Builds the coefficient-of-variation table that fit_lrp(), fit_qrp() and
fit_mcm() consume, starting from the raw grid of basic experimental units
(BEU) as the trial was harvested. Adjacent BEU are grouped into every
rectangular plot shape the grid admits: for a grid of \(L\) rows by \(C\)
columns, each shape is \(X_L \times X_C\) basic units with \(X_L\) a
divisor of \(L\) and \(X_C\) a divisor of \(C\). For each shape the
plot totals are formed and their mean, standard deviation and CV reported.
Usage
calc_cv_shapes(
.data,
value = NULL,
row_id = NULL,
col_id = NULL,
trial = NULL,
min_plots = 2
)Arguments
- .data
a matrix (one trial), a named list of matrices (several trials), or a long data frame with one row per basic unit.
- value
name of the column holding the BEU measurement (long format).
- row_id, col_id
names of the row and column index columns (long format).
- trial
optional column name identifying the trial (long format).
- min_plots
minimum number of plots a shape must yield to be kept (default 2).
Value
A data frame with one row per shape and trial: trial,
X_L, X_C (shape in basic units), x (plot size),
n (number of plots), mean, sd and cv (percent),
ordered by plot size.
Details
This closes the pipeline: the grid goes in, the CV table comes out, and it
feeds the fitters directly, since the returned columns are already named
x, cv and trial.
Shapes and plot counts
A shape of area \(X = X_L X_C\) yields \(n = LC/X\) plots, so the CV of a
large plot size rests on few plots and is estimated with little information:
the last rows of the table are the least reliable. The n column is
returned for exactly this reason and is the natural weight for a weighted
fit. Shapes leaving fewer than min_plots plots are dropped, which by
default removes only the whole grid (a single plot, no variance).
Shapes are not interchangeable at equal area: \(1 \times 2\) and
\(2 \times 1\) cover the same two basic units but run along different
directions of the field, and their CVs differ whenever fertility is not
isotropic. Both are reported, which is why the CV table has repeated
x values.
References
Cargnelutti Filho, A. et al. (2025). Determinacao do tamanho de parcela para
avaliar a massa de parte aerea de grao-de-bico. Revista Vivencias,
21(43), 499-513.
Paranaiba, P. F., Ferreira, D. F. & Morais, A. R. (2009). Revista
Brasileira de Biometria, 27(2), 255-268.
Examples
## Three trials of the bundled simulated uniformity trial, each an 8 x 12
## grid of basic units (see ?uniformity_trial).
grids <- lapply(split(uniformity_trial, uniformity_trial$trial),
function(d) as.matrix(d[, grep("^col", names(d))]))
tab <- calc_cv_shapes(grids)
#> CV by shape for 3 trial(s).
head(tab, 8)
#> trial X_L X_C x n mean sd cv
#> 1 T1 1 1 1 96 251.0129 58.92214 23.47375
#> 2 T1 1 2 2 48 502.0258 91.52677 18.23149
#> 3 T1 2 1 2 48 502.0258 87.47753 17.42491
#> 4 T1 1 3 3 32 753.0388 109.57170 14.55061
#> 5 T1 1 4 4 24 1004.0517 145.29792 14.47116
#> 6 T1 2 2 4 24 1004.0517 135.13136 13.45861
#> 7 T1 4 1 4 24 1004.0517 128.77483 12.82552
#> 8 T1 1 6 6 16 1506.0775 170.84259 11.34355
## Same area, different orientation, different CV
tab[tab$trial == "T1" & tab$x == 2, ]
#> trial X_L X_C x n mean sd cv
#> 2 T1 1 2 2 48 502.0258 91.52677 18.23149
#> 3 T1 2 1 2 48 502.0258 87.47753 17.42491
## The table feeds the fitters unchanged
fit_lrp(tab[tab$trial == "T1", ], x = "x", cv = "cv", step = 0.05)
#> Using x = 'x', cv = 'cv' (single series).
#> Linear Response Plateau (LRP) fit
#> Method: segment
#> Breakpoint (Xo): 9.150
#> CV at breakpoint: 6.960
#> R2: 0.893 RMSE: 1.513 AIC: 92.3 BIC: 96.9
#>
#> Local minima of the SSE profile (8):
#> Xo = 7.400 SSE +15.3% vs optimum
#> Xo = 12.800 SSE +34.5% vs optimum
#> Xo = 5.750 SSE +50.1% vs optimum
#> ... see $local_minima for all
# \donttest{
## One model per trial, straight from the grids
fit_lrp(tab, x = "x", cv = "cv", trial = "trial", step = 0.01)$summary
#> Using x = 'x', cv = 'cv', trial = 'trial' -> 3 trials.
#> trial a b breakpoint plateau R2 RMSE AIC BIC
#> 1 T1 21.0495 -1.5398 9.16 6.9448 0.8926 1.5130 92.321 96.863
#> 2 T2 19.3597 -1.0725 14.40 3.9162 0.8341 2.3486 112.547 117.089
#> 3 T3 21.3271 -1.5075 10.11 6.0860 0.8019 2.4137 113.805 118.347
#> n_local
#> 1 8
#> 2 7
#> 3 8
## n falls as the plot grows: the last shapes rest on very few plots
unique(tab[, c("x", "n")])
#> x n
#> 1 1 96
#> 2 2 48
#> 4 3 32
#> 5 4 24
#> 8 6 16
#> 10 8 12
#> 13 12 8
#> 16 16 6
#> 18 24 4
#> 21 32 3
#> 22 48 2
# }