Principle of marginality
Encyclopedia
In statistics
, the principle of marginality refers to the fact that the average (or main
) effects, of variables in an analysis are marginal to their interaction effect. The principle of marginality argues that, in general, it is wrong to test, estimate, or interpret main effects of explanatory variables
where the variables interact or, similarly, to model interaction effects but delete main effects that are marginal to
them. While such models are interpretable, they lack applicability, as they ignore the effects of their marginal main effects.
Nelder
and Venables have argued strongly for the importance of this principle in regression analysis
.
Statistics
Statistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
, the principle of marginality refers to the fact that the average (or main
Main effect
In the design of experiments and analysis of variance, a main effect is the effect of an independent variable on a dependent variable averaging across the levels of any other independent variables...
) effects, of variables in an analysis are marginal to their interaction effect. The principle of marginality argues that, in general, it is wrong to test, estimate, or interpret main effects of explanatory variables
Dependent and independent variables
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...
where the variables interact or, similarly, to model interaction effects but delete main effects that are marginal to
them. While such models are interpretable, they lack applicability, as they ignore the effects of their marginal main effects.
Nelder
John Nelder
John Ashworth Nelder FRS was a British statistician known for his contributions to experimental design, analysis of variance, computational statistics, and statistical theory.-Contributions:...
and Venables have argued strongly for the importance of this principle in regression analysis
Regression analysis
In statistics, regression analysis includes many techniques for modeling and analyzing several variables, when the focus is on the relationship between a dependent variable and one or more independent variables...
.