polynomial.model.lsd {LSDsensitivity}

Fit a polynomial meta-model to a LSD model sample data

Description

This function fits a Polynomial meta-model of first or second order, with or without interactions, to the sampled data from a LSD simulation model. Polynomial meta-models are usually inadequate to fit nonlinear simulation models, please use the estimated meta-model carefully.

Usage

polynomial.model.lsd( data, ext.wgth = 0.5, ols.sig = 0.2,
                      orderModel = 0, interactModel = 0, digits = 4 )

Arguments

data

an object created by a previous call to read.doe.lsd which contains all the required experimental data for the analysis.

ext.wgth

numeric in [0, 1]: the weight given to the fitting metrics calculated over the out-of-sample (external) validation sample in regard to the in-sample metrics. The default value is 0.5.

ols.sig

numeric in [0, 1]: the minimum significance considered in the OLS regression.

orderModel

a number corresponding to the polynomial model order: 0 = automatic selection (according to fitting metrics, the default); 1 = first order; 2 = second order.

interactModel

a number indicating the presence of interaction terms in the model: 0 = automatic selection (according to fitting metrics, the default); 1 = no , 2 = yes.

digits

integer: the number of significant digits to show in results. The default is 4.

Details

This function fits a polynomial meta-model to the experimental data set previously loaded with read.doe.lsd using the ordinary least-squares (OLS) method.

This function is a wrapper to the function lm in stats-package.

Value

The function returns an object/list of class polynomial-model containing several items:

selected

an object containing the selected estimated meta-model.

comparison

a print-ready table with all fitting statistics for all fitted meta-model specifications.

R2

the adjusted R2 in-sample fitting statistic for the selected meta-model.

rmse

the RMSE out-of-sample fitting statistic for the selected meta-model.

mae

the MAE out-of-sample fitting statistic for the selected meta-model.

rma

the RMA out-of-sample fitting statistic for the selected meta-model.

extN

number of out-of-sample observations.

estimation

a print-ready table with the coefficients (hyper-parameters) of the selected estimated meta-model.

estimation.std

a print-ready table with the standardized coefficients (hyper-parameters) of the selected estimated meta-model.

coefficients

a vector with the coefficients (hyper-parameters) of the selected estimated meta-model.

coefficients.std

a vector with the standardized coefficients (hyper-parameters) of the selected estimated meta-model.

order

order of the selected polynomial model.

polyNames

name of the selected polynomial model.

interact

number of the selected interaction mode.

interactNames

name of the selected interaction mode.

Note

See the note in LSDsensitivity-package for step-by-step instructions on how to perform the complete sensitivity analysis process using LSD and R.

Author(s)

NA

See Also

read.doe.lsd()

Examples

# get the example directory name
path <- system.file( "extdata/sobol", package = "LSDsensitivity" )

# Steps to use this function:
# 1. define the variables you want to use in the analysis
# 2. load data from a LSD simulation saved results using read.doe.lsd,
#    preferrably using two sets of sampled data (DoEs), one for model
#    estimation and the other for out-of-sample (external) validation
# 3. fit the polynomial meta-model using polynomial.model.lsd

lsdVars <- c( "var1", "var2", "var3" )         # the definition of existing variables

dataSet <- read.doe.lsd( path,                 # data files folder
                         "Sim3",               # data files base name (same as .lsd file)
                         "var3",               # variable name to perform the sensitivity analysis
                         does = 2,             # number of experiments (data + external validation)
                         saveVars = lsdVars )  # LSD variables to keep in dataset

model <- polynomial.model.lsd( dataSet )       # estimate best polynomial meta-model
                                               # using defaults (auto model selection)

print( model$comparison )                      # model comparison table
print( model$estimation.std )                  # model estimation (standardized) table