Does the addition of a product term cause certain coefficients that are significant in an additive model to be non-significant in an interactive model?
It is possible that significant coefficients in an additive model can be non-significant in the interactive model. It is important to recognize that this occurrence does not mean that the parameter estimates of the interactive model are wrong, rather these coefficients are estimates of particular trends of change in Y with changes in the independent variables. Specifically, b1 and b2 in the interactive model are estimates of the change in Y with changes in X1 and X 2, when X2 and X1 respectively equal zero. These beta coefficients estimate particular conditional relationships rather than general ones. Thus it is possible that at this level, the effect of the independent variables on the dependent variables is non-significant.
