To determine the interactive effect of independent variables on the dependent variable, we administer Analysis of Variance (ANOVA). particularly in the case of a factorial design. Is there any other parametric test that can serve the same purpose?
Both factorial experiment and split plot design explains the interactive effects of the two variables.Regards
Factorial anova is a special case of ordinary least squares regression. 1) There is an analogous procedure you could use with other regression approaches, like a generalized linear model like Poisson regression or Gamma regression. 2) There are other regression techniques like quartile regression. 3) There are non-parametric approaches like aligned ranks transformation that will result in analogous results. 4) There are other ways to estimate the coefficients for a general linear model. Robust techniques. Bootstrap or re-sampling.
We can determine the interactive effect of independent variables on the dependent variable through multiple regression analysis as well
In a regression equation, an interaction effect is represented as the product of two or more independent variables. For example, here is a typical regression equation without an interaction:
ŷ = b0 + b1X1 + b2X2
where ŷ is the predicted value of a dependent variable, X1 and X2 are independent variables, and b0, b1, and b2 are regression coefficients.
And here is the same regression equation with an interaction:
ŷ = b0 + b1X1 + b2X2 + b3X1X2
Here, b3 is a regression coefficient, and X1X2 is the interaction. The interaction between X1 and X2 is called a two-way interaction, because it is the interaction between two independent variables. Higher-order interactions are possible, as illustrated by the three-way interaction in the following equation:
ŷ = b0 + b1X1 + b2X2 + b3X3 + b4X1X2 + b5X1X3 + b6X2X3 + b7X1X2X3
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