flexFitR: Flexible Non-Linear Least Square Model Fitting

Description

Provides tools for flexible non-linear least squares model fitting using general-purpose optimization techniques. The package supports a variety of optimization algorithms, including those provided by the 'optimx' package, making it suitable for handling complex non-linear models. Features include parallel processing support via the 'future' and 'foreach' packages, comprehensive model diagnostics, and visualization capabilities. Implements methods described in Nash and Varadhan (2011, doi:10.18637/jss.v043.i09).

Author(s)

Maintainer: Johan Aparicio aparicioarce@wisc.edu

Authors:

• Jeffrey Endelman endelman@wisc.edu

Other contributors:

• University of Wisconsin Madison [copyright holder]

See Also

Useful links:

• https://apariciojohan.github.io/flexFitR/

• https://github.com/AparicioJohan/flexFitR

• Report bugs at https://github.com/AparicioJohan/flexFitR/issues

Delta method point estimation

Description

Delta method point estimation

Usage

.delta_method(fit, x_new, se_interval = "confidence")

Arguments

Value

A data.frame of the evaluated values.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# Point Prediction
predict(mod_1, x = 45, type = "point", id = 2)

Delta method AUC estimation

Description

Delta method AUC estimation

Usage

.delta_method_auc(fit, x_new, n_points = 1000)

Arguments

Value

A data.frame of the evaluated values.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# AUC Prediction
predict(mod_1, x = c(0, 108), type = "auc", id = 2)

Delta method for derivative estimation

Description

Delta method for derivative estimation

Usage

.delta_method_deriv(fit, x_new, which = "fd")

Arguments

Value

A data.frame of the evaluated values.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# First Derivative
predict(mod_1, x = 45, type = "fd", id = 2)

Delta method generic function

Description

Delta method generic function

Usage

.delta_method_gen(fit, formula)

Arguments

Value

A data.frame of the evaluated formula.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# Function of the parameters
predict(mod_1, formula = ~ t2 - t1, id = 2)

General-purpose optimization

Description

The function .fitter_curve is used internally to find the parameters requested.

Usage

.fitter_curve(data, id, fn, method, lower, upper, control, metadata, trace)

Arguments

Value

A list containing the following elements:

kkopt

opm object.

param

Data frame with best solution parameters.

rr

Data frame with all methods tested.

details

Additional details of the best solution.

hessian

Hessian matrix.

type

Data frame describing the type of coefficient (estimable of fixed)

conv

Convergency.

p

Number of parameters estimated.

n_obs

Number of observations.

uid

Unique identifier.

fn_name

Name of the curve-fitting function used.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = GLI,
    grp = Plot,
    fn = "fn_lin_pl_lin",
    parameters = c(t1 = 38.7, t2 = 62, t3 = 90, k = 0.32, beta = -0.01),
    subset = 195,
    options = list(add_zero = TRUE)
  )

Extra Sum-of-Squares F-Test for modeler objects

Description

Perform an extra sum-of-squares F-test to compare two nested models of class modeler. This test assesses whether the additional parameters in the full model significantly improve the fit compared to the reduced model.

Usage

## S3 method for class 'modeler'
anova(object, full_model = NULL, ...)

Arguments

Value

A tibble containing columns with the F-statistic and corresponding p-values, indicating whether the full model provides a significantly better fit than the reduced model.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
dt <- data.frame(X = 1:6, Y = c(12, 16, 44, 50, 95, 100))
mo_1 <- modeler(dt, X, Y, fn = "fn_lin", param = c(m = 10, b = -5))
plot(mo_1)
mo_2 <- modeler(dt, X, Y, fn = "fn_quad", param = c(a = 1, b = 10, c = 5))
plot(mo_2)
anova(mo_1, mo_2)

Augment a modeler object with influence diagnostics

Description

This function computes various influence diagnostics, including standardized residuals, studentized residuals, and Cook's distance, for an object of class modeler.

Usage

augment(x, id = NULL, metadata = TRUE, ...)

Arguments

Value

A tibble containing the following columns:

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_logistic",
    parameters = c(a = 0.199, t0 = 47.7, k = 100),
    subset = 2
  )
print(mod_1)
augment(mod_1)

Combine objects of class modeler

Description

Combine objects of class modeler. Use with caution, some functions might not work as expected.

