`R/get_enviro_cor.R`

`get_enviro_cor.Rd`

Calculates the correlation between columns of the response matrix, due to similarities in the response to explanatory variables i.e., shared environmental response.

`get_enviro_cor(mod, type = "mean", prob = 0.95)`

- mod
An object of class

`"jSDM"`

- type
A choice of either the posterior median (

`type = "median"`

) or posterior mean (`type = "mean"`

), which are then treated as estimates and the fitted values are calculated from. Default is posterior mean.- prob
A numeric scalar in the interval \((0,1)\) giving the target probability coverage of the intervals, by which to determine whether the correlations are "significant". Defaults to 0.95.

results A list including :

- cor, cor.lower, cor.upper
A set of \(np \times np\) correlation matrices, containing either the posterior median or mean estimate over the MCMC samples plus lower and upper limits of the corresponding 95 % highest posterior interval.

- cor.sig
A \(np \times np\) correlation matrix containing only the “significant" correlations whose 95 % highest posterior density (HPD) interval does not contain zero. All non-significant correlations are set to zero.

- cov
Average over the MCMC samples of the \(np \times np\) covariance matrix.

In both independent response and correlated response models, where each of the columns of the response matrix \(Y\) are fitted to a set of explanatory variables given by \(X\), the covariance between two columns \(j\) and \(j'\), due to similarities in their response to the model matrix, is thus calculated based on the linear predictors \(X \beta_j\) and \(X \beta_j'\), where \(\beta_j\) are species effects relating to the explanatory variables. Such correlation matrices are discussed and found in Ovaskainen et al., (2010), Pollock et al., (2014).

Hui FKC (2016). “boral: Bayesian Ordination and Regression Analysis of Multivariate Abundance Data in R.” *Methods in Ecology and Evolution*, 7, 744–750.

Ovaskainen et al. (2010). Modeling species co-occurrence by multivariate logistic regression generates new hypotheses on fungal interactions. *Ecology*, 91, 2514-2521.

Pollock et al. (2014). Understanding co-occurrence by modelling species simultaneously with a Joint Species Distribution Model (JSDM). *Methods in Ecology and Evolution*, 5, 397-406.

```
library(jSDM)
# frogs data
data(frogs, package="jSDM")
# Arranging data
PA_frogs <- frogs[,4:12]
# Normalized continuous variables
Env_frogs <- cbind(scale(frogs[,1]),frogs[,2],
scale(frogs[,3]))
colnames(Env_frogs) <- colnames(frogs[,1:3])
Env_frogs <- as.data.frame(Env_frogs)
# Parameter inference
# Increase the number of iterations to reach MCMC convergence
mod <- jSDM_binomial_probit(# Response variable
presence_data=PA_frogs,
# Explanatory variables
site_formula = ~.,
site_data = Env_frogs,
n_latent=0,
site_effect="random",
# Chains
burnin=100,
mcmc=100,
thin=1,
# Starting values
alpha_start=0,
beta_start=0,
V_alpha=1,
# Priors
shape=0.5, rate=0.0005,
mu_beta=0, V_beta=10,
# Various
seed=1234, verbose=1)
#>
#> Running the Gibbs sampler. It may be long, please keep cool :)
#>
#> **********:10.0%
#> **********:20.0%
#> **********:30.0%
#> **********:40.0%
#> **********:50.0%
#> **********:60.0%
#> **********:70.0%
#> **********:80.0%
#> **********:90.0%
#> **********:100.0%
# Calcul of residual correlation between species
enviro.cors <- get_enviro_cor(mod)
```