Model Order and Design Resolution
Model Order
A model's order is an indication of its complexity and flexibility. Low order models provide a less detailed picture of the data and estimate fewer model aspects than high order models. For example: First order models are only able to estimate main effects (i.e., changes in the response variable/dependent variable caused by a factor/independent variable) in the form of mean differences between categorical factors or linear relationships among continuous factors. Second order models are able to estimate first order effects plus two-way interaction effects and quadratic terms for continuous factors. Third order models contribute above second order effects by also estimating three-way interaction effects and cubic terms for continuous factors. There are no theoretical limits to the height of a model's order. However, second order models are generally sufficient to support the goal of characterization in operational testing. Lower order models can also be appropriate for screening goals, whereas high order models are necessary for fitting more detailed response surfaces to test data.
Model Order and Test Size
Knowing the order of effects you wish to estimate is important to assessing design adequacy, as higher order models require more test points (i.e., larger sample size). This greater investment provides greater information, so the size of the test should match the level of detail/degree of information the evaluators desire.
Design Resolution
For two-level full and fractional factorial experiments, the order of the statistical model is often discussed in terms of their design “resolution.” A design with greater resolution can accommodate higher order model terms than a design with lower resolution. In lower resolution models, more terms are confounded with one-another than in higher resolution models. When terms are confounded, the design is unable to resolve the cause of differences in the response variable (e.g., it is unclear whether the AxB interaction or the AxC interaction is responsible for an observed pattern in results). Resolution III, IV, and V designs are particularly important because they address second order models, which are commonly fit in operational testing. Definitions of these designs are shown below: Resolution III designs: Main effects may be indistinguishable from some two-factor interactions. Resolution IV designs: All main effects can be estimated independently but some two-factor interactions may be indistinguishable from other two-factor interactions. Resolution V designs: All main effects and two-factor interactions can be estimated independently from each other.
