optimum_param {doremi} R Documentation

## Function to find the optimum parameter for derivative estimation (embedding or spar according to derivative estimation method chosen)

### Description

optimum_param calculates the optimum parameter for derivative estimation by varying the latter in a range introduced as input and keeping the parameter and coefficients having the $R^2$ closest to 1.

### Usage

optimum_param(
data,
id = NULL,
input = NULL,
time,
signal,
dermethod = "gold",
model = "1order",
order = 2,
pmin = 3,
pmax = 21,
pstep = 2,
verbose = FALSE
)


### Arguments

 data Is a data frame containing at least one column, that is the signal to be analyzed. id Is a CHARACTER containing the NAME of the column of data containing the identifier of the individual. If this parameter is not entered when calling the function, a single individual is assumed and a linear regression is done instead of the linear mixed-effects regression. input Is a CHARACTER or a VECTOR OF CHARACTERS containing the NAME(s) of data column(s) containing the EXCITATION vector(s). If this parameter is not entered when calling the function, the excitation is assumed to be unknown. In this case, the linear mixed-effect regression is still carried out but no coefficient is calculated for the excitation term. The function then uses the parameters estimated by the regression to carry out an exponential fit of the signal and build the estimated curve. The function will consider as an excitation each column of data having a name contained in the input vector. The function will return a coefficient for each one of the excitation variables included in the input vector. time Is a CHARACTER containing the NAME of the column of data containing the time vector. If this parameter is not entered when calling the function, it is assumed that time steps are of 1 unit and the time vector is generated internally in the function. signal Is a CHARACTER containing the NAME of the column of the data frame containing the SIGNAL to be studied. dermethod is the derivative estimation method. The methods currently available are: "gold","glla" and "fda" (see their respective function for more details) model is the model to be used for analysis of the signal. The models available are "1order" and "2order" order is the maximum order of the derivative estimated when using calculate.gold or calculate.glla. Using a higher order can enhance derivative estimation (see doi: 10.1080/00273171.2015.1123138Chow et al.(2016)) pmin is the minimum of the interval in which to vary the parameter (embedding number or spar according to derivative method chosen) pmax is the maximum of the interval in which to vary the parameter (embedding number or spar according to derivative method chosen) pstep is the step that will be considered when varying the parameter. For instance pmin=3, pmax=7 and pstep=2 and dermethod="gold" will make the embedding number take the values 3,5 and 7. verbose Is a boolean that displays status messages of the function (and functions it calls) when set to TRUE.

### Value

Returns a list of three objects:

• analysis is a data.frame containing the resultmean object of the analysis made (result of the analyze.1order or analyze.2order function according to model chosen) with the different values of embedding/spar and the resulting $R^2$.

• summary_opt is a data.frame containing the analysis that had the best $R^2$ from the analysis data.frame previously mentioned

• d contains the optimum value of the embedding/spar

analyze.1order and analyze.2order for the estimation of equation coefficients in signals following a first and second order differential equation respectively

### Examples

s2 <- generate.panel.2order(time = 0:100,
excitation = c(rep(0,25),rep(1,76)),
y0 = 0,
v0= 0,
xi = 0.05,
period=10,
k=1,
yeq=0,
nind=4,
internoise = 0.2,
intranoise = 8)
resgold <- optimum_param (data=s2,
id="id",
input="excitation",
time="time",
signal="signal",
model = "2order",
dermethod = "gold",
pmin = 3,
pmax = 13,
pstep = 2,
verbose = TRUE)


[Package doremi version 1.0.0 Index]