Package {midasINLA}

Compute posterior summaries of MIDAS coefficients

Description

Computes posterior summaries of the MIDAS regression coefficients from a fitted spatial MIDAS model returned by fit_Minla_spatial(). The output depends on whether the MIDAS coefficient is spatially varying and on the specified spatial prior.

Usage

compute_beta_spatial(model, n_loc)

Arguments

Details

For spatially varying coefficients with an ICAR prior, the function returns summaries and marginal distributions for the global coefficient, the location-specific spatial deviations, and the resulting location-specific total coefficients. Posterior samples of the total coefficients are also returned.

For spatially varying coefficients with an IID prior, the function returns posterior summaries and marginal distributions for the location-specific coefficients.

For non-spatially varying coefficients, the function returns the posterior marginal distribution and summary of the MIDAS coefficient associated with each high-frequency covariate.

Value

A list containing one element for each high-frequency MIDAS covariate in model$hf_input. The elements are named "hf_index_1", "hf_index_2", and so on. The contents of each element depend on the spatial structure of the corresponding MIDAS covariate:

Spatially varying coefficient with ICAR prior

A list containing summary.global.beta, marginal.global.beta, summary.icar.beta, marginal.icar.beta, summary.total.beta, and sample.total.beta.

Spatially varying coefficient with IID prior

A list containing summary.beta and marginal.beta.

Non-spatially varying coefficient

A list containing summary.beta and marginal.beta.

The summary data frames contain the posterior mean, standard deviation, and 2.5%, 50%, and 97.5% posterior quantiles.

Examples

if (requireNamespace("INLA", quietly = TRUE)) {
  INLA::inla.setOption(num.threads = 1)

  data(data_spatialpoisson_example)

  # Read the spatial adjacency graph
  g <- INLA::inla.read.graph(
    filename = system.file("map.adj", package = "midasINLA")
  )

  # Prepare a spatial MIDAS predictor
  Midas_x1 <- prepare_Minla_spatial(
    x = data_spatialpoisson_example$data_x1$x1,
    loc_x = data_spatialpoisson_example$data_x1$loc,
    constraint = "hyperbolic",
    K = 0:29,
    m = 30,
    svc = TRUE,
    svc_prior = "icar",
    g = g
  )

  # Fit the spatial Poisson MIDAS model
  fit <- fit_Minla_spatial(
    formula = y ~ 1,
    data = data_spatialpoisson_example$data_y,
    loc_var = "loc",
    time_var = "Time",
    family = "poisson",
    hf_input = list(Midas_x1),
    inla_options = list(
      verbose = FALSE,
      control.predictor = list(
        compute = TRUE,
        link = 1
      )
    )
  )

  # Compute posterior summaries of the MIDAS coefficients
  beta_summary <- compute_beta_spatial(
    model = fit,
    n_loc = 16
  )

  # Inspect summaries of the location-specific total coefficients
  beta_summary$hf_index_1$summary.total.beta
}

Compute posterior estimates of MIDAS lag weights

Description

Computes posterior estimates of the normalized MIDAS lag weights from a fitted MIDAS model returned by fit_Minla_spatial(). The function draws samples from the posterior marginal distributions of the MIDAS hyperparameters and uses these samples to obtain the corresponding lag-weight functions.

Usage

compute_weights(model, n.samples = 200)

Arguments

Details

The supported MIDAS lag constraints are "hyperbolic", "gaussian", "beta1", "beta2", and "almon2". For each high-frequency covariate, the resulting weights are normalized to sum to one across all included lags.

Value

A list containing one data frame for each high-frequency covariate in model$hf_input. The elements are named "hf_1", "hf_2", and so on. Each data frame contains:

lag

The MIDAS lag index.

mean

The posterior mean of the normalized lag weight.

q2.5

The 2.5% posterior quantile of the lag weight.

q97.5

The 97.5% posterior quantile of the lag weight.

