Linear-plateau response

Adrian Correndo & Austin Pearce

Description

This tutorial is intended to show how to deploy the linear_plateau() function for estimating a continuous response model with a critical soil test value. This function fits the classical regression response model that follows two phases: i) a first linear phase described as y = b0 + b1 x, and ii) a second phase were the RY response to increasing STV becomes NULL (flat), described as plateau = y = b0 + b1 Xc, where Xc represents the CSTV. The function works automatically with self starting initial values to facilitate the model’s convergence. This approach is one of the regression models with simple interpretation of its parameters. Some disadvantages are that: i) the user does not have control to estimate the critical value (the model parameter) for an specific ry level; and ii) the confidence interval of the critical level is generally unreliable. We recommend the user to use a re-sampling technique (e.g. bootstrapping) for a more reliable confidence interval estimation for parameters and CSTV

General Instructions

  1. Load your dataframe with soil test value (stv) and relative yield (ry) data.

  2. Specify the following arguments into the function -linear_plateau()-:

(a). data (optional),

(b). stv (soil test value) and ry (relative yield) columns or vectors,

(c). target (optional) if want a CSTV for a different `ry`` than the plateau.

(d). tidy TRUE (produces a data.frame with results) or FALSE (store results as list),

(e). plot TRUE (produces a ggplot as main output) or FALSE (no plot, only results as data.frame),

(f). resid TRUE (produces plots with residuals analysis) or FALSE (no plot),

  1. Run and check results.

  2. Check residuals plot, and warnings related to potential limitations of this model.

  3. Adjust curve plots as desired.

Tutorial

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) # Mapping

This is a basic example using three different datasets:

Load 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::freitas1966

Fit linear_plateau()

1. Individual fits

RY target = 90%, confidence level = 0.95, replace with your desired values

1.1. 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::linear_plateau(data = data_1, 
                               ry = RY, 
                               stv = STV, 
                               tidy = FALSE)

utils::head(fit_1_tidy_false)
#> $intercept
#> [1] 65.87
#> 
#> $slope
#> [1] 5.09
#> 
#> $equation
#> [1] "65.9 + 5.09x if x<CSTV"
#> 
#> $plateau
#> [1] 97.4
#> 
#> $target
#> [1] 97.4
#> 
#> $CSTV
#> [1] 6.2

1.2. tidy = TRUE

It returns a data.frame (more organized results) 


# Using dataframe argument, tidy = FALSE -> return a LIST
fit_1_tidy_true <- 
  soiltestcorr::linear_plateau(data = data_1, 
                               ry = RY, 
                               stv = STV,
                               tidy = TRUE)

fit_1_tidy_true
#>   intercept slope               equation plateau target CSTV LL_cxp UL_cxp
#> 1     65.87  5.09 65.9 + 5.09x if x<CSTV    97.4   97.4  6.2    5.1    7.4
#>               CI_type AIC AICc  R2
#> 1 Wald Conf. Interval  82   86 0.9

1.3. Alternative using the vectors

You can call stv and ry vectors using the $.

The tidy argument still applies for controlling the output type


fit_1_vectors_list <-
  soiltestcorr::linear_plateau(ry = data_1$RY,
                               stv = data_1$STV,
                               tidy = FALSE)

fit_1_vectors_tidy <- 
  soiltestcorr::linear_plateau(ry = data_1$RY,
                               stv = data_1$STV,
                               tidy = TRUE)

1.4. Data 2. Test dataset 


fit_2 <-
  soiltestcorr::linear_plateau(data = data_2, 
                               ry = RY,
                               stv = STV)

utils::head(fit_2)
#> $intercept
#> [1] 53.72
#> 
#> $slope
#> [1] 1.55
#> 
#> $equation
#> [1] "53.7 + 1.55x if x<CSTV"
#> 
#> $plateau
#> [1] 96.2
#> 
#> $target
#> [1] 96.2
#> 
#> $CSTV
#> [1] 27.4

1.5. Data 3. Freitas et al. 1966 


fit_3 <-
  soiltestcorr::linear_plateau(data = data_3, 
                               ry = RY,
                               stv = STK)
utils::head(fit_3)
#> $intercept
#> [1] 39.24
#> 
#> $slope
#> [1] 0.75
#> 
#> $equation
#> [1] "39.2 + 0.75x if x<CSTV"
#> 
#> $plateau
#> [1] 95.6
#> 
#> $target
#> [1] 95.6
#> 
#> $CSTV
#> [1] 75

