LORI (LOw-Rank Interaction) model for count data with covariates
The LORI model is designed to analyse count data with covariates, using a Poisson log-linear model. In particular, it can be used to assess the effect of temporal and geographical covariates on species abundances.
Let \(Y\in\mathbb{N}^{n\times p}\) be a (incomplete) matrix of counts, and \(L\in\mathbb{R}^{np\times K}\) a matrix of covariates about the rows and columns of \(Y\). For example if \(Y\) counts the abundance of species across sites (rows) and time stamps (columns), \(L\) might contain temporal, spatial, and spatio-temporal information.
## Loading required package: Matrix## Loading required package: foreach## Loaded glmnet 2.0-16Example: Aravo data set
The {Aravo data set} measures the abundance of \(82\) species of alpine plants in \(75\) sites in France. The data consist of a contingency table collecting the abundance of species across sampling sites. Covariates about the environments and species are also available.
## Aspect Slope Form PhysD ZoogD Snow
## AR07 7 2 1 50 no 140
## AR71 1 35 3 40 no 140
## AR26 5 0 3 20 no 140
## AR54 9 30 3 80 no 140
## AR60 9 5 1 80 no 140
## AR70 1 30 3 40 no 140## Height Spread Angle Area Thick SLA N_mass Seed
## Agro.rupe 6 10 80 60.0 0.12 8.1 218.70 0.08
## Alop.alpi 5 20 20 190.9 0.20 15.1 203.85 0.21
## Anth.nipp 15 5 50 280.0 0.08 18.0 219.60 0.54
## Heli.sede 0 30 80 600.0 0.20 10.6 233.20 1.72
## Aven.vers 12 30 60 420.0 0.14 12.5 156.25 1.17
## Care.rosa 30 20 80 180.0 0.40 6.5 208.65 1.68d <- dim(aravo$spe)
n <- d[1]
p <- d[2]
# Create covariate matrix, choose quantitative variables in Row and Column covariates
# and use covmat function to replicate species/environments
# center and scale covariate matrix
cov <- scale(covmat(aravo$env[, c(1,2,4,6)], aravo$traits, n, p))##
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100 / 100## [1] "fitting model..."
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100% - iter: 1000 - error: 1.054841e-05 - objective: 0.6544968## Aspect Slope PhysD Snow Height Spread
## 0.03812487 0.07070402 -0.01872686 -0.07311364 0.09327172 -0.23549705
## Angle Area Thick SLA N_mass Seed
## -0.18366508 -0.19437829 -0.10844523 -0.16766109 0.18173165 -0.11695309