Why “spatially balanced”
Classical design names such as completely randomised design and randomised complete block design describe two things at once: a structure (no blocks, or complete blocks) and the way treatments are allocated to that structure, which is at random. The randomisation is part of the design. It is what justifies the standard analysis of that structure, because every permissible allocation was equally likely to be used.
speed keeps the structures but allocates treatments differently. It searches for the allocation that minimises an objective function. By default, that objective penalises like treatments sitting next to each other, and treatments being unevenly spread across rows, columns and any other spatial factors. The allocation that comes out is chosen for its spatial properties rather than drawn at random, so a name containing “randomised” would describe it wrongly. “Spatially balanced” describes how the allocation was actually chosen.
Note
The search itself uses random numbers: simulated annealing proposes random swaps, and
optim_params(random_initialisation = )shuffles the starting layout. That is randomness in how the optimum is found, not in which allocation is used. Different seeds can return different designs, but each one is returned because it scored well.
The names
| Structure | Name in speed
|
Abbreviation |
|---|---|---|
| No blocking | Spatially Balanced Design | SBD |
| Complete blocks | Spatially Balanced Block Design | SBBD |
Names that describe only a structure are unchanged, because the structure holds however the allocation was chosen. A Latin square still has each treatment once in every row and column; a split-plot still has sub-plots nested in whole plots. The same applies to strip-plot, incomplete block, row-column and p-rep designs.
What this means for analysis
The allocation was optimised over the spatial factors given in spatial_factors (rows and columns by default), so those factors are part of the design, and they belong in the analysis model. For example, an SBBD laid out in rows and columns should be analysed with terms for the rows and columns it was balanced over, alongside its blocks, rather than with blocks alone. The rows and columns can enter as fixed or random effects, or through a spatial model of the residuals (for example, AR1 × AR1), whichever suits the trial.
summary() reports the structure each design was optimised over; see the Evaluating a Design section of the main vignette.