2. Multiple fits at once

2.1. Using map

Create nested data

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"))

Fit


# Run multiple examples at once with map()
fit_multiple_map <-
  data.all %>%
  mutate(linear_plateau = purrr::map(data, 
                                     ~ soiltestcorr::linear_plateau(ry = .$RY,
                                                                    stv = .$STV,
                                                                    tidy = TRUE)))

utils::head(fit_multiple_map)
#> # A tibble: 3 x 3
#>   id    data               linear_plateau
#>   <chr> <list>             <list>        
#> 1 1     <tibble [15 x 2]>  <df [1 x 12]> 
#> 2 2     <tibble [137 x 2]> <df [1 x 12]> 
#> 3 3     <tibble [24 x 2]>  <df [1 x 12]>

2.1. Using group_map

Alternatively, 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::linear_plateau(data = ., 
                                           ry = RY,
                                           stv = STV,
                                           tidy = TRUE))

utils::head(fit_multiple_group_map)
#> [[1]]
#>   intercept slope               equation plateau target CSTV LL_cxp UL_cxp
#> 1     65.87  5.09 65.9 + 5.09x if x<CSTV    97.4   97.4  6.2    5.1    7.4
#>               CI_type AIC AICc  R2
#> 1 Wald Conf. Interval  82   86 0.9
#> 
#> [[2]]
#>   intercept slope               equation plateau target CSTV LL_cxp UL_cxp
#> 1     53.72  1.55 53.7 + 1.55x if x<CSTV    96.2   96.2 27.4     24   30.7
#>               CI_type  AIC AICc   R2
#> 1 Wald Conf. Interval 1026 1026 0.52

3. Plots

3.1. Calibration Curve

We can generate a ggplot with the same linear_plateau() function.

We just need to specify the argument plot = TRUE. 


linear_plateau_plot <- 
  soiltestcorr::linear_plateau(data = data_3, 
                               ry = RY, 
                               stv = STK, 
                               plot = TRUE)

linear_plateau_plot

### 3.1.2 Fine-tune the plots

As ggplot object, plots can be adjusted in several ways.

For example, modifying titles 

linear_plateau_plot_2 <- 
  linear_plateau_plot +
  # Main title
  ggtitle("My own plot title")+
  # Axis titles
  labs(x = "Soil Test K (ppm)",
       y = "Cotton RY(%)")

linear_plateau_plot_2

Or modifying axis scales 

linear_plateau_plot_3 <-
linear_plateau_plot_2 +
  # Axis scales
  scale_x_continuous(limits = c(20,220),
                     breaks = seq(0,220, by = 20))+
  # Axis limits
  scale_y_continuous(limits = c(30,100),
                     breaks = seq(30,100, by = 10))

linear_plateau_plot_3

3.3. Residuals

We can generate a plot with the same linear_plateau() function.

We just need to specify the argument resid = TRUE`. 


# Residuals plot

soiltestcorr::linear_plateau(data = data_3, 
                               ry = RY, 
                               stv = STK, 
                               resid = TRUE)

#> $intercept
#> [1] 39.24
#> 
#> $slope
#> [1] 0.75
#> 
#> $equation
#> [1] "39.2 + 0.75x if x<CSTV"
#> 
#> $plateau
#> [1] 95.6
#> 
#> $target
#> [1] 95.6
#> 
#> $CSTV
#> [1] 75
#> 
#> $LL_cxp
#> [1] 46.4
#> 
#> $UL_cxp
#> [1] 103.6
#> 
#> $CI_type
#> [1] "Wald Conf. Interval"
#> 
#> $AIC
#> [1] 188
#> 
#> $AICc
#> [1] 190
#> 
#> $R2
#> [1] 0.66

References

Anderson, R. L., and Nelson, L. A. (1975). A Family of Models Involving Intersecting Straight Lines and Concomitant Experimental Designs Useful in Evaluating Response to Fertilizer Nutrients. Biometrics, 31(2), 303–318. 10.2307/2529422