This tutorial is intended to show how to deploy the mitscherlich()
function for estimating a continuous response model with a critical soil
test value. This function fits the classical exponential regression
response model that follows a curve shape described as
y = a * (1-exp(-c(x + b)), where
a = asymptote, b = xintercept,
c = rate or curvature parameter. The mitscherlich()
function works automatically with self starting initial values to
facilitate the model’s convergence. This approach is extensively used in
agriculture to describe crops response to input since the biological
meaning of its curved response. With 3 alternatives to fit the model,
the mitscherlich() function brings the advantage of controlling the
parameters quantity: i) type = 1 (DEFAULT), corresponding to the model
without any restrictions to the parameters
(y = a * (1-exp(-c(x + b))); ii) type = 2 (“asymptote
100”), corresponding to the model with only 2 parameters by setting the
asymptote = 100 (y = 100 * (1-exp(-c(x + b))), and iii)
type = 3 (“asymptote 100 from 0”), corresponding to the model with only
1 parameter by constraining the asymptote = 100 and xintercept = 0
(y = 100 * (1-exp(-c(x))). As disadvantages we can mention
that: i) there is no critical value the asymptote (as it would result
equal to Inf); and ii) consequently, there is no confidence
interval for the CSTV. For this latter purpose, we recommend the user
would to use a re-sampling technique (e.g. bootstrapping) for a reliable
confidence interval estimation of parameters and CSTV
Load your dataframe with soil test value (stv) and relative yield
(ry) data.
Specify the following arguments into the function
-mitscherlich()-:
(a). type select the type of parameterization of the
model. i) type = 1 corresponds to the model without any restrictions to
the parameters (y = a * (1-exp(-c(x + b))); ii) type = 2
(“asymptote 100”), corresponding to the model with only 2 parameters by
setting the asymptote = 100 (y = 100 * (1-exp(-c(x + b))),
and iii) type = 3 (“asymptote 100 from 0”), corresponding to the model
with only 1 parameter by constraining the asymptote = 100 and xintercept
= 0 (y = 100 * (1-exp(-c(x))).
(b). data (optional),
(c). stv (soil test value) and ry (relative
yield) columns or vectors,
(d). target (optional) if want a CSTV for a different
`ry`` than the plateau.
(e). tidy TRUE (produces a data.frame with results) or
FALSE (store results as list),
(f). plot TRUE (produces a ggplot as main output) or
FALSE (no plot, only results as data.frame),
(g). resid TRUE (produces plots with residuals analysis)
or FALSE (no plot),
Run and check results.
Check residuals plot, and warnings related to potential
limitations of this model.
Adjust curve plots as desired.
library(soiltestcorr)Suggested packages
# Install if needed
library(ggplot2) # Plots
library(dplyr) # Data wrangling
library(tidyr) # Data wrangling
library(utils) # Data wrangling
library(data.table) # Mapping
library(purrr) # MappingThis is a basic example using three different datasets:
# Example 1 dataset
# Fake dataset manually created
data_1 <- data.frame("RY" = c(65,80,85,88,90,94,93,96,97,95,98,100,99,99,100),
