Models were given earlier for comparative designs (completely randomized designs, randomized block designs and Latin square designs). 

For full factorial screening designs with k factors (2^k runs, not counting any center points or replication runs), the full model contains all the main effects and all orders of  interaction terms. Usually, higher order (three level or beyond) interaction terms are included initially to construct the normal (or half-normal) plot of effects, but later dropped when a simpler, adequate model is fit.  Depending on the software available or the analyst's preferences, various techniques such as normal or half-normal plots, Youden plots, p-value comparisons and stepwise regression routines are used to reduce the model down to the minimum number of needed terms. A JMP example of model selection is shown later in this section and a Dataplot example is given as a case study.

For fractional factorial screening designs, it is necessary to know the alias chain structure in order to write an appropriate starting model  containing only the interaction terms the experiment was designed to be able to estimate (assuming all terms confounded with these selected terms are insignificant). This is illustrated by the JMP fractional factorial example later in this section.  The starting model is then reduced by the same techniques described above for full factorial models.

Response surface initial models include quadratic terms and may occasionally also include cubic terms. These models were described in section 3. 

Of course, as in all cases of model fitting, residual analysis and other tests of model fit are used to confirm or adjust models, as needed.