MicrobialGrowth (version 1.0.0)

.getDefaultNlsValues: Default NLS values

Description

Gives default values for NLS regression from x and y values. The method of calculating default values differs depending on the amount of data available in y. Default values can be pre-set by providing them in the start, lower and upper arguments.

Usage

.getDefaultNlsValues(x, y, start = list(), lower = list(), upper = list())

Value

the default values of start, lower and upper for NLS regression.

Arguments

x

index series or time series.

y

values or list of values to regress (should not be logged, must be strictly greater than zero).

start

a named list of starting estimates. The coefficients specified in this list will not be calculated.

lower

a named list of lower bounds. The coefficients specified in this list will not be calculated.

upper

a named list of upper bounds. The coefficients specified in this list will not be calculated.

Details

default values are calculated as follows:

• start

  • N0: the minimum value of y

  • Nmax: the maximum value of y

  • mu:

    • if length(y) <= THRESHOLD_FEW_DATA: the greatest slope between two contiguous points (on logged y values)

    • else: the linear regression on data positioned in the middle ±25% of the amplitude on logged y

  • lambda: the highest value of x which is within the lowest 5% of amplitude of y

• lower

  • N0: the smallest value greater than zero calculated with 1/.Machine$double.xmax

  • Nmax: the mean value of y

  • mu: the amplitude on y divided by the amplitude on x

  • lambda:the minimum value of x

• upper

  • N0: the mean value of y

  • Nmax: twice the max value of y

  • mu:

    • if length(y) <= THRESHOLD_FEW_DATA: the amplitude on logged y divided by the smallest step between two contiguous x values

    • else: the greatest slope between two contiguous points (on logged y values)

  • lambda: the maximum value of x

Note that it is possible, particularly when there is little data, that linear regression for start$mu is not possible, hence the presence of condition with THRESHOLD_FEW_DATA.

Examples

# Example data
x = c(0.00, 5.26, 10.53, 15.79, 21.05, 26.32, 31.58, 36.84, 42.11, 47.37, 52.63,
      57.89, 63.16, 68.42, 73.68, 78.95, 84.21, 89.47, 94.74, 100.00)
y = c(0.15, 0.15, 0.15, 0.16, 0.19, 0.26, 0.38, 0.58, 0.85, 1.18, 1.53, 1.86,
      2.15, 2.38, 2.55, 2.66, 2.78, 2.85, 2.89, 2.93)

# Simple example
values = .getDefaultNlsValues(x, y)
cat("N0=", values$start$N0, " with limits [", values$lower$N0, ", ", values$upper$N0,"]", sep="")
## N0=0.15 with limits [5.562685e-309, 1.4315]

# Example with specifying a starting value (which will therefore not be calculated)
values = .getDefaultNlsValues(x, y, start=list(N0=0.1))
cat("N0=", values$start$N0, " with limits [", values$lower$N0, ", ", values$upper$N0,"]", sep="")
## N0=0.1 with limits [5.562685e-309, 1.4315]