Estimate_Param_FBM: Estimating Parameters of EstParmFunc_FBM

In CoDaLoMic: Compositional Models to Longitudinal Microbiome Data

Estimating Parameters of EstParmFunc_FBM

Description

This function estimates the parameters of the FBM model.

Usage

Estimate_Param_FBM(
  tau,
  ridge.final,
  Iter.EstParmFunc = 80,
  especie,
  EspecieMaxima,
  Tt,
  E,
  seed = NULL
)

Arguments

tau	Number. Value of the tau parameter.
ridge.final	Object of class "ridgelm". Values obtained with the ridge regression.
Iter.EstParmFunc	Number. Number of iterations. Default: 80 iterations.
especie	Matrix that contains at row i the bacterial taxa of bacteria i at all time points. The bacteria placed in the last row of the matrix will be used as reference in the alr transformation and will be at the denominator of the balance.
EspecieMaxima	Row in which the bacteria chosen as reference is in especie. This is the bacteria that is going to be at the denominator of the balance and in the deniminator of the alr tranformation. As a result, in this function, EspecieMaxima must be equal to E.
Tt	Number of time points available
E	Number. Number of bacteria available.
seed	Number. Set a seed. Default seed=NULL.

Details

Maximum likelihood estimation is used. This function makes an iterative process, for a given value of tau, it obtains the value of the rest of the parameters that maximize the dirichlet loglikelihood (defined in EstParmFunc_FBM) using the Nelder-Mead method and the values obtained in the ridge regression as initial parameters. Then it uses the values obtained as initial parameters and repeats the process Iter.EstParmFunc times.

The regression of this model is defined by

\mu_{it}=a_{i1}+a_{i2}\cdot\text{alr}(x_{i,(t-1)})+a_{i3}\cdot\text{Balance}(x_{i,(t-1)})\text{ for }i=1,\dots, D-1\text{ where } D \text{ is the number of bacteria}

Value

Returns a list with:

• All.iter: Matrix. Each row has the parameters obtained in each iteration. The parameters are in the columns written in following order: a11,a12,a13, a21, a22,a23, ...a(D-1)1,a(D-1)2,a(D-1)3,tau. Where D is the number of bacterial species present in the matrix especie. In this matrix we must observe that in the last iterations the values has really similar or equal values, it not, we need to increase the value of Iter.EstParmFunc.

• Param.Estimates: Vector with the estimated parameters, in the following order: a11,a12,a13, a21, a22,a23, ...a(D-1)1,a(D-1)2,a(D-1)3,tau. Where D is the number of bacterial species present in the matrix especie.

• AIC Number: Value of the AIC.

References

Creus-Martí, I., Moya, A., Santonja, F. J. (2021). A Dirichlet autoregressive model for the analysis of microbiota time-series data. Complexity, 2021, 1-16.

Examples

set.seed(123)
especie=t(gtools::rdirichlet(5,c(1,3,1)))
Tt=5
E=3
EspecieMaxima=3
ridge.final=ridgeregression(Tt,especie, E, EspecieMaxima)
tau=20
Iter.EstParmFunc=40

Estimate_Param_FBM(tau,ridge.final,Iter.EstParmFunc, especie,EspecieMaxima,Tt,E, 714)

CoDaLoMic documentation built on April 12, 2025, 2:18 a.m.