Usage

## S3 method for class 'modeler'
c(...)

Arguments

Value

A modeler object.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_logistic",
    parameters = c(a = 0.199, t0 = 47.7, k = 100),
    subset = 1:2
  )
mod_2 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 100),
    subset = 1:2
  )
mod <- c(mod_1, mod_2)
print(mod)
plot(mod, id = 1:2)

Coefficients for an object of class modeler

Description

Extract the estimated coefficients from an object of class modeler.

Usage

## S3 method for class 'modeler'
coef(object, id = NULL, metadata = FALSE, df = FALSE, ...)

Arguments

Value

A data.frame containing the model's estimated coefficients, standard errors, and optional metadata or degrees of freedom if specified.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
coef(mod_1, id = 2)

Compute tangent line(s) from a modeler object

Description

Computes the slope and intercept of the tangent line(s) to a fitted curve at one or more specified x-values.

Usage

compute_tangent(object, x = NULL, id = NULL)

Arguments

Value

A tibble with one row per tangent line and the following columns:

• uid: unique identifier of the group.

• fn_name: Name of the fitted function.

• x: x-value where the tangent line is evaluated.

• y: Fitted y-value at x.

• slope: First derivative (slope of tangent) at x.

• intercept: y-intercept of the tangent line.

Examples

library(flexFitR)
library(ggplot2)
data(dt_potato)
mod <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_logistic",
    parameters = c(a = 4, t0 = 40, k = 100),
    subset = 2
  )
plot(mod)
tl <- compute_tangent(mod, x = c(48.35, 65))
print(tl)
plot(mod) +
  geom_abline(
    data = tl,
    mapping = aes(slope = slope, intercept = intercept),
    linetype = 2,
    color = "blue"
  ) +
  geom_point(
    data = tl,
    mapping = aes(x = x, y = y),
    shape = 8,
    color = "blue",
    size = 2
  )

Confidence intervals for a modeler object

Description

Extract confidence intervals for the estimated parameters of an object of class modeler.

Usage

## S3 method for class 'modeler'
confint(object, parm = NULL, level = 0.95, id = NULL, ...)

Arguments

Value

A tibble containing the lower and upper confidence limits for each specified parameter.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 35, 45)
  )
print(mod_1)
confint(mod_1)

Drone-derived data from a potato breeding trial

Description

Canopy and Green Leaf Index for a potato trial arranged in a p-rep design.

Usage

dt_potato

Format

A tibble with 1372 rows and 8 variables:

Trial

chr trial name

Plot

dbl denoting the unique plot id

Row

dbl denoting the row coordinate

Range

dbl denoting range coordinate

gid

chr denoting the genotype id

DAP

dbl denoting Days after planting

Canopy

dbl Canopy UAV-Derived

GLI

dbl Green Leaf Index UAV-Derived

Source

UW - Potato Breeding Program

Explore data

Description

Explores data from a data frame in wide format.

Usage

explorer(data, x, y, id, metadata)

Arguments

Details

This function helps to explore the dataset before being analyzed with modeler().

Value

An object of class explorer, which is a list containing the following elements:

summ_vars

A data.frame containing summary statistics for each trait at each x point, including minimum, mean, median, maximum, standard deviation, coefficient of variation, number of non-missing values, percentage of missing values, and percentage of negative values.

summ_metadata

A data.frame summarizing the metadata.

locals_min_max

A data.frame containing the local minima and maxima of the mean y values over x.

dt_long

A data.frame in long format, with columns for uid, metadata, var, x, and y

metadata

A character vector with the names of the variables to keep across.

Examples

library(flexFitR)
data(dt_potato)
results <- dt_potato |>
  explorer(
    x = DAP,
    y = c(Canopy, GLI),
    id = Plot,
    metadata = c(gid, Row, Range)
  )
names(results)
head(results$summ_vars)
plot(results, label_size = 4, signif = TRUE, n_row = 2)
# New data format
head(results$dt_long)

Function for point estimation

Description

Function for point estimation

Usage

ff(params, x_new, curve, fixed_params = NA)

Arguments

Value

A vector of the evaluated values.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# Point Prediction
predict(mod_1, x = 45, type = "point", id = 2)

Function for AUC estimation

Description

Function for AUC estimation

Usage

ff_auc(params, x_new, curve, fixed_params = NA, n_points = 1000)

