Create prior object for jsdmstan models and data simulation

This function creates all of the potential priors used within a jsdmstan model and can be used as the input to all stan_jsdm() family of functions and the jsdm_sim_data() functions.

Usage

jsdm_prior(
  sigmas_preds = "normal(0,1)",
  z_preds = "normal(0,1)",
  cor_preds = "lkj_corr(1)",
  betas = "normal(0,1)",
  a = "normal(0,1)",
  a_bar = "normal(0,1)",
  sigma_a = "normal(0,1)",
  sigmas_species = "normal(0,1)",
  z_species = "normal(0,1)",
  cor_species = "lkj_corr(1)",
  cor_species_chol = "lkj_corr_cholesky(1)",
  LV = "normal(0,1)",
  L = "normal(0,1)",
  sigma_L = "normal(0,1)",
  sigma = "normal(0,1)",
  kappa = "normal(0,1)",
  zi = "beta(1,1)",
  zi_betas = "normal(0,1)",
  shp_betas = "normal(0,1)"
)

# S3 method for class 'jsdmprior'
print(x, ...)

Arguments

sigmas_preds: The standard deviation of the covariate effects, constrained to be positive (default standard normal)
z_preds: The covariate effects (default standard normal)
cor_preds: The correlation matrix on the covariate effects (npred by npred correlation matrix) (default "lkj_corr(1)")
betas: If covariate effects are unstructured, the prior on the covariate effects
a: The site level intercepts (default standard normal)
a_bar: The mean site level intercept
sigma_a: The standard deviation of the site level intercepts, constrained to be positive and default prior is half standard normal
sigmas_species: For MGLMM method, the standard deviations of the species covariances, constrained to be positive (default half standard normal)
z_species: For MGLMM method, the S by N matrix of species covariance by site (default standard normal)
cor_species: For MGLMM method (data simulation only), the correlation between species as the nspecies by nspecies correlation matrix (default "lkj_corr(1)")
cor_species_chol: For MGLMM method (model fit only), the correlation between species represented as a Cholesky decomposition of the nspecies by nspecies correlation matrix (default "lkj_corr_cholesky(1)"). Note that lkj_corr_cholesky(eta) is the cholesky decomposition of lkj_corr(eta)
LV: For GLLVM method, the per site latent variable loadings (default standard normal)
L: For GLLVM method, the non-zero species latent variable loadings (default standard normal)
sigma_L: For GLLVM method, the variance of the species loadings, constrained to be positive (default standard normal)
sigma: For Gaussian response, the standard deviation parameter. Constrained to be positive (default standard normal)
kappa: For negative binomial response, the negative binomial variance parameter. Constrained to be positive (default standard normal)
zi: For zero-inflated poisson or negative binomial with no environmental covariate effects upon the zero-inflation, the proportion of inflated zeros (default beta distribution with both alpha and beta parameters set to 1).
zi_betas: For zero-inflated poisson or negative binomial with environmental effects upon the zero-inflation, the covariate effects on the zero-inflation on the logit scale
shp_betas: For gaussian or negative binomial with environmental effects upon the family parameter (i.e. sigma or kappa), the covariate effects on the family parameter on the log scale
x: Object of class jsdmprior
...: Currently unused

Value

An object of class "jsdmprior" taking the form of a named list

Details

Each prior has to be specified as a character string corresponding to the appropriate stan command. The most common versions of these are supported by the simulated data functions, however there are functions that can be fed to the stan fitting procedure that will not be able to be used as input for jsdm_sim_data(). Parameters sigmas_preds, sigma_a, sigmas_species, sigma_L, sigma, and kappa are fixed to be positive only in the stan code and this cannot be changed. Parameters cor_preds and cor_species are assumed to be the Cholesky factor of a correlation matrix. All other parameters are real numbers. For all parameters that represent vectors or matrices the prior has to be the same across the entire vector or matrix (note that for the species latent variable loadings in a GLLVM model the prior is set on the non-zero matrix components L and not on the entire matrix).

Prior distributions supported by jsdm_sim_data() are "normal(mean, sd)", "student_t(df, mu, sigma)", "cauchy(location, scale)", "gamma(shape, scale)", "inv_gamma(shape, scale)" and "lkj_corr_cholesky(eta)".

Functions

print(jsdmprior): Print method for object of class jsdmprior

Examples

pr <- jsdm_prior(kappa = "gamma(0.01,0.01)")
pr
#>           Parameter             Group      Constraint                Prior
#> 1      sigmas_preds covariate_effects         lower=0          normal(0,1)
#> 2           z_preds covariate_effects            none          normal(0,1)
#> 3         cor_preds covariate_effects            none          lkj_corr(1)
#> 4             betas covariate_effects            none          normal(0,1)
#> 5                 a    site_intercept            none          normal(0,1)
#> 6             a_bar    site_intercept            none          normal(0,1)
#> 7           sigma_a    site_intercept         lower=0          normal(0,1)
#> 8    sigmas_species             mglmm         lower=0          normal(0,1)
#> 9         z_species             mglmm            none          normal(0,1)
#> 10      cor_species             mglmm            none          lkj_corr(1)
#> 11 cor_species_chol             mglmm            none lkj_corr_cholesky(1)
#> 12               LV             gllvm            none          normal(0,1)
#> 13                L             gllvm            none          normal(0,1)
#> 14          sigma_L             gllvm         lower=0          normal(0,1)
#> 15            sigma          gaussian         lower=0          normal(0,1)
#> 16            kappa      neg_binomial         lower=0     gamma(0.01,0.01)
#> 17               zi    zero_inflation lower=0,upper=1            beta(1,1)
#> 18         zi_betas    zero_inflation            none          normal(0,1)
#> 19        shp_betas            family            none          normal(0,1)