There are two main functions in this package. The first one is \(lglasso\) which can output a sparse network representing the precision matrix by maximizing the \(l_1\) penalized likelihood function. The second function if \(mle\), which can compute the maximum likelihood estimates of precision matrix and the correlation parameter \(\tau\) for a given network structure produced from function \(lglasso\).
##The sample data are subset of a larger longitudinal data set from a clinical project.
##There are 13 clusters are involved in the sample data.
sample_data=lglasso:::sample_data
dim(sample_data)
#> [1] 100 22
sample_data[1:5,1:5]
#> subject age Bifidobacterium Escherichia.Shigella Phocaeicola
#> 1 103 14 -2.7038308 -4.793854 -9.414017
#> 2 103 15 -0.4770604 -2.342624 -8.203014
#> 3 103 16 3.3974623 5.241120 -5.532109
#> 4 103 17 -1.5783620 -2.432638 -8.656051
#> 5 104 1 -5.8001556 -6.262590 -7.033613
#sample_data=as.matrix(sample_data)a=lglasso(data = sample_data, rho = 0.7, heter=T, ty=2)
# Individual dampening rate:
round(a$tau,3)
#> [1] 3.272 0.418 3.272 2.660 1.233 2.457 0.622 3.272 0.826 1.029 1.233 0.826
#> [13] 2.457
# Number of edge in the estimated network:
(length(which(a$omega!=0))-ncol(a$omega))/2
#> [1] 106
# Subnetwork:
a$omega[1:5,1:5]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.168210106 -0.02328179 0.00000000 -0.05663374 -0.004241546
#> [2,] -0.023274705 0.13588280 -0.01162514 0.00000000 -0.023387341
#> [3,] 0.000000000 -0.01163005 0.13855159 0.00000000 -0.012298354
#> [4,] -0.056646205 0.00000000 0.00000000 0.23769213 0.000000000
#> [5,] -0.004263599 -0.02339186 -0.01229982 0.00000000 0.173754573
# loglikelihood:
a$ll
#> [1] -2856.348b=lglasso(data = sample_data, rho = 0.7, heter=F,ty=2)
# Shared dampening rate
round(b$tau,3)
#> [1] 1.826
# Number of edge in the estimated network
(length(which(b$omega!=0))-ncol(b$omega))/2
#> [1] 107
# Subnetwork
b$omega[1:5,1:5]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.180419574 -0.02917221 0.000000000 -0.05672336 -0.007079478
#> [2,] -0.029167026 0.13966946 -0.013716293 0.00000000 -0.023584343
#> [3,] 0.000000000 -0.01372621 0.145078330 0.00000000 -0.008861326
#> [4,] -0.056729735 0.00000000 0.000000000 0.26418730 0.000000000
#> [5,] -0.007092007 -0.02358701 -0.008859485 0.00000000 0.176894920
# loglikelihood
b$ll
#> [1] -2841.08c=lglasso(data = sample_data, rho = 0.7, heter=T, ty=0)
# indvidual dampening rate
round(c$tau,3)
#> [1] 3.272 3.272 3.272 3.068 1.029 2.253 0.418 2.864 0.826 3.680 1.437 0.826
#> [13] 2.660
# Number of edge in the estimated network
(length(which(c$omega!=0))-ncol(c$omega))/2
#> [1] 119
# subnetwork
c$omega[1:5,1:5]
#> [,1] [,2] [,3] [,4] [,5]
#> [1,] 0.137195407 -0.02263919 0.000000000 -0.05285821 -0.0045570955
#> [2,] -0.022638117 0.12906228 -0.013961526 0.00000000 -0.0205830624
#> [3,] 0.000000000 -0.01396010 0.111558902 0.00000000 -0.0004726525
#> [4,] -0.052857467 0.00000000 0.000000000 0.21813779 0.0000000000
#> [5,] -0.004554955 -0.02058416 -0.000472173 0.00000000 0.1373557823
# loglikelihood
c$ll
#> [1] -2921.594[1] Zhou, J., Gui, J., Viles, W.D., Chen, H., Madan, J.C., Coker, M.O., Hoen, A.G., 2021a. Identifying Microbial Interaction Networks Based on Irregularly Spaced Longitudinal 16S rRNA sequence data. https://doi.org/10.1101/2021.11.26.470159
[2] Friedman J., Hastie T., Tibshirani R. (2019) Graphical Lasso: Estimation of Gaussian Graphical Models, Version: 1.11. https://CRAN.R-project.org/package=glasso.