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)

## Arguments

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.

## Value

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.

## Details

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).

## References

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.

cov2cor get_residual_cor jSDM-package jSDM_binomial_probit
jSDM_binomial_logit jSDM_poisson_log

## Author

Jeanne Clément <jeanne.clement16@laposte.net>

## Examples

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 :)
#>
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# Calcul of residual correlation between species
enviro.cors <- get_enviro_cor(mod)