nls_tac {nlstac}

Nonlinear fit with the TAC algorithm

Description

Fits a nonlinear function to data.

Usage

nls_tac(
  formula,
  data = parent.frame(),
  functions = NULL,
  nlparam,
  lp_bounds = NULL,
  N = 10,
  tol = 1e-04,
  parallel = FALSE,
  maxiter = 50,
  quiet = FALSE,
  silent = TRUE,
  compute_errors = TRUE
)

Arguments

formula

A formula given in the form "LHS ~ a1 * F_1(x,p1) + a2 * F_2(x,p2) + ... + an F_n(x,pn)"

data

Data frame with the data points to be fitted.

functions

A string array with the nonlinear functions. If get_functions fails to properly provide the functions they should be explicitly introduced.

nlparam

A list with the names of the nonlinear parameters and their lower and upper bounds in the form c(lower,upper).

lp_bounds

An optional list with the bounding restrictions over the linear parameters.

N

Size of the partition of the nonlinear parameters. Defaults to 10.

tol

Stopping condition. The algorithm stops whenever the maximum difference between two consecutive iterations is less than tol. Default value is 1e-4

parallel

Logical. If TRUE then multicore parallelization of for loops is done with the parallel package. Defaults to FALSE.

maxiter

Integer. The maximum number of iterations. Defaults to 50.

quiet

Logical. If TRUE, all progress messages are supressed (defaults to FALSE).

silent

Logical. Parameter to be passed to get_best_parameters function. If TRUE (default) suppresses any warnings regarding the collinearity of the columns of the matrix in the determination of the best linear parameters.

compute_errors

Logical. If TRUE (default value) the function computes the standard error of the estimates.

Value

An object of class nlstac. A list of

coefficients

Best coefficients obtained.

stdError

Standard errors for the obtained coefficients

convInfo

Convergence information: a list with the number of iterations performed (niter) and the tolerance attained at convergence (tol)

SSR

Sum of the squares of the residuals

resid

Residuals

data

Data frame used. Columns of variables not used in the formula fitted will be removed

formula

Formula used

df

Degrees of freedom

sigma

Standard deviation estimate.

Rmat

R matrix in the QR decomposition of the gradient matrix used for the computation of the standard errors of the coefficients

Author(s)

Mariano Rodríguez-Arias ([e-mail]). Deptartment of Mathematics

Juan Antonio Fernández Torvisco ([e-mail]). Department of Mathematics

University of Extremadura (Spain)

Rafael Benítez ([e-mail]). Department of Business Mathematics

University of Valencia (Spain)

References

Fernández Torvisco, J. A.; Rodríguez-Arias Fernández, M.; Cabello Sánchez, J. (2018). “A New Algorithm to Fit Exponential Decays without Initial Guess”, Filomat 32:12, 4233–4248.

Bates, D. M. and Watts, D. G. (1988) Nonlinear Regression Analysis and Its Applications, Wiley

Examples

### Examples from 'nls' doc ###

DNase1 <- subset(DNase, Run == 1)
## using logistic formula
fm2DNase1 <- nls_tac(density ~ Asym/(1 + exp((xmid - log(conc))/scal)),
                   data = DNase1,
                   nlparam = list(xmid = c(1e-7,10), scal = c(1e-7,3)))
## some generics are applicable
coefficients(fm2DNase1)
summary(fm2DNase1)
## obtaining extra information
fm2DNase1$resid # residuals
fm2DNase1$formula # formula used
fm2DNase1$df # degrees of freedom
fm2DNase1$convInfo # Convergence information (n. iterations, tolerance attained)
fm2DNase1$SSR # SSR
fm2DNase1$data$density - fm2DNase1$resid # fitted values

## Synthetic examples

## Double exponential
x <- seq(from = 0, to = 20, length.out = 1000)
y <- 3*exp(-0.12*x) + 0.6*exp(-3.05*x) +  5 + 0.1*rnorm(length(x))
df <- data.frame(time = x, Temp = y)
# The nonlinear parameter list (with lower and upper values)
nlparam <- list(b1 = c(0,2), b2 = c(0,8))
fittac <- nls_tac('Temp ~ a1*exp(-b1*time) +  a2*exp(-b2*time) + a3',
                   data = df,
                   nlparam = nlparam,
                   N = 5)
summary(fittac)
plot(Temp ~ time, data = df)
lines(x, predict(fittac), col = "red", lwd = 2)

##
N <- 100
x <- seq(from = 0, to = 3, length.out = N)
y <- 3*sin(5*x)^2 + 2 + 0.2*rnorm(N)
df <- data.frame(x = x, y = y)
form <- y ~ a1*sin(b1*x)^2 + a2
nlbnds <- list(b1 = c(0.5,10)) # rough bouds for tac
tac_model <-  nls_tac(formula = form,
                      data = df,
                      nlparam = nlbnds,
                      N = 10,
                      tol = 1e-5)
yhat <- predict(tac_model)
plot(x,y)
lines(x,yhat, col = "blue")