Arguments

Value

Area under the fitted curve.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# AUC Prediction
predict(mod_1, x = c(0, 108), type = "auc", id = 2)

Function for derivatives

Description

Function for derivatives

Usage

ff_deriv(params, x_new, curve, fixed_params = NA, which = "fd")

Arguments

Value

First or second derivative.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# First Derivative
predict(mod_1, x = 45, type = "fd", id = 2)

Extract fitted values from a modeler object

Description

Extract fitted values from a modeler object

Usage

## S3 method for class 'modeler'
fitted(object, ...)

Arguments

Value

A numeric vector of fitted values.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
fitted(mod_1)

Super-exponential exponential function

Description

A piecewise function that models an initial exponential phase with quadratic time dependence, followed by a second exponential phase with a different growth rate.

Usage

fn_exp2_exp(t, t1, t2, alpha, beta)

Arguments

Details

f(t; t_1, t_2, \alpha, \beta) = \begin{cases} 0 & \text{if } t < t_1 \\ e^{\alpha \cdot (t - t_1)^2} - 1 & \text{if } t_1 \leq t \leq t_2 \\ \left(e^{\alpha \cdot (t_2 - t_1)^2} - 1\right) \cdot e^{\beta \cdot (t - t_2)} & \text{if } t > t_2 \end{cases}

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_exp2_exp",
  params = c(t1 = 35, t2 = 55, alpha = 1 / 600, beta = -1 / 30),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3,
  y_auc_label = 0.15
)

Super-exponential linear function

Description

A piecewise function that models an initial exponential growth phase based on a squared time difference, followed by a linear phase.

Usage

fn_exp2_lin(t, t1, t2, alpha, beta)

Arguments

Details

f(t; t_1, t_2, \alpha, \beta) = \begin{cases} 0 & \text{if } t < t_1 \\ e^{\alpha \cdot (t - t_1)^2} - 1 & \text{if } t_1 \leq t \leq t_2 \\ \beta \cdot (t - t_2) + \left(e^{\alpha \cdot (t_2 - t_1)^2} - 1\right) & \text{if } t > t_2 \end{cases}

The exponential section rises gradually from 0 at t1 and accelerates as time increases. The linear section starts at t2 with a value matching the end of the exponential phase, ensuring continuity but not necessarily matching the derivative.

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_exp2_lin",
  params = c(t1 = 35, t2 = 55, alpha = 1 / 600, beta = -1 / 80),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Double-exponential function

Description

A piecewise function with two exponential phases. The first exponential phase occurs between t1 and t2, and the second phase continues after t2 with a potentially different growth rate. The function ensures continuity at the transition point but not necessarily smoothness (in derivative).

Usage

fn_exp_exp(t, t1, t2, alpha, beta)

Arguments

Details

f(t; t_1, t_2, \alpha, \beta) = \begin{cases} 0 & \text{if } t < t_1 \\ e^{\alpha \cdot (t - t_1)} - 1 & \text{if } t_1 \leq t \leq t_2 \\ \left(e^{\alpha \cdot (t_2 - t_1)} - 1\right) \cdot e^{\beta \cdot (t - t_2)} & \text{if } t > t_2 \end{cases}

The function rises from 0 starting at t1 with exponential growth rate alpha, and transitions to a second exponential phase with rate beta at t2. The value at the transition point is preserved, ensuring continuity.

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_exp_exp",
  params = c(t1 = 35, t2 = 55, alpha = 1 / 20, beta = -1 / 30),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3,
  y_auc_label = 0.2
)

Exponential-linear function

Description

A piecewise function that models a response with an initial exponential growth phase followed by a linear phase. Commonly used to describe processes with rapid early increases that slow into a linear trend, while maintaining continuity.

Usage

fn_exp_lin(t, t1, t2, alpha, beta)

Arguments

Details

f(t; t_1, t_2, \alpha, \beta) = \begin{cases} 0 & \text{if } t < t_1 \\ e^{\alpha \cdot (t - t_1)} - 1 & \text{if } t_1 \leq t \leq t_2 \\ \beta \cdot (t - t_2) + \left(e^{\alpha \cdot (t_2 - t_1)} - 1\right) & \text{if } t > t_2 \end{cases}

The exponential segment starts from 0 at t1, and the linear segment continues smoothly from the end of the exponential part. This ensures value continuity at t2, but not necessarily smoothness in slope.

