generate.panel.1order {doremi}

Generation of first order differential equation solutions for several individuals with intra-individual and inter-individual noise

Description

generate.panel.1order Generation of first order differential equation solutions for several individuals with intra-individual and inter-individual noise. For a panel of nind individual, the function generates nind solutions of a first order differential equation with constant coefficients distributed along a normal distribution. Measurement noise is added to each individual signal according to the value of the intranoise parameter.

Usage

generate.panel.1order(
  time,
  excitation = NULL,
  y0 = 0,
  t0 = NULL,
  tau = 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 (u(t) in the equation). If NULL, it is considered to be 0.

y0

Signal initial value y(t=t0). Default is 0

t0

Time corresponding to the signal initial value y(t=t0). Default is the minimum value of the time vector. Must be a value between minimum and maximum value of the time vector

tau

Signal decay time. It represents the characteristic response time of the solution of the differential equation. A negative value will produce divergence from equilibrium.

k

Signal gain. 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

Signal equilibrium value. Stationary value when the excitation term is 0.

nind

number of individuals.

internoise

Is the inter-individual noise added. The tau across individuals follows a normal distribution centered on the input parameter tau with a standard deviation of internoise*tau, except if any decay time is negative (see Details section). The same applies to the other coefficients of the differential equation (k and yeq)

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

Details

Used for simulations in the context of the package. The function currently simulates only positive decay times corresponding to a regulated system. When the decay time is low and the inter individual noise is high, some individuals' decay time could be negative. In that case, the decay time distribution is truncated at 0.1*deltat and values below are set to this limit. High values are symmetrically set at the upper percentile value similar to a Winsorized mean. A warning provides the initial inter individual noise set as input argument and the inter individual noise obtained after truncation.

Value

Returns a data frame containing the following columns:

• id - individual identifier (from 1 to nind).

• excitation - excitation signal

• time - time values

• signalraw - signal with no noise (internoise provided added for each individual)

• dampedsignal - signal with intranoise added

See Also

generate.1order for calculation of the numerical solution to the differential equation and generate.excitation for excitation signal generation

Examples

generate.panel.1order(time = generate.excitation(3, 6, 2, 1, 200, 2)$t,
                      excitation = generate.excitation(3, 6, 2, 1, 200, 2)$exc,
                      y0 = 0,
                      tau = 10,
                      k = 1,
                      yeq = 0,
                      nind = 5,
                      internoise = 0.2,
                      intranoise = 1)