researchers to evaluate complicated congruence conceptual models rigorously.
Finally, as an illustration, how the person-organization value congruence affects persons’ affective commitment to change in four dimensions are examed, which specifies the characters of surfaces and puts forward theoretical implications. This paper deliberately interprets how data analytical results deduce theoretical conclusions based on the framework mentioned above. The results reveal that the congruence effects completely supported by traditional methods are not perfect, and should even be rejected as to two of four value dimensions with the same data.
In sum, current research testifies that polynomial regression equation not only can explain more variance of dependent variables than difference scores, but also uncover more valuable relations and information. Firstly, it exhibits whether the perfect congruence effects exist. Secondly, it exams main effects, congruence effects and interaction effect at the same time. Thirdly, it reveals scores and changing rate of dependents under imperfect congruence condition. Admittedly, the framework and the required analytical modes presented in this paper are more complicated than previous methods. However, approach to this method enables researchers to study congruence in a more comprehensive way. Practical implications derived from this study point toward the actual effect of person-organization value congruence in management activities.
Keywords polynomial regression      congruence      response surface analysis      difference scores     
Corresponding Authors: MO Li   
Issue Date: 30 December 2011
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TANG Jie,LIN Zhi-Yang,MO Li. On the Use of Polynomial Regression in Congruence Research: Application and Analysis [J]. , 2011, 43(12): 1454-1461.
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