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_exp_lin",
  params = c(t1 = 35, t2 = 55, alpha = 1 / 20, beta = -1 / 40),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Linear function

Description

A basic linear function of the form f(t) = m * t + b, where m is the slope and b is the intercept.

Usage

fn_lin(t, m, b)

Arguments

Details

f(t; m, b) = m \cdot t + b

Value

A numeric vector of the same length as t, giving the linear function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_lin",
  params = c(m = 2, b = 10),
  interval = c(0, 108),
  n_points = 2000
)

Linear-logistic function

Description

A piecewise function that models an initial linear increase followed by a logistic saturation.

Usage

fn_lin_logis(t, t1, t2, k)

Arguments

Details

f(t; t_1, t_2, k) = \begin{cases} 0 & \text{if } t < t_1 \\ \dfrac{k}{2(t_2 - t_1)} \cdot (t - t_1) & \text{if } t_1 \leq t \leq t_2 \\ \dfrac{k}{1 + e^{-2(t - t_2) / (t_2 - t_1)}} & \text{if } t > t_2 \end{cases}

The linear segment rises from 0 starting at t1, and the logistic segment begins at t2, smoothly approaching the plateau value k.

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_lin_logis",
  params = c(t1 = 35, t2 = 50, k = 100),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Linear plateau linear function

Description

A piecewise function that models an initial linear increase up to a plateau, maintains that plateau for a duration, and then decreases linearly.

Usage

fn_lin_pl_lin(t, t1, t2, t3, k, beta)

Arguments

Details

f(t; t_1, t_2, t_3, k, \beta) = \begin{cases} 0 & \text{if } t < t_1 \\ \dfrac{k}{t_2 - t_1} \cdot (t - t_1) & \text{if } t_1 \leq t \leq t_2 \\ k & \text{if } t_2 \leq t \leq t_3 \\ k + \beta \cdot (t - t_3) & \text{if } t > t_3 \end{cases}

The function transitions continuously between all three phases but is not differentiable at the transition points t1, t2, and t3.

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_lin_pl_lin",
  params = c(t1 = 38.7, t2 = 62, t3 = 90, k = 0.32, beta = -0.01),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Linear plateau linear with constrains

Description

A piecewise function that models an initial linear increase to a plateau, followed by a specified duration of stability, and then a linear decline. This version parameterizes the plateau using its duration rather than an explicit end time, making it convenient for box type of constraints optimizations.

Usage

fn_lin_pl_lin2(t, t1, t2, dt, k, beta)

Arguments

Details

f(t; t_1, t_2, dt, k, \beta) = \begin{cases} 0 & \text{if } t < t_1 \\ \dfrac{k}{t_2 - t_1} \cdot (t - t_1) & \text{if } t_1 \leq t \leq t_2 \\ k & \text{if } t_2 \leq t \leq (t_2 + dt) \\ k + \beta \cdot (t - (t_2 + dt)) & \text{if } t > (t_2 + dt) \end{cases}

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_lin_pl_lin2",
  params = c(t1 = 38.7, t2 = 62, dt = 28, k = 0.32, beta = -0.01),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Linear plateau function

Description

A simple piecewise function that models a linear increase from zero to a plateau. The function rises linearly between two time points and then levels off at a constant value.

Usage

fn_lin_plat(t, t1 = 45, t2 = 80, k = 0.9)

Arguments

Details

f(t; t_1, t_2, k) = \begin{cases} 0 & \text{if } t < t_1 \\ \dfrac{k}{t_2 - t_1} \cdot (t - t_1) & \text{if } t_1 \leq t \leq t_2 \\ k & \text{if } t > t_2 \end{cases}

This function is continuous but not differentiable at t1 and t2 due to the piecewise transitions. It is often used in agronomy and ecology to describe growth until a resource limit or developmental plateau is reached.

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_lin_plat",
  params = c(t1 = 34.9, t2 = 61.8, k = 100),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Logistic function

Description

A standard logistic function commonly used to model sigmoidal growth. The curve rises from near zero to a maximum value k, with inflection point at t0 and growth rate a.

Usage

fn_logistic(t, a, t0, k)

Arguments

Details

f(t; a, t0, k) = \frac{k}{1 + e^{-a(t - t_0)}}

This is a classic sigmoid (S-shaped) curve that is symmetric around the inflection point t0.

