Generates a data frame expressing a block experimental structure using Nelder's formula
nelder(formula)A list with the first member being the data frame
A model formula. See details
Nelder (1965) suggested a simple notation that could express a large variety of different blocked designs. The function `nelder()` that generates a data frame of a design using the notation. There are two operations:
`>` (or \(\to\) in Nelder's notation) indicates "clustered in".
`*` (or \(\times\) in Nelder's notation) indicates a crossing that generates all combinations of two factors.
The implementation of this notation includes a string indicating the name of the variable and a number for the number of levels, such as `abc(12)`. So for example `~cl(4) > ind(5)` means in each of five levels of `cl` there are five levels of `ind`, and the individuals are different between clusters. The formula `~cl(4) * t(3)` indicates that each of the four levels of `cl` are observed for each of the three levels of `t`. Brackets are used to indicate the order of evaluation. Some specific examples:
`~person(5) * time(10)`: A cohort study with five people, all observed in each of ten periods `time`
`~(cl(4) * t(3)) > ind(5)`: A repeated-measures cluster study with four clusters (labelled `cl`), each observed in each time period `t` with cross-sectional sampling and five indviduals (labelled `ind`) in each cluster-period.
`~(cl(4) > ind(5)) * t(3)`: A repeated-measures cluster cohort study with four clusters (labelled `cl`) wth five individuals per cluster, and each cluster-individual combination is observed in each time period `t`.
`~((x(100) * y(100)) > hh(4)) * t(2)`: A spatio-temporal grid of 100x100 and two time points, with 4 households per spatial grid cell.
nelder(~(j(4) * t(5)) > i(5))
nelder(~person(5) * time(10))
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