The linear model diagram: A graphical method for the display of factor relationships in experimental design

Following specification of all variables of interest as well as their interrelationships, the validity of an ecological model (or of any of its components) is often tested by analysis of variance (ANOVA)-based procedures, either through experimentation, 'screening' of predictors, or simulation. To this end, the linear model diagram (LMD) is introduced as a graphical method for the display of factor relationships in ANOVA balanced complete designs. As an analysis-oriented diagram, hence in contrast with layout-oriented diagrams useful for the allocation of experimental units to factor levels (or vice versa), the purpose of the LMD is to streamline specification of a design's underlying linear model. This contains all available information about each observation and its correct specification is essential for computing reliable ANOVA error terms. In the LMD, factor relationships, especially higher order interactions in complex fully factorial or nested/factorial designs, are more effectively visualised than in the other existing analysis-oriented diagrams. Further, by assigning a unique label to a design, including those sharing an otherwise identical linear model, the LMD provides the ecologist with a graphic 'shorthand' that streamlines the statistical analysis of an experiment as well as may help clarify terminological inconsistencies.