Value

A numeric vector of the same length as t, representing the logistic function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_logistic",
  params = c(a = 0.199, t0 = 47.7, k = 100),
  interval = c(0, 108),
  n_points = 2000
)

Quadratic function

Description

A standard quadratic function of the form f(t) = a * t^2 + b * t + c, where a controls curvature, b is the linear coefficient, and c is the intercept.

Usage

fn_quad(t, a, b, c)

Arguments

Details

f(t; a, b, c) = a \cdot t^2 + b \cdot t + c

This function represents a second-degree polynomial. The sign of a determines whether the parabola opens upward (a > 0) or downward (a < 0).

Value

A numeric vector of the same length as t, representing the quadratic function values.

Examples

library(flexFitR)
plot_fn(fn = "fn_quad", params = c(a = 1, b = 10, c = 5))

Smooth Quadratic-plateau function

Description

A piecewise function that models a quadratic increase from zero to a plateau value. The function is continuous and differentiable, modeling growth processes with a smooth transition to a maximum response.

Usage

fn_quad_pl_sm(t, t1, t2, k)

Arguments

Details

f(t; t_1, t_2, k) = \begin{cases} 0 & \text{if } t < t_1 \\ -\dfrac{k}{(t_2 - t_1)^2} (t - t_1)^2 + \dfrac{2k}{t_2 - t_1} (t - t_1) & \text{if } t_1 \leq t \leq t_2 \\ k & \text{if } t > t_2 \end{cases}

The coefficients of the quadratic section are chosen such that the curve passes through (t1, 0) and (t2, k) with a continuous first derivative (i.e., smooth transition).

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_quad_pl_sm",
  params = c(t1 = 35, t2 = 80, k = 100),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Quadratic-plateau function

Description

Computes a value based on a quadratic-plateau growth curve.

Usage

fn_quad_plat(t, t1 = 45, t2 = 80, b = 1, k = 100)

Arguments

Details

f(t; t_1, t_2, b, k) = \begin{cases} 0 & \text{if } t < t_1 \\ b (t - t_1) + \frac{k - b (t_2 - t_1)}{(t_2 - t_1)^2} (t - t_1)^2 & \text{if } t_1 \leq t \leq t_2 \\ k & \text{if } t > t_2 \end{cases}

This function allows the user to specify the initial slope b. The curvature term is automatically calculated so that the function reaches the plateau value k exactly at t2. The transition to the plateau is continuous in value but not necessarily smooth in derivative.

Value

A numeric vector of the same length as t, representing the function values.

Examples

library(flexFitR)
plot_fn(
  fn = "fn_quad_plat",
  params = c(t1 = 35, t2 = 80, b = 4, k = 100),
  interval = c(0, 108),
  n_points = 2000,
  auc_label_size = 3
)

Akaike's An Information Criterion for an object of class modeler

Description

Generic function calculating Akaike's ‘An Information Criterion’ for fitted model object of class modeler.

Usage

## S3 method for class 'modeler'
AIC(object, ..., k = 2)

## S3 method for class 'modeler'
BIC(object, ...)

Arguments

Value

A tibble with columns giving the corresponding AIC and BIC.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
dt <- data.frame(X = 1:6, Y = c(12, 16, 44, 50, 95, 100))
mo_1 <- modeler(dt, X, Y, fn = "fn_lin", param = c(m = 10, b = -5))
mo_2 <- modeler(dt, X, Y, fn = "fn_quad", param = c(a = 1, b = 10, c = 5))
AIC(mo_1)
AIC(mo_2)
BIC(mo_1)
BIC(mo_2)

Generic for inverse prediction

Description

Generic for inverse prediction

Usage

inverse_predict(object, ...)

Arguments

Inverse prediction from a modeler object

Description

Computes the x-value at which a fitted model reaches a user-specified response value (y-value).

Usage

## S3 method for class 'modeler'
inverse_predict(
  object,
  y,
  id = NULL,
  interval = NULL,
  tol = 1e-06,
  resolution = 1000,
  ...
)

Arguments

Details

The function uses numeric root-finding to solve f(t, ...params) = y. If no root is found in the interval, NA is returned.

