Correçoes no texto.

parent f67b8b5d
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......@@ -32,6 +32,10 @@ library(wzCoop)
```
```{r setup, include = FALSE}
source("config/setup.R")
tbn_ <- captioner(prefix = "Table")
fgn_ <- captioner(prefix = "Figure")
tbl_ <- function(label) tbn_(label, display = "cite")
fgl_ <- function(label) fgn_(label, display = "cite")
```
# Experiment and Data Description
......@@ -141,11 +145,11 @@ xyplot(dm ~ dos^0.2 | iso,
ylab = "Second diameter (mm)")
```
Figure `r fgl_("dm-x-dos")` (top) shows that doses are very skewed.
Figure `r fgl_("dm-x-dos")` (bottom) shows that in the log-log scale
`r fgl_("dm-x-dos")` (top) shows that doses are very skewed.
`r fgl_("dm-x-dos")` (bottom) shows that in the log-log scale
there isn't a linear relation between mean diameter and fungicide dose.
Figure `r fgl_("dm-x-dos0.2")` shows that, under the transformed
`r fgl_("dm-x-dos0.2")` shows that, under the transformed
5th-root scale, doses levels are close to equally spaced. In fact, 0.2
was found by minimization of the variance of distance between doses
($\sigma^2$) a power transformation ($p$) of dose rescaled to a unit
......@@ -187,12 +191,33 @@ plot(log(v) ~ p, type = "o")
abline(v = op$minimum)
```
So $x^0.2$ is the most equally spaced set obtained with a power
So $x^{0.2}$ is the most equally spaced set obtained with a power
transformation. Equally spaced levels are beneficial beacause reduce
problems related to leverage.
# Half Effective Concentration (EC~50~) Estimation
A cubic spline is function constructed of piecewise third-order
polynomials which pass through a set of $m + 1$ knots. These knots spans
the observed domain of the continous factor $x$, so the set of knots is
$$
K = \{\xi_0, \xi_1, \ldots, \xi_m\}.
$$
A function $s(x)$ is a cubic spline if it is made of cubic polynomials
$s_{i}(x)$ in each interval $[x_{i-1}, x_{m}]$, $i = 1, \ldots, m$.
Those adjacent cubic pylinomials pieces must bind and be smooth at the
internal knots , so additional constrais are made to result in a
composite continuous smooth function. Requering continous derivatives,
we ensure that the resulting function is as smooth as possible.
For natural splines, two aditional boundary conditions are made
$$
s^{''}_{1}(x) = 0, \quad s^{''}_{m}(x) = 0,
$$
that is, the pieces at borders aren't cubic but instead linear.
Natural cubic splines were used to estimate the half effective
concentration (EC~50~). A non linear model is usually applied in this
context but wasn't found a non linear model flexible enough to give a
......@@ -201,7 +226,7 @@ haven't a model equation, they are vey flexible and numerical
root-finding algorithms can e used to compute EG~50~ based on a linear
interpolated function on a predicted grid. Also, area under the
sensibility curve (AUSC) were computed by numerical integration under
dose studied domain.
studied dose domain.
```{r}
sen$iso <- factor(sen$iso, levels = sort(unique(sen$iso)))
......@@ -210,7 +235,7 @@ sen$doz <- sen$dos^0.2
# A data frame without dose.
senu <- unique(subset(sen,
select = c(ue, iso, fun, tra, hed, pop, yr)))
select = c(ue, iso, fun, tra, hed, pop, yr, plot)))
# Splines.
library(splines)
......@@ -350,6 +375,28 @@ p <- xyplot(auc ~ pop | tra + fun,
useOuterStrips(p)
```
```{r}
#-----------------------------------------------------------------------
# Creates block, treatment cell and plants.
ec$blk <- as.integer(as.integer(substr(ec$plot, 0, 1)) > 2)
ec$cell <- with(ec, interaction(yr, blk, hed, tra, drop = TRUE))
# TODO FIXME: Falta o Paulo passar a coluna que indentifica as plantas
# (1, 2, e 3) em cada cela experimental.
# ec <- arrange(df = ec, yr, blk, hed, tra, iso, fun)
# head(ec)
# # Experimental units (plants)
# ec$plnt <- with(ec, interaction(blk, pop, hed, tra, drop = TRUE))
# nlevels(ec$plnt)
#
# xtabs(~plnt, ec)
#
# m0 <- lm()
```
****
# Session information
......
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