PredictionFBM: Predicting using FBM

In CoDaLoMic: Compositional Models to Longitudinal Microbiome Data

Predicting using FBM

Description

This function calculates the expected value and variance of the bacteria at time point Tt. Then, this function calculates the expected value and variance of the bacteria at time point t=(Tt+1),...,K

Usage

PredictionFBM(
  paramEstimadosFinal,
  EspecieMaxima,
  alpha,
  K,
  esperanza,
  Var,
  E,
  Tt
)

Arguments

paramEstimadosFinal	The estimate 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.
EspecieMaxima	Row in which the bacteria chosen as reference is in especie.This bacteria is used as reference in the alr transformation that the model does and it is placed at the denominator of the balance)
alpha	Matrix that contains at the row i the Dirichlet parameter of the bacteria i at t=1,2,3,...,Tt.
K	Number. The function will calculate the value of the expected value and the variance at Tt and predict for the time points t=Tt+1,..,K. To predict all the time points available at the data we K=dim(especie.All)-1
esperanza	Matrix that contains at row i the expected value of the bacterial taxa of bacteria i at t=1,2,3,...,Tt-1.
Var	Matrix that contains at row i the variance of the bacterial taxa of bacteria i at t=1,2,3,...,Tt-1.
E	Number of bacteria available
Tt	Number of bacteria available

Details

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:

• ExpectedValue.All: Matrix. Matrix that contains at row i the expected value of the bacteria i at all time points t=1,2,...,K. The bacteria are placed at the same order than in especies.

• VarianceValue.All: Matrix. Matrix that contains at row i the variance of the bacteria i at all time points t=1,2,...,K. The bacteria are placed at the same order than in especies.

• DirichlerParam.All: Matrix. Matrix that contains at row i the dirichlet parameter of the bacteria i at all time points t=1,2,...,K. The bacteria are placed at the same order than in especies.

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

Tt=2
E=3
tau=5
EspecieMaxima=3
K=3
parms11=c(0.1,0.2,0.3,0.4,0.5,0.6,tau)
alpha=cbind(c(1.726793,1.892901,1.380306),
           c(1,1,3))
Expected=cbind(c(alpha[1,1]/tau, alpha[2,1]/tau, alpha[3,1]/tau  ),
              c(alpha[1,2]/tau,alpha[2,2]/tau,alpha[3,2]/tau))
Variance=cbind(c(0.03768101, 0.03920954, 0.03330857 ),
              c( 0.03683242,0.02784883, 0.0413761 ))
Expected.final=Expected[,-2]
Variance.final=Variance[,-2]

PredictionFBM(parms11,EspecieMaxima, alpha,K,Expected.final,Variance.final,E,Tt )

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