Value

A tibble with one row per group, containing:

• uid – unique identifier of the group,

• fn_name – the name of the fitted function,

• lower and upper – the search interval used,

• y – the predicted y-value (from the function at the root),

• x – the x-value at which the function reaches y.

See Also

predict.modeler, uniroot

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
inverse_predict(mod_1, y = 50)
inverse_predict(mod_1, y = 75, interval = c(20, 80))

Print available functions in flexFitR

Description

Print available functions in flexFitR

Usage

list_funs()

Value

A vector with available functions

Examples

library(flexFitR)
list_funs()

Print available methods in flexFitR

Description

Print available methods in flexFitR

Usage

list_methods(bounds = FALSE, check_package = FALSE)

Arguments

Value

A vector with available methods

Examples

library(flexFitR)
list_methods()

Extract Log-Likelihood for an object of class modeler

Description

logLik for an object of class modeler

Usage

## S3 method for class 'modeler'
logLik(object, ...)

Arguments

Value

A tibble with the Log-Likelihood for the fitted models.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
dt <- data.frame(X = 1:6, Y = c(12, 16, 44, 50, 95, 100))
mo_1 <- modeler(dt, X, Y, fn = "fn_lin", param = c(m = 10, b = -5))
plot(mo_1)
logLik(mo_1)

Metrics for an object of class modeler

Description

Computes various performance metrics for a modeler object. The function calculates Sum of Squared Errors (SSE), Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), and the Coefficient of Determination (R-squared).

Usage

metrics(x, by_grp = TRUE)

Arguments

Details

Sum of Squared Errors (SSE):

SSE = \sum_{i=1}^{n} (y_i - \hat{y}_i)^2

Mean Absolute Error (MAE):

MAE = \frac{1}{n} \sum_{i=1}^{n} |y_i - \hat{y}_i|

Mean Squared Error (MSE):

MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2

Root Mean Squared Error (RMSE):

RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}

Coefficient of Determination (R-squared):

R^2 = 1 - \frac{\sum_{i=1}^{n} (y_i - \hat{y}_i)^2}{\sum_{i=1}^{n} (y_i - \bar{y})^2}

Value

A data frame containing the calculated metrics grouped by uid, metadata, and variables.

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(1:2)
  )
plot(mod_1, id = c(1:2))
print(mod_1)
metrics(mod_1)

Modeler: Non-linear regression for curve fitting

Description

A versatile function for performing non-linear least squares optimization on grouped data. It supports customizable optimization methods, flexible initial/fixed parameters, and parallel processing.

Usage

modeler(
  data,
  x,
  y,
  grp,
  keep,
  fn = "fn_lin_plat",
  parameters = NULL,
  lower = -Inf,
  upper = Inf,
  fixed_params = NULL,
  method = c("subplex", "pracmanm", "anms"),
  subset = NULL,
  options = modeler.options(),
  control = list()
)

Arguments

Value

An object of class modeler, which is a list containing the following elements:

param

Data frame containing optimized parameters and related information.

dt

Data frame with input data, fitted values, and residuals.

metrics

Metrics and summary of the models.

execution

Total execution time for the analysis.

response

Name of the response variable analyzed.

keep

Metadata retained based on the keep argument.

fun

Name of the curve-fitting function used.

parallel

List containing parallel execution details (if applicable).

fit

List of fitted models for each group.

Examples

library(flexFitR)
data(dt_potato)
explorer <- explorer(dt_potato, x = DAP, y = c(Canopy, GLI), id = Plot)
# Example 1
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = GLI,
    grp = Plot,
    fn = "fn_lin_pl_lin",
    parameters = c(t1 = 38.7, t2 = 62, t3 = 90, k = 0.32, beta = -0.01),
    subset = 195
  )
plot(mod_1, id = 195)
print(mod_1)
# Example 2
mod_2 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = 195
  )
plot(mod_2, id = 195)
print(mod_2)

Compare performance of different models

Description

Computes indices of model performance for different models at once and hence allows comparison of indices across models.

Usage

performance(..., metrics = "all", metadata = FALSE, digits = 2)

Arguments

Value

A data.frame with performance metrics for models in (...).