"STV" = c(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15))
# Example 2. Native fake dataset from soiltestcorr package
data_2 <- soiltestcorr::data_test
# Example 3. Native dataset from soiltestcorr package, Freitas et al. (1966), used by Cate & Nelson (1971)
data_3 <- soiltestcorr::freitas1966type = 1 Type = “no restrictions” or Type = 1 for model with ‘no restrictions’
fit_1_type_1 <-
soiltestcorr::mitscherlich(data = data_1,
ry = RY,
stv = STV,
type = 1,
target = 90)
utils::head(fit_1_type_1)
#> $a
#> [1] 98.71
#>
#> $b
#> [1] 2.07
#>
#> $c
#> [1] 0.37
#>
#> $equation
#> [1] "98.7(1-e^(-0.371(x+2.1)"
#>
#> $target
#> [1] 90
#>
#> $CSTV
#> [1] 4.5type = 2 Type = “asymptote 100” or Type = 2 for model with ‘asymptote = 100’
fit_1_type_2 <-
soiltestcorr::mitscherlich(data = data_1,
ry = RY,
stv = STV,
type = 2,
target = 90)
utils::head(fit_1_type_2)
#> $a
#> [1] 100
#>
#> $b
#> [1] 2.56
#>
#> $c
#> [1] 0.32
#>
#> $equation
#> [1] "100(1-e^(-0.318(x+2.6)"
#>
#> $target
#> [1] 90
#>
#> $CSTV
#> [1] 4.7type = 3 Type = “asymptote 100 from 0” or Type = 3 for model with ‘asymptote =
100 and xintercept = 0’
fit_1_type_3 <-
soiltestcorr::mitscherlich(data = data_1,
ry = RY,
stv = STV,
type = 3,
target = 90)
utils::head(fit_1_type_3)
#> $a
#> [1] 100
#>
#> $b
#> [1] 0
#>
#> $c
#> [1] 0.81
#>
#> $equation
#> [1] "100(1-e^(-0.811x)"
#>
#> $target
#> [1] 90
#>
#> $CSTV
#> [1] 2.8RY type = 1, target = 90%, confidence level = 0.95, replace with your
desired values
tidy = FALSE It returns a LIST (more efficient for multiple fits at once)
# Using dataframe argument, tidy = FALSE -> return a LIST
fit_1_tidy_false <-
soiltestcorr::mitscherlich(data = data_1,
ry = RY,
stv = STV, type = 1, target = 90,
tidy = FALSE)
utils::head(fit_1_tidy_false)
#> $a
#> [1] 98.71
#>
#> $b
#> [1] 2.07
#>
#> $c
#> [1] 0.37
#>
#> $equation
#> [1] "98.7(1-e^(-0.371(x+2.1)"
#>
#> $target
#> [1] 90
#>
#> $CSTV
#> [1] 4.5tidy = TRUE It returns a data.frame (more organized results)
# Using dataframe argument, tidy = FALSE -> return a LIST
fit_1_tidy_true <-
soiltestcorr::mitscherlich(data = data_1,
ry = RY,
stv = STV, type = 1, target = 90,
tidy = TRUE)
fit_1_tidy_true
#> a b c equation target CSTV AIC AICc R2
#> 1 98.71 2.07 0.37 98.7(1-e^(-0.371(x+2.1) 90 4.5 64 68 0.97You can call stv and ry vectors using the
$.
The tidy argument still applies for controlling the
output type
fit_1_vectors_list <-
soiltestcorr::mitscherlich(ry = data_1$RY,
stv = data_1$STV,
type = 1,
tidy = FALSE)
fit_1_vectors_tidy <-
soiltestcorr::mitscherlich(ry = data_1$RY,
stv = data_1$STV,
type = 1,
tidy = TRUE)
fit_2 <-
soiltestcorr::mitscherlich(data = data_2,
ry = RY,
stv = STV,
type = 1,
target = 90)
utils::head(fit_2)
#> $a
#> [1] 97.98
#>
#> $b
#> [1] 3.91
#>
#> $c
#> [1] 0.09
#>
#> $equation
#> [1] "98(1-e^(-0.089(x+3.9)"
#>
#> $target
#> [1] 90
#>
#> $CSTV
#> [1] 24.4
fit_3 <-
soiltestcorr::mitscherlich(data = data_3,
ry = RY,
stv = STK,
type = 1,
target = 90)
utils::head(fit_3)
#> $a
#> [1] 96.38
#>
#> $b
#> [1] -8.69
#>
#> $c
#> [1] 0.05
#>
#> $equation
#> [1] "96.4(1-e^(-0.046(x-8.7)"