Examples

if (requireNamespace("INLA", quietly = TRUE)) {
  data(data_spatialpoisson_example)

  g <- INLA::inla.read.graph(
    filename = system.file("map.adj", package = "midasINLA")
  )

  Midas_x1 <- prepare_Minla_spatial(
    x = data_spatialpoisson_example$data_x1$x1,
    loc_x = data_spatialpoisson_example$data_x1$loc,
    constraint = "hyperbolic",
    K = 0:29,
    m = 30,
    svc = TRUE,
    svc_prior = "icar",
    g = g
  )

  fit <- fit_Minla_spatial(
    formula = y ~ 1,
    data = data_spatialpoisson_example$data_y,
    loc_var = "loc",
    time_var = "Time",
    family = "poisson",
    hf_input = list(Midas_x1),
    inla_options = list(
      verbose = FALSE,
      control.predictor = list(
        compute = TRUE,
        link = 1
      )
    )
  )

  weights <- compute_weights(
    model = fit,
    n.samples = 200
  )

  head(weights$hf_1)
}

Example MIDAS dataset

Description

This dataset contains simulated high-frequency covariates and a binomial response constructed using MIDAS lag weights.

Usage

data_binomial_example

Format

A list with the following components:

x1

Numeric vector of high-frequency covariate 1

x2

Numeric vector of high-frequency covariate 2

y

Integer vector of binomial response counts

p

Underlying success probabilities

Ntrials

Number of trials for each observation

weights1

Lag weights used in the MIDAS structure for covariate 1

weights2

Lag weights used in the MIDAS structure for covariate 2

beta0

True value of intercept \beta_0

beta1

True value of \beta_1

beta2

True value of \beta_2

beta3

True value of \beta_3

Details

Simulated dataset generated using a binomial sampling model

The dataset is generated using two covariates. The first one has a hyperbolic weighting scheme with parameter gamma = 0.9 and lag length 13. The second one has gaussian weighting scheme with parameters mu = 8, sigma = 7, and lag length of 20.

Source

Simulated data

Example MIDAS dataset

Description

This dataset contains simulated high-frequency covariates and a poisson response constructed using MIDAS lag weights.

Usage

data_spatialpoisson_example

Format

A list with the following components:

data_x1

High-frequency covariate 1 data frame

data_x2

High-frequency covariate 2 data frame

data_y

Response data frame

weights1

Lag weights used in the MIDAS structure for covariate 1

weights2

Lag weights used in the MIDAS structure for covariate 2

eta

Linear predictor log lambda

beta0

True value of intercept \beta_0

beta1

True value of \beta_1

beta2

True value of \beta_2

icar

Vector of region-specific deviations from \beta_1

tau

Precision parameter of the ICAR model

Details

Simulated dataset generated using a spatial poisson sampling model

The dataset is generated using two covariates. The first one has a hyperbolic weighting scheme with parameter gamma = 0.9 and lag length 29. The second one has Gaussian constraint with parameters mu = 10 and sigma = 12.

Source

Simulated data

Fit a spatial MIDAS model using INLA

Description

Fits a Mixed Data Sampling (MIDAS) regression model with optional spatially varying coefficients using Integrated Nested Laplace Approximation (INLA). High-frequency covariates are supplied as MIDAS objects created by prepare_Minla_spatial().

Usage

fit_Minla_spatial(
  formula,
  data,
  loc_var,
  time_var,
  family,
  hf_input = NULL,
  Ntrials = NULL,
  E = NULL,
  inla_options = list()
)

Arguments

Details

The function constructs the INLA model by incorporating the MIDAS components specified in hf_input. Multiple high-frequency covariates can be included by supplying multiple MIDAS objects in hf_input.

Value

A list containing:

formula_final

The final INLA model formula, including the MIDAS components.

data_final

The response data used for model fitting after ordering by location and time and removing rows with incomplete lagged covariate information.

rm_max

The maximum number of initial observations removed across locations because of incomplete MIDAS lagged covariates.

res

The fitted INLA model returned by INLA::inla().

hf_input

The list of MIDAS objects supplied through hf_input.

