When calculating the slope of the congruence (a1) in polynomial regression with response surface analysis I have been confused by some author's interpretations. This is calculated by adding the x-predictor beta coefficient (x1) to the y-preductor beta coefficient (x2); however, numerous authors interpret this as meaning that the DV is higher when BOTH the x-predictor and y-predictor are high. When I look at the actual betas, sometimes one of the predictor coefficients will be as low as zero or even negative. Here, the adding of the two will be dominated by one large coefficient. Am I misinterpreting this? Any help would be appreciated.
I'm a bit confused about what you are looking at.
If you are working with a response surface, you can fit a "full model": Y = B0 + B1X1 + B2X2 + B3X1^2 + B4X2^2 + B5X1X2... Each of these terms is linearly independent from each other. So, the coefficients B1 and B2 have no effect on the size or sign of B3, B4 or B5.
This seems to be some sort of specialised terminology. This publication may help: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2988441/ ( Ayala Cohen, Inbal Nahum-Shani, and Etti Doveh (2010) " Further Insight and Additional Inference Methods for Polynomial Regression Applied to the Analysis of Congruence", Multivariate Behavioral Research, Volume 45, Issue 5, 828-852)
Thank you David. I will be sure to read your recommended paper.
Andrew - Many papers I am reading in management and psycholgoy are reporting the addition of B1 and B2 as a significant predictor of Y as evidence of a "congruence effect". Meaning that when BOTH are high, Y is maximized. However, for some papers, one of the predictor variables, B1 or B2, is really high (sig by itself) and the other is very low and sometimes even zero or in the opposite direction.
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