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.

library(lori)
library(glmnet)

## Loading required package: Matrix

## Loading required package: foreach

## Loaded glmnet 2.0-16

library(gridExtra)
data("aravo")

Example: 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.

# Environment characteristics
head(aravo$env)

##      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

# Species traits
head(aravo$traits)

##           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 1.68

d <- 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))

lambda2 <- cv.glmnet(cov, unlist(c(aravo$spe)), family = "poisson")$lambda.min
lambda1 <- qut(aravo$spe, cov, lambda2)

res <- lori(aravo$spe, cov, lambda1=lambda1, lambda2=lambda2, trace.it = T)
res$alpha

##  [1] -1.6986393 -1.2711974 -0.7957705 -1.2711985 -1.8417378 -0.9409538
##  [7] -0.9101852 -1.2711949 -1.0393942 -0.9727056 -1.2286363 -0.9409528
## [13] -0.9101784 -0.7691116 -0.9101843 -0.9101815 -1.0394059 -1.1486007
## [19] -1.1486010 -1.3621735 -0.8513499 -0.9727056 -1.0744933 -0.7178215
## [25] -1.0394021 -0.6225047 -1.1108598 -1.6986449 -1.1108601 -0.6931328
## [31] -0.9102007 -0.9101930 -1.6341092 -2.4607678 -2.6149128 -1.6986469
## [37] -1.5163266 -1.4109736 -1.0055112 -0.7178280 -1.0055149 -1.1108726
## [43] -1.3621866 -1.0055163 -0.7431563 -1.2286591 -1.3621893 -1.0745091
## [49] -1.8417482 -1.9217884 -1.2712144 -1.2286605 -1.3156690 -1.6341164
## [55] -1.0745125 -1.5163365 -1.0745113 -1.0745122 -1.4622703 -1.3621881
## [61] -1.3156680 -1.3621869 -1.2712183 -1.0745090 -1.1878366 -1.5163337
## [67] -0.9409742 -1.0394147 -0.9101961 -1.2712164 -1.0394191 -1.0745073
## [73] -1.5734936 -1.0394085 -1.2712151

res$beta

##  [1]  0.78697994  1.12620719  0.01378591 -1.21831151 -0.02875385
##  [6]  0.80602633  0.78699428 -0.52518249 -0.67932996  0.01378486
## [11] -1.77790082 -0.02875339  0.01378533  0.86108574 -1.08478478
## [16]  1.48013239 -0.21980042 -0.76633937  1.13982119  0.05460798
## [21] -0.86164629 -0.33102826 -0.21980598 -1.77790072 -1.77790086
## [26] -2.47098642 -2.47098640  0.44665260  0.01379271  0.26972078
## [31] -0.39164834  0.47332310 -1.21831085 -0.59928915 -2.47098640
## [36] -0.07320453 -0.52518267 -1.08478481  0.20302940  1.19245003
## [41]  0.82473078 -0.27387201 -0.76633932 -1.37245620  0.86109382
## [46] -0.11972330 -1.55476951  0.82472040 -0.76633938 -2.47098645
## [51]  1.13980804  0.59693555  1.01012469 -0.67933029 -1.55476962
## [56] -0.16851362  0.33224389  0.41926178  1.04043418 -2.06556228
## [61] -1.77790072 -2.06556231 -0.76633944 -0.02875112  0.01378498
## [66] -0.86164654  0.91328127 -0.96700510 -2.06556230 -0.21980059
## [71] -2.06556229  0.54930754 -0.21980567 -0.59928626 -2.47098650
## [76] -2.47098637 -1.55476961 -1.37245609 -0.76633932 -0.67932977
## [81] -2.47098647 -1.55476945

Analysis of count data with covariates in R using LORI - tutorial

Genevieve Robin

2019-02-19

LORI (LOw-Rank Interaction) model for count data with covariates

Example: Aravo data set