acceptedMaxSSR {CGNM}

acceptedMaxSSR

Description

CGNM find multiple sets of minimizers of the nonlinear least squares (nls) problem by solving nls from various initial iterates. Although CGNM is shown to be robust compared to other conventional multi-start algorithms, not all initial iterates minimizes successfully. By assuming sum of squares residual (SSR) follows the chai-square distribution we first reject the approximated minimiser who SSR is statistically significantly worse than the minimum SSR found by the CGNM. Then use elbow-method (a heuristic often used in mathematical optimisation to balance the quality and the quantity of the solution found) to find the "acceptable" maximum SSR.

Usage

acceptedMaxSSR(
  CGNM_result,
  cutoff_pvalue = 0.05,
  numParametersIncluded = NA,
  useAcceptedApproximateMinimizers = TRUE,
  algorithm = 2
)

Arguments

CGNM_result

(required input) A list stores the computational result from Cluster_Gauss_Newton_method() function in CGNM package.

cutoff_pvalue

(default: 0.05) A number defines the rejection p-value for the first stage of acceptable computational result screening.

numParametersIncluded

(default: NA) A natural number defines the number of parameter sets to be included in the assessment of the acceptable parameters. If set NA then use all the parameters found by the CGNM.

useAcceptedApproximateMinimizers

(default: TRUE) TRUE or FALSE If true then use chai-square and elbow method to choose maximum accepted SSR. If false returnsnumParametersIncluded-th smallest SSR (or if numParametersIncluded=NA then returns the largest SSR).

algorithm

(default: 2) 1 or 2 specify the algorithm used for obtain accepted approximate minimizers. (Algorithm 1 uses elbow method, Algorithm 2 uses Grubbs' Test for Outliers.)

Value

A positive real number that is the maximum sum of squares residual (SSR) the algorithm has selected to accept.

Examples

model_analytic_function=function(x){

 observation_time=c(0.1,0.2,0.4,0.6,1,2,3,6,12)
 Dose=1000
 F=1

 ka=x[1]
 V1=x[2]
 CL_2=x[3]
 t=observation_time

 Cp=ka*F*Dose/(V1*(ka-CL_2/V1))*(exp(-CL_2/V1*t)-exp(-ka*t))

 log10(Cp)
}

observation=log10(c(4.91, 8.65, 12.4, 18.7, 24.3, 24.5, 18.4, 4.66, 0.238))

CGNM_result=Cluster_Gauss_Newton_method(
nonlinearFunction=model_analytic_function,
targetVector = observation,
initial_lowerRange = c(0.1,0.1,0.1), initial_upperRange =  c(10,10,10),
num_iter = 10, num_minimizersToFind = 100, saveLog = FALSE)

acceptedMaxSSR(CGNM_result)