Examples

if (requireNamespace("INLA", quietly = TRUE)) {
  data(data_spatialpoisson_example)

  # Read the spatial adjacency graph
  g <- INLA::inla.read.graph(
    filename = system.file("map.adj", package = "midasINLA")
  )

  # Prepare a spatial MIDAS predictor
  Midas_x1 <- prepare_Minla_spatial(
    x = data_spatialpoisson_example$data_x1$x1,
    loc_x = data_spatialpoisson_example$data_x1$loc,
    constraint = "hyperbolic",
    K = 0:29,
    m = 30,
    svc = TRUE,
    svc_prior = "icar",
    g = g
  )

  # Fit the spatial Poisson MIDAS model
  fit <- fit_Minla_spatial(
    formula = y ~ 1,
    data = data_spatialpoisson_example$data_y,
    loc_var = "loc",
    time_var = "Time",
    family = "poisson",
    hf_input = list(Midas_x1),
    inla_options = list(
      verbose = FALSE,
      control.predictor = list(
        compute = TRUE,
        link = 1
      )
    )
  )

  # Inspect the fitted INLA model
  fit$res
}

Generate posterior predictive samples from a MIDAS model

Description

Generates posterior predictive samples from a fitted MIDAS model using posterior samples of the latent linear predictor. The function supports Gaussian, Poisson, and binomial response distributions.

Usage

predict_midas(model, family = "gaussian", Ntrials = NULL, nsamples = 1000)

Arguments

Details

For a Gaussian response, posterior samples of the observation variance are obtained from the posterior samples of the Gaussian precision parameter and used to generate predictive observations. For Poisson and binomial responses, observations are generated using the appropriate inverse-link function.

Value

A list with two components:

computed_y

A list containing posterior predictive summaries:

mean

Posterior predictive mean for each observation.

sd

Posterior predictive standard deviation for each observation.

q2.5

2.5% posterior predictive quantile for each observation.

q97.5

97.5% posterior predictive quantile for each observation.

samples

A list containing posterior samples of the latent predictor and, for Gaussian responses, the posterior samples of the observation variance.

Examples

if (requireNamespace("INLA", quietly = TRUE)) {
  data(data_spatialpoisson_example)

  Midas_x1 <- prepare_Minla_spatial(
    x = data_spatialpoisson_example$data_x1$x1,
    loc_x = data_spatialpoisson_example$data_x1$loc,
    constraint = "hyperbolic",
    K = 0:29,
    m = 30,
    svc = FALSE
  )

  fit <- fit_Minla_spatial(
    formula = y ~ 1,
    data = data_spatialpoisson_example$data_y,
    loc_var = "loc",
    time_var = "Time",
    family = "poisson",
    hf_input = list(Midas_x1),
    inla_options = list(verbose = FALSE)
  )

  predictions <- predict_midas(
    model = fit,
    family = "poisson",
    nsamples = 1000
  )

  # Inspect posterior predictive summaries
  head(predictions$computed_y$mean)
  head(predictions$computed_y$q2.5)
  head(predictions$computed_y$q97.5)
}

Prepare a spatial MIDAS object for INLA estimation

Description

Constructs the MIDAS design matrix and associated model specifications for use with fit_Minla_spatial(). The function creates lagged high-frequency covariate values for each location and optionally specifies a spatially varying coefficient (SVC) component.

Usage

prepare_Minla_spatial(
  x,
  loc_x,
  constraint,
  K,
  m,
  svc = FALSE,
  svc_prior = "iid",
  g = NULL
)

Arguments

Value

A list containing the MIDAS design matrix and model specifications. The returned object includes:

X_matrix

The MIDAS design matrix, including a location index.

constraint

The MIDAS constraint used for the lag-response association.

lag_k

The maximum lag specified in K.

K

The vector of lags used to construct the design matrix.

m

The number of high-frequency observations associated with each response observation.

rm.row

The number of initial rows removed from each location because of incomplete lagged observations.

svc

Whether a spatially varying coefficient component is specified.

svc_prior

The prior specified for the spatially varying coefficient component.

g

The INLA graph object, included when svc_prior = "icar".

Examples

if (requireNamespace("INLA", quietly = TRUE)) {
  data(data_spatialpoisson_example)

  # Prepare a MIDAS object using a hyperbolic lag constraint
  # and a spatially varying coefficient with an ICAR prior.
  g <- INLA::inla.read.graph(
    filename = system.file("map.adj", package = "midasINLA")
  )

  Midas_x1 <- prepare_Minla_spatial(
    x = data_spatialpoisson_example$data_x1$x1,
    loc_x = data_spatialpoisson_example$data_x1$loc,
    constraint = "hyperbolic",
    K = 0:29,
    m = 30,
    svc = TRUE,
    svc_prior = "icar",
    g = g
  )

  # Inspect the resulting MIDAS design matrix
  head(Midas_x1$X_matrix)
}