EstParmFunc: Writting the loglikelihood of the dirichlet

In CoDaLoMic: Compositional Models to Longitudinal Microbiome Data

Writting the loglikelihood of the dirichlet

Description

This function calculates the loglikelihood of the dirichlet for the Dirich-gLV model.

Usage

EstParmFunc(parms.vector, especie)

Arguments

parms.vector	Vector equal to c(tau,as.vector( pam)) where: pam: Matrix. Each row has the parameters of each bacteria. Following our example, pam has the parameters placed as follows: r1 a11 a12 r2 a21 a22 tau: Number. Value of the tau parameter in the model
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 this matrix is the one used as reference in the alr transfromation that the model apply

Details

In an example with three bacteria, the regression of this model is defined by

r_{1}\cdot log(x_{1}(t)/x_{3}(t))+log(x_{1}(t)/x_{3}(t))\cdot [a_{11}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{12}\cdot log(x_{2}(t)/x_{3}(t))]

r_{2}\cdot log(x_{2}(t)/x_{3}(t))+log(x_{2}(t)/x_{3}(t))\cdot [a_{21}\cdot log(x_{1}(t)/x_{3}(t))(t)+a_{22}\cdot log(x_{2}(t)/x_{3}(t))]

Value

Returns a number with the value of the dirichlet loglikelihood.

References

Creus-Martí, I. and Moya, A. and Santonja, F. J. (2018). A Statistical Model with a Lotka-Volterra Structure for Microbiota Data. Lucas Jodar, Juan Carlos Cortes and Luis Acedo, Modelling or engineering and human behavior 2018, Instituto Universitario de Matematica Multidisciplinar. ISBN: 978-84-09-07541-6

Examples

especie1=cbind(c(0.5,0.3,0.2), c(0.1,0.3,0.6))
tau1=0.4
parms1= cbind(c(0.1,0.2),c(-0.2,0.1),c(0.3,0.2))
parms11=c(tau1,as.vector( parms1))

EstParmFunc(parms11,especie1)

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