Is it true that including an multiplicative term in a model drastically increases the level of collinearity?
Yes, including a product term in a general linear model can drastically increase the level of collinearity. The product term (X1X2) is an exact nonlinear function of the constituent variables (X1 and X2), thus correlations of the constituent variables with the product term are usually high. Critics speculate that the increase in collinearity impacts the quality of the parameter estimate of the effect of the independent variables on the dependent variable by increasing the covariance and variances of regression coefficients (Friedrich 1982). According to the regression assumptions the only time that multicollinearity is crippling to analysis is in the presence of perfect collinearity. In this situation the model estimation is unable to produce results.
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