generate.panel.2order: Generation of second order differential equation solutions for several individuals with intra-individual and inter-individual noise

Description

generate.panel.2order Generation of second order differential equation solutions for several individuals with intra-individual and inter-individual noise. The function generates the equation coefficients following a normal distribution based on the parameter internoise and the coefficients provided as input. It then calls the function generate.2order to generate a solution of a second order differential equation with these parameters for the nind individuals. Finally it adds measurement noise to each signal according to the value of the parameter intranoise.

Usage

generate.panel.2order(
  time,
  excitation = NULL,
  y0 = 1,
  v0 = 0,
  t0 = NULL,
  xi = 0.1,
  period = 10,
  k = 1,
  yeq = 0,
  nind = 1,
  internoise = 0,
  intranoise = 0
)

Arguments

time

is a vector containing the time values corresponding to the excitation signal.

excitation

Is a vector containing the values of the excitation signal.

is the initial condition for the variable y(t=t0), (0, by default), it is a scalar.

is the initial condition for the derivative dy(t=t0), (0, by default), it is a scalar.

is the time corresponding to the initial condition y0 and v0. Default is the minimum value of the time vector.

is the damping factor. A negative value will produce divergence from equilibrium.

period

is the period T of the oscillation, \(T = \frac{2*\pi}{\omega_{n}}\) as mentioned

Default is 1. It represents the proportionality between the stationary increase of signal and the excitation increase that caused it. Only relevant if the excitation is non null.

yeq

is the signal equilibrium value, i.e. the stationary value reached when the excitation term is 0.

nind

number of individuals.

internoise

Is the inter-individual noise added. The damping factor across individuals follows a normal distribution centered on the input parameter xi with a standard deviation of internoise*xi. The same applies to the other coefficients of the differential equation (T,k and yeq) and to the initial conditions (y0 and v0)

intranoise

Is the noise to signal ratio: dynamic noise added to each signal defined as the ratio between the variance of the noise and the variance of the signal

Value

Returns a data frame with signal and time values for the time and excitation vectors provided. It contains the following columns:

id - individual identifier (from 1 to nind).
excitation - excitation signal provided as input
time - time values provided as input
signalraw - signal with no noise (inter noise added for each individual)
signal - signal with intra noise added

Details

Used for simulations in the context of the package.

Examples

Run this code

# NOT RUN {
generate.panel.2order(time = generate.excitation(3, 6, 2, 1, 200, 2)$t,
                      excitation = generate.excitation(3, 6, 2, 1, 200, 2)$exc,
                      xi = 0.1,
                      period = 0.5,
                      k = 1,
                      nind = 5,
                      internoise = 0.2,
                      intranoise = 0.1)
# }