Instability of Regression Coefficients Illustrated

In the two-factor factorial fixed effects ANOVA, no interaction between factors may be demonstrated graphically by connecting population cell means to form a set of parallel piecewise linear curves. The three-factor case is considerably more complicated, because both three-factor and two-factor interactions may be present. However, if no three-factor interaction is assumed, or, in addition, if one or more of the two-factor interactions is also assumed to be zero, then the resulting constrained model may be characterized in a manner similar to the two-factor case. Details are presented for three such constrained models.