Examples

library(flexFitR)
data(dt_potato)
# Model 1
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 90),
    subset = 40
  )
print(mod_1)
# Model 2
mod_2 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_logistic",
    parameters = c(a = 0.199, t0 = 47.7, k = 100),
    subset = 40
  )
print(mod_2)
# Model 3
mod_3 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin",
    parameters = c(m = 20, b = 2),
    subset = 40
  )
print(mod_3)
performance(mod_1, mod_2, mod_3, metrics = c("AIC", "AICc", "BIC", "Sigma"))

Plot an object of class explorer

Description

Creates various plots for an object of class explorer. Depending on the specified type, the function can generate plots that show correlations between variables over x, correlations between x values for each variable, or the evolution of variables over x.

Usage

## S3 method for class 'explorer'
plot(
  x,
  type = "var_by_x",
  label_size = 4,
  signif = FALSE,
  method = "pearson",
  filter_var = NULL,
  id = NULL,
  n_row = NULL,
  n_col = NULL,
  base_size = 13,
  return_gg = FALSE,
  add_avg = FALSE,
  ...
)

Arguments

Value

A ggplot object and an invisible data.frame containing the correlation table when type is "var_by_x" or "x_by_var".

Examples

library(flexFitR)
data(dt_potato)
results <- explorer(dt_potato, x = DAP, y = c(Canopy, GLI), id = Plot)
table <- plot(results, label_size = 4, signif = TRUE, n_row = 2)
table
plot(results, type = "x_by_var", label_size = 4, signif = TRUE)

Plot an object of class modeler

Description

Creates several plots for an object of class modeler.

Usage

## S3 method for class 'modeler'
plot(
  x,
  id = NULL,
  type = 1,
  label_size = 4,
  base_size = 14,
  linewidth = 0.5,
  color = "red",
  color_points = "black",
  parm = NULL,
  n_points = 1000,
  title = NULL,
  add_points = FALSE,
  add_ci = TRUE,
  color_ci = "blue",
  color_pi = "red",
  add_ribbon_ci = FALSE,
  add_ribbon_pi = FALSE,
  color_ribbon_ci = "blue",
  color_ribbon_pi = "red",
  ...
)

Arguments

Value

A ggplot object representing the specified plot.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
# Example 1
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(1:3)
  )
print(mod_1)
plot(mod_1, id = 1:2)
plot(mod_1, id = 1:3, type = 2, label_size = 10)

Plot an object of class performance

Description

Creates plots for an object of class performance

Usage

## S3 method for class 'performance'
plot(
  x,
  id = NULL,
  type = 1,
  rescale = FALSE,
  linewidth = 1,
  base_size = 12,
  return_table = FALSE,
  ...
)

Arguments

Value

A ggplot object representing the specified plot.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
# Model 1
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 90),
    subset = 40
  )
# Model 2
mod_2 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_logistic",
    parameters = c(a = 0.199, t0 = 47.7, k = 100),
    subset = 40
  )
# Model 3
mod_3 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin",
    parameters = c(m = 20, b = 2),
    subset = 40
  )
plot(performance(mod_1, mod_2, mod_3), type = 1)
plot(performance(mod_1, mod_2, mod_3, metrics = c("AICc", "BIC")), type = 3)

Plot user-defined function

Description

This function plots a function over a specified interval and annotates the plot with the calculated Area Under the Curve (AUC) and parameter values. The aim of 'plot_fn' is to allow users to play with different starting values in their functions before fitting any models.

Usage

plot_fn(
  fn = "fn_lin_plat",
  params = c(t1 = 34.9, t2 = 61.8, k = 100),
  interval = c(0, 100),
  n_points = 1000,
  auc = FALSE,
  x_auc_label = NULL,
  y_auc_label = NULL,
  auc_label_size = 4,
  param_label_size = 4,
  base_size = 12,
  color = "red",
  label_color = "grey30"
)

Arguments

Value

A ggplot object representing the plot.

Examples

# Example usage
plot_fn(
  fn = "fn_lin_plat",
  params = c(t1 = 34.9, t2 = 61.8, k = 100),
  interval = c(0, 100),
  n_points = 1000
)
plot_fn(
  fn = "fn_lin_pl_lin",
  params <- c(t1 = 38.7, t2 = 62, t3 = 90, k = 0.32, beta = -0.01),
  interval = c(0, 100),
  n_points = 1000,
  base_size = 12
)

Predict an object of class modeler

Description

Generate model predictions from an object of class modeler. This function allows for flexible prediction types, including point predictions, area under the curve (AUC), first or second order derivatives, and functions of the parameters.

