Diagnostic checks for the latent Gaussianity assumption in R-INLA

Computes the BF sensitivity measures \(s_0(\mathbf{y})\) and \(I_0(\mathbf{y})\) of the non-Gaussianity parameter at the base Gaussian model: \( \log \pi(\eta|\mathbf{y}) \propto (s_0(\mathbf{y}) - \theta_\eta)\eta - \frac{I_0(\mathbf{y})}{2} \eta^2 + \mathcal{O}(\eta^2)\), where \(\theta_\eta\) is the rate parameter of the exponential PC prior on \(\eta\).

Usage

ng.check(
  fit,
  Dfunc = NULL,
  h = NULL,
  selection = NULL,
  compute.I0 = FALSE,
  compute.predictor = FALSE,
  compute.fixed = TRUE,
  compute.random = FALSE,
  plot = TRUE
)

Arguments

fit: The inla object that fits the LGM.
Dfunc: Function that receives as input the hyperparameter vector \(\boldsymbol{\theta}\) in internal scale and the output is \(\mathbf{D}(\boldsymbol{\theta})\), where \(\mathbf{D}\) is the dependency matrix that specifies the non-Gaussian latent field. If there is more than one latent component to be extended to non-Gaussianity, this should be a list of functions \(\mathbf{D}_i(\boldsymbol{\theta})\), where \(\mathbf{D}_i(\boldsymbol{\theta})\) is the dependency matrix that specifies component i.
h: Predefined constant \(\mathbf{h}\) vector that contains the distance between locations or area of the basis functions. For models defined in discrete space this should be a vector of ones. If there is more than one latent component to be extended to non-Gaussianity, this should be a list of vectors \(\mathbf{h_i}\) where \(\mathbf{h_i}\) is the predefined constant vector of component i.
selection: List which specifies which model components of the LGM are to be extended to non-Gaussianity. Same syntax as the argument selection of the function inla.posterior.sample.
compute.I0: Boolean. If TRUE compute \(I_0(\mathbf{y}, \hat{\boldsymbol{\gamma}})\) (asymptotic variance of the reference distribution) and p-value.
compute.predictor: Boolean. If TRUE computes the sensitivity measures for each predictor: \(\partial_\eta E[z_i|\mathbf{y},\eta]\), where \(z_i\) is the i\(^th\) element of the linear predictor
compute.fixed: Boolean. If TRUE computes the sensitivity measures for each fixed effect. \(\partial_\eta E[z_i|\mathbf{y},\eta]\), where \(z_i\) is the i\(^th\) fixed effect
plot: Boolean. Generate diagnostic plots.

Value

A list that for each model component in selection returns:

BF.check The BF sensitivities \(s_0(\mathbf{y})\) and \(s_0(\mathbf{y}, \hat{\boldsymbol{\gamma}})\), where \(\hat{\boldsymbol{\gamma}}\) is the posterior mode of the hyperparameters. The variance of the reference distribution for LGMS with Gaussian response is also shown.
BF.index The contribution of each index to the overall BF sensitivity.
sens.fixed.matrix Sensitivity matrix, containing \(\partial_{\eta_i}E[z_j|\mathbf{y},\eta_i]\), where \(z_j\) is the j\(^th\) fixed effect and \(\eta_i\) is the non-Gaussianity parameter of the i\(^th\) random effect
sens.fixed.matrix Sensitivity matrix, containing \(\partial_{\eta_i}E[z_j|\mathbf{y},\eta_i]\), where \(z_j\) is the j\(^th\) index of the linear predictor and \(\eta_i\) is the non-Gaussianity parameter of the j\(^th\) random effect.

If plot = TRUE, the BF sensitivities \(d_i(\mathbf{y})\) for each index are shown, and also the BF sensitivity at the observed data \(s_0(\mathbf{y}, \hat{\boldsymbol{\gamma}})\) is compared to \(s_0(\mathbf{y}^\text{pred}, \hat{\boldsymbol{\gamma}}) \sim N(0,\eqn{I_0(\mathbf{y}), \hat{\boldsymbol{\gamma}}})\). For

Examples

if (FALSE) {
 #Here we fit an RW1 latent process to the jumpts time series
 plot(jumpts)

 #Fit LGM with INLA
 LGM     <- inla(y ~ -1 + f(x,  model = "rw1"),
                 data = jumpts,
                 control.compute = list(config = TRUE))

 #Fit LnGM with ngvb
 check.list <- ng.check(fit = LGM)
 }