#>
#> $target
#> [1] 90
#>
#> $CSTV
#> [1] 67.9 Note: the stv column needs to have the same name for
all datasets
#
data.all <- dplyr::bind_rows(data_1, data_2,
data_3 %>% dplyr::rename(STV = STK),
.id = "id") %>%
tidyr::nest(data = c("STV", "RY"))
# Run multiple examples at once with map()
fit_multiple_map <-
data.all %>%
dplyr::mutate(models = purrr::map(data,
~ soiltestcorr::mitscherlich(ry = .$RY,
stv = .$STV,
type = 1,
target = 90,
tidy = TRUE)))
utils::head(fit_multiple_map)
#> # A tibble: 3 x 3
#> id data models
#> <chr> <list> <list>
#> 1 1 <tibble [15 x 2]> <df [1 x 9]>
#> 2 2 <tibble [137 x 2]> <df [1 x 9]>
#> 3 3 <tibble [24 x 2]> <df [1 x 9]>
unnest(fit_multiple_map, models)
#> # A tibble: 3 x 11
#> id data a b c equation target CSTV AIC AICc R2
#> <chr> <list> <dbl> <dbl> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
#> 1 1 <tibble> 98.7 2.07 0.37 98.7(1-e^(-0.~ 90 4.5 64 68 0.97
#> 2 2 <tibble> 98.0 3.91 0.09 98(1-e^(-0.08~ 90 24.4 1022 1022 0.54
#> 3 3 <tibble> 96.4 -8.69 0.05 96.4(1-e^(-0.~ 90 67.9 187 189 0.67Alternatively, with group_map, we do not require nested data.
However, it requires to dplyr::bind_rows and add an id
column specifying the name of each dataset.
This option return models as lists objects.
fit_multiple_group_map <-
dplyr::bind_rows(data_1, data_2, .id = "id") %>%
dplyr::group_by(id) %>%
dplyr::group_map(~ soiltestcorr::mitscherlich(data = .,
ry = RY,
stv = STV, type = 1, target = 90,
tidy = TRUE))
utils::head(fit_multiple_group_map)
#> [[1]]
#> a b c equation target CSTV AIC AICc R2
#> 1 98.71 2.07 0.37 98.7(1-e^(-0.371(x+2.1) 90 4.5 64 68 0.97
#>
#> [[2]]
#> a b c equation target CSTV AIC AICc R2
#> 1 97.98 3.91 0.09 98(1-e^(-0.089(x+3.9) 90 24.4 1022 1022 0.54We can generate a ggplot with the same mitscherlich() function.
We just need to specify the argument plot = TRUE.
mitscherlich_plot <-
soiltestcorr::mitscherlich(data = data_3,
ry = RY,
stv = STK, type = 1, target = 90,
plot = TRUE)
mitscherlich_plot
### 3.1.2 Fine-tune the plots
As ggplot object, plots can be adjusted in several ways.
For example, modifying titles
mitscherlich_plot_2 <-
mitscherlich_plot +
labs(
# Main title
title = "My own plot title",
# Axis titles
x = "Soil Test K (ppm)",
y = "Cotton RY(%)")
mitscherlich_plot_2
Or modifying axis scales
mitscherlich_plot_3 <-
mitscherlich_plot_2 +
# Axis scales
scale_x_continuous(breaks = seq(0,220, by = 20))+
# Axis limits
scale_y_continuous(breaks = seq(0,100, by = 10))
mitscherlich_plot_3
We can generate a plot with the same mitscherlich() function.
We just need to specify the argument resid = TRUE`.
# Residuals plot
soiltestcorr::mitscherlich(data = data_3,
ry = RY,
stv = STK, type = 1, target = 90,
resid = TRUE)
#> $a
#> [1] 96.38
#>
#> $b
#> [1] -8.69
#>
#> $c
#> [1] 0.05
#>
#> $equation
#> [1] "96.4(1-e^(-0.046(x-8.7)"
#>
#> $target
#> [1] 90
#>
#> $CSTV
#> [1] 67.9
#>
#> $AIC
#> [1] 187
#>
#> $AICc
#> [1] 189
#>
#> $R2
#> [1] 0.67 References
Melsted, S.W. and Peck, T.R. (1977). The Mitscherlich-Bray Growth
Function. In Soil Testing (eds T. Peck, J. Cope and D. Whitney).
10.2134/asaspecpub29.c1