Usage

## S3 method for class 'modeler'
predict(
  object,
  x = NULL,
  id = NULL,
  type = c("point", "auc", "fd", "sd"),
  se_interval = c("confidence", "prediction"),
  n_points = 1000,
  formula = NULL,
  metadata = FALSE,
  parallel = FALSE,
  workers = NULL,
  ...
)

Arguments

Value

A data.frame containing the predicted values, their associated standard errors, and optionally the metadata.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
# Point Prediction
predict(mod_1, x = 45, type = "point", id = 2)
# AUC Prediction
predict(mod_1, x = c(0, 108), type = "auc", id = 2)
# First Derivative
predict(mod_1, x = 45, type = "fd", id = 2)
# Second Derivative
predict(mod_1, x = 45, type = "sd", id = 2)
# Function of the parameters
predict(mod_1, formula = ~ t2 - t1, id = 2)

Print an object of class modeler

Description

Prints information about modeler function.

Usage

## S3 method for class 'modeler'
print(x, ...)

Arguments

Value

an object inheriting from class modeler.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(1:5)
  )
plot(mod_1, id = c(1:4))
print(mod_1)

Extract residuals from a modeler object

Description

Extract residuals from a modeler object

Usage

## S3 method for class 'modeler'
residuals(object, ...)

Arguments

Value

A numeric vector of residuals

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
residuals(mod_1)

Transform variables in a data frame

Description

This function performs transformations on specified columns of a data frame, including truncating maximum values, handling negative values, and adding a zero to the series. It allows for grouping and supports retaining metadata in the output.

Usage

series_mutate(
  data,
  x,
  y,
  grp,
  metadata,
  max_as_last = FALSE,
  check_negative = FALSE,
  add_zero = FALSE,
  interval = NULL
)

Arguments

Value

A transformed data.frame with the specified modifications applied.

Examples

data(dt_potato)
new_data <- series_mutate(
  data = dt_potato,
  x = DAP,
  y = GLI,
  grp = gid,
  max_as_last = TRUE,
  check_negative = TRUE
)

Subset an object of class modeler

Description

Subset an object of class modeler

Usage

## S3 method for class 'modeler'
subset(x, id = NULL, ...)

Arguments

Value

A modeler object.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_logistic",
    parameters = c(a = 0.199, t0 = 47.7, k = 100),
    subset = 1:2
  )
print(mod)
mod_new <- subset(mod, id = 2)
print(mod_new)

Update a modeler object

Description

It creates a new fitted object using the parameter values from the current model as initial values. It can also be used to perform a few additional iterations of a model that has not converged.

Usage

## S3 method for class 'modeler'
update(object, method = NULL, track = TRUE, eps = 1e-06, ...)

Arguments

Value

An object of class modeler, which is a list containing the following elements:

param

Data frame containing optimized parameters and related information.

dt

Data frame with input data, fitted values, and residuals.

metrics

Metrics and summary of the models.

execution

Total execution time for the analysis.

response

Name of the response variable analyzed.

keep

Metadata retained based on the keep argument.

fun

Name of the curve-fitting function used.

parallel

List containing parallel execution details (if applicable).

fit

List of fitted models for each group.

Examples

library(flexFitR)
data(dt_potato)
mo_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = GLI,
    grp = Plot,
    fn = "fn_lin_pl_lin",
    parameters = c(t1 = 10, t2 = 62, t3 = 90, k = 0.32, beta = -0.01),
    subset = 195
  )
plot(mo_1)
mo_2 <- update(mo_1)
plot(mo_2)

Variance-Covariance matrix for an object of class modeler

Description

Extract the variance-covariance matrix for the parameter estimates from an object of class modeler.

Usage

## S3 method for class 'modeler'
vcov(object, id = NULL, ...)

Arguments

Value

A list of matrices, where each matrix represents the variance-covariance matrix of the estimated parameters for each group or fit.

Author(s)

Johan Aparicio [aut]

Examples

library(flexFitR)
data(dt_potato)
mod_1 <- dt_potato |>
  modeler(
    x = DAP,
    y = Canopy,
    grp = Plot,
    fn = "fn_lin_plat",
    parameters = c(t1 = 45, t2 = 80, k = 0.9),
    subset = c(15, 2, 45)
  )
print(mod_1)
vcov(mod_1)