nls_multstart function

Finds the best fit of non-linear model based on AIC score

Finds the best estimated model using non-linear least squares regression using nlsLM(). The best fit is determined using AIC scores.

Arguments

• formula: a non-linear model formula, with the response on the left of a ~ operator and an expression involving parameters on the right.

• data: (optional) data.frame, list or environment in which to evaluate the variables in formula and modelweights.

• iter: number of combinations of starting parameters which will be tried . If a single value is provided, then a shotgun/random-search/lhs approach will be used to sample starting parameters from a uniform distribution within the starting parameter bounds. If a vector of the same length as the number of parameters is provided, then a gridstart approach will be used to define each combination of that number of equally spaced intervals across each of the starting parameter bounds respectively. Thus, c(5,5,5) for three fitted parameters yields 125 model fits. Supplying a vector for iter will override convergence_count.

• start_lower: lower boundaries for the start parameters. If missing, this will default to -1e+10.

• start_upper: upper boundaries for the start parameters. If missing, this will default to 1e+10.

• supp_errors: if supp_errors = 'Y', then warning messages will be suppressed and no error messages from nlsLM will be shown, reducing the number of error messages printed while the model attempts to converge using poor starting parameters. We advise to only use supp_errors = 'Y' when confident in the bounds of your starting parameters.

• convergence_count: The number of counts that the winning model should be undefeated for before it is declared the winner. This argument defaults to 100. If specified as FALSE, then all of the iterations will be fitted, and the best model selected. Note that convergence_count can only be used with a shotgun/random-search approach, and not with a gridstart approach. This argument will be ignored if a gridstart approach is specified by a vector input for iter.

• control: specific control can be specified using nls.lm.control.

• modelweights: Optional model weights for the nls. If data is specified, then this argument should be the name of the numeric weights vector within the data object.

• lhstype: Method to use for Latin Hypercube Sampling using lhs. Choice of "random" (simple random lhs, fast), "improved" (lhs with optimised euclidean distance between points, medium speed), "maximin"

  (lhs with maximised minimum distance between points, medium speed), or "genetic" (lhs optimised to the S optimilaity criterion using a genetic algorithm, slow). If not set, a purely random (shotgun) approach is taken. Only used if iter is a single number.

• ...: Extra arguments to pass to nlsLM if necessary.

Returns

returns a nls object of the best estimated model fit.

Note

Useful additional arguments for nlsLM

include: na.action = na.omit, lower/upper = c() where these represent upper and lower boundaries for parameter estimates.

Examples

# load in data

data("Chlorella_TRC")
Chlorella_TRC_test <- Chlorella_TRC[Chlorella_TRC$curve_id == 1,]

# run nls_multstart()

# define the Sharpe-Schoolfield equation
schoolfield_high <- function(lnc, E, Eh, Th, temp, Tc) {
 Tc <- 273.15 + Tc
 k <- 8.62e-5
 boltzmann.term <- lnc + log(exp(E/k*(1/Tc - 1/temp)))
 inactivation.term <- log(1/(1 + exp(Eh/k*(1/Th - 1/temp))))
 return(boltzmann.term + inactivation.term)
}

fits <- nls_multstart(ln.rate ~ schoolfield_high(lnc, E, Eh, Th, temp = K, Tc = 20),
                data = Chlorella_TRC_test,
                iter = 500,
                start_lower = c(lnc=-10, E=0.1, Eh=0.5, Th=285),
                start_upper = c(lnc=10, E=2, Eh=5, Th=330),
                lower = c(lnc=-10, E=0, Eh=0, Th=0),
                supp_errors = 'Y')

See Also

nlsLM for details on additional arguments to pass to the nlsLM function. lhs for details of Latin Hypercube Sampling

Author(s)

Daniel Padfield

Granville Matheson

Francis Windram