Computes the partial responses curves of joint probability of CWM traits as a function of a focal variable. The regions in which joint probabilities are computed are specified by bounds. In order to build the response curve, the function builds a dataframe where the focal variable varies along a gradient and the other (non-focal) variables are fixed to their mean (but see FixX parameter for fixing non-focal variables to user-defined values). Then, uses joint_trait_prob to compute the joint probability in these dataset.

joint_trait_prob_gradient(
m,
indexTrait,
bounds,
grid.length = 200,
XFocal = NULL,
FixX = NULL,
FullPost = FALSE,
samples = NULL,
parallel = FALSE
)

## Arguments

m

A model fitted with jtdm_fit

indexTrait

A vector of the names (as specified in the column names of Y) of the two (or more!) traits we want to compute the joint probabilities of.

The name (as specified in the column names of X) of the focal variable.

bounds

The parameter to specify a region in the community-trait space where the function computes the joint probabilities of traits. It is a list of the length of "indexTrait", each element of the list is a vector of length two. The vector represents the inferior and superior bounds of the region for the specified trait. For example, if we consider two traits, bounds=list(c(10,Inf),c(10,Inf)) corresponds to the region in the community-trait space where both traits both take values greater than 10.

grid.length

The number of points along the gradient of the focal variable. Default to 200.

XFocal

Optional. A gradient of the focal variable provided by the user. If provided, the function will used this gradient instead of building a regular one. Default to NULL.

FixX

Optional. A parameter to specify the value to which non-focal variables are fixed. This can be useful for example if we have some categorical variables (e.g. forest vs meadows) and we want to obtain the partial response curve for a given value of the variable. It has to be a list of the length and names of the columns of X. For example, if the columns of X are "MAT","MAP","Habitat" and we want to fix "Habitat" to 1, then FixX=list(MAT=NULL,MAP=NULL,Habitat=1.). Default to NULL.

FullPost

If FullPost = TRUE, the function returns samples from the predictive distribution of joint probabilities, thus allowing the computation of credible intervals. If FullPost= FALSE, joint probabilities are computed only using the posterior mean of the parameters. FullPost cannot be equal to "mean" here.

samples

Optional, default to NULL, only works when FullPost=FALSE. Defines the number of samples to compute the posterior distribution of joint probabilities. Needs to be between 1 the total number of samples drawn from the posterior distribution.

parallel

Optional, only works when FullPost = TRUE. When TRUE, the function uses mclapply to parallelise the calculation of the posterior distribution joint probabilities.

## Value

A list containing:

Sample from the posterior distribution of the joint probability along the gradient. It is a vector whose length is the number of posterior samples. NULL if FullPost=FALSE.

Posterior mean of the joint probability along the gradient.

97.5% and 0.25% posterior quantiles of the joint probability along the gradient. NULL if FullPost=FALSE.

The gradient of the focal variable built by the function.

## Details

This function is time consuming when FullPost = TRUE. Consider setting parallel = TRUE and/or to set samples to a value smaller than the total number of posterior samples.

## Examples

data(Y)
data(X)
# We sample only few samples from the posterior in order to reduce
# the computational time of the examples.
# Increase the number of samples to obtain robust results
m = jtdm_fit(Y = Y, X = X, formula = as.formula("~GDD+FDD+forest"),  sample = 10)
# Compute probability of SLA and LNC to be joint-high at sites in the studies

# Compute the joint probability of SLA and LNC
# to be joint-high along the GDD gradient