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Fit Semiparametric Spatiotemporal Model with Mixed Frequencies

Source: R/semiparMF.R
semiparMF.Rd

Fits a spatiotemporal model where the response variable is observed at a lower frequency (e.g., quarterly) than a non-parametric covariate (e.g., monthly). The model combines a non-parametric component for the high-frequency predictor, parametric components for low-frequency predictors and spatial neighborhood effects, and an autoregressive error structure.

Usage

semiparMF(
  formula,
  data_sf,
  high_freq_data,
  time_col,
  id_col,
  w_matrix = NULL,
  ...
)

Arguments

formula

A formula object (e.g., Y ~ Z). The left-hand side is the response variable (low frequency). The first predictor on the right-hand side is the parametric covariate ($Z$) measured at the same frequency.

data_sf

An sf object containing the panel data in long format. Must contain columns for the response, the parametric covariate, the time index, and the location ID.

high_freq_data

A numeric array of dimensions (N x T x K), where:

  • N: Number of unique spatial locations (must match data_sf).

  • T: Number of time points (must match data_sf).

  • K: The frequency ratio (e.g., 3 if predictor is monthly and response is quarterly).

time_col

Character string. The name of the column in data_sf representing the time index.

id_col

Character string. The name of the column in data_sf representing the location ID.

w_matrix

Optional numeric matrix (N x T). A pre-calculated spatial weight or neighborhood variable. If NULL (default), a spatial lag of the variable $Z$ is calculated using Queen Contiguity weights.

...

Additional arguments passed to the internal backfitting function (e.g., max_iter, tol, spar).

Value

An object of class semiparMF containing:

coefficients

A list of estimated parameters: beta (parametric covariate effect), gamma (neighborhood effect), and rho (autoregressive parameter).

nonparam

A list containing the fitted smoothing spline and the aggregated non-parametric component f_hat.

residuals

Matrix (N x T) of model residuals.

fitted.values

Matrix (N x T) of the fitted values (structural part only).

dims

Dimensions of the data (N, T).

meta

Metadata containing location IDs and time indices.

history

Convergence history (MSPE per iteration).

call

The function call.

References

Malabanan, V. A., Lansangan, J. R. G., & Barrios, E. B. (2022). Semiparametric Spatiotemporal Model with Mixed Frequencies: With Application in Crop Forecasting. Science & Engineering Journal, 15(2), 90-107.

Examples

# Simulate data using the package's included simulation function
sim <- simulate_semipar_data(n_side = 4, t_len = 20, k = 3, rho_error = 0.5)

# Fit the model
fit <- semiparMF(
  formula = Y ~ Z, 
  data_sf = sim$data, 
  high_freq_data = sim$X_high,
  time_col = "time_id", 
  id_col = "location_id"
)
#> Calculating spatial weights (Queen Contiguity)...

# Inspect results
summary(fit)
#> 
#> -- Model Summary --
#> Call:
#> semiparMF(formula = Y ~ Z, data_sf = sim$data, high_freq_data = sim$X_high, 
#>     time_col = "time_id", id_col = "location_id")
#> 
#> Coefficients:
#>   Beta (Parametric):    0.4805 
#>   Gamma (Spatial):      -0.02814 
#>   Rho (Temporal):       0.01043 
#> 
#> Residuals:
#>       Min.    1st Qu.     Median       Mean    3rd Qu.       Max. 
#> -6.9374035 -1.6515231 -0.1171669  0.0000537  1.5207869 10.1848119 
#> 
#> Convergence:
#>   Iterations:  5 
#>   Final MSPE:  6.249991