Predict the Latent Factors of a spifa Model

Predicts the latent factors of (spatial) item factor analysis for new subjects/locations and/or for new predictor values, using the posterior samples from a fitted spifa model.

Usage

# S3 method for class 'spifa'
predict(object, newdata = NULL, burnin = 0, thin = 1, joint = FALSE, ...)

Arguments

object: A fitted spifa object, as returned by spifa.
newdata: New data to predict at, mirroring spifa's own data argument: an sf/sfc object (for spatial, i.e. spifa/spifa_pred, models – its geometry gives the new locations, and its CRS is used directly, so it need not match the training data's CRS) or a plain data frame (for cifa_pred), with columns matching the predictors used on the right-hand side of formula when the model was fitted. Its design matrix is built the same way spifa built the training one, using the same terms and factor levels. For a spatial model, its geometry may also be POLYGON/MULTIPOLYGON (e.g. a prediction grid): the centroid of each cell is used for the spatial kernel, but the original polygons are kept (see Value) so plot_predict can draw them as a filled map instead of points.
burnin: Number of initial (post-fitting) iterations to discard before using the posterior samples for prediction.
thin: Thinning interval applied to the posterior samples used for prediction.
joint: Logical; for spatial models (spifa/spifa_pred), whether the posterior predictive draws should respect the full predictive covariance across new locations and factors (TRUE), or be drawn marginally/independently per location-factor combination (FALSE, the default, cheaper). Each draw still propagates posterior parameter uncertainty (one draw per retained MCMC iteration) either way – this only controls whether, within a single draw, the values across new locations/factors are jointly correlated as the model implies. Marginal draws are fine for per-location summaries (e.g. means, credible intervals computed independently per column); set TRUE when the samples themselves will be used as input to another model or computation that depends on their joint structure (e.g. a spatial contrast or aggregate across new locations). Ignored for cifa_pred, whose draws are already jointly correct across factors.
...: Further arguments (currently unused).

Value

A draws_array of posterior predictive samples of the latent abilities (theta) for the requested new locations and/or predictor values (or, if no prediction was requested, for the originally observed subjects). For a spatial model, the locations used (newdata, or the training locations if newdata was omitted) are attached as the "newdata" attribute, so plot_predict can map the result without needing it supplied again.

Details

If the fitted model has no spatial or predictor structure (eifa or cifa), or if newdata is not supplied for a model that has one, there is nothing to predict beyond the latent abilities' own posterior samples already available from the fit, so those are returned directly (subject to burnin/thin) – this case is fast, since no new sampling is needed. Otherwise, new draws are sampled for the new locations and/or predictor values, which takes longer.

If the fitted model has predictors (cifa_pred/spifa_pred), newdata must include those predictor columns, the same as predict.lm and similar methods require – this is an error otherwise. There's no synthesized reference-level fallback for missing predictors (e.g. an sf/sfc object holding only new locations, with no predictor columns at all): for a factor predictor under the no-intercept encoding spifa uses, an automatically-filled all-zero row wouldn't correspond to any real category, so any reference profile – including all zeros for numeric predictors – must be supplied explicitly in newdata, matching the original data's format.

Author

Erick A. Chacón-Montalván

Examples

# \donttest{
library(sf)
data(ipixuna)

nitems <- ncol(ipixuna$items)
nfactors <- 3
A <- matrix(1, nitems, nfactors)
A[c(4, 8), 1] <- 0
A[c(2, 4, 5, 6, 7, 8, 10), 2] <- 0
A[c(5, 6), 3] <- 0

# Spifa model
samples <- spifa(items ~ 1, data = ipixuna, nfactors = nfactors, niter = 5,
  constraints = list(discrimination = A))
# latent abilities for observed locations
predict(samples)
#> # A draws_array: 5 iterations, 1 chains, and 300 variables
#> , , variable = Theta[1,1]
#> 
#>          chain
#> iteration     1
#>         1 -1.38
#>         2 -1.58
#>         3 -1.50
#>         4 -0.81
#>         5 -0.68
#> 
#> , , variable = Theta[2,1]
#> 
#>          chain
#> iteration     1
#>         1  1.64
#>         2  1.30
#>         3  0.92
#>         4  0.54
#>         5 -0.22
#> 
#> , , variable = Theta[3,1]
#> 
#>          chain
#> iteration     1
#>         1 -0.40
#>         2  1.11
#>         3 -0.13
#>         4  0.89
#>         5  0.88
#> 
#> , , variable = Theta[4,1]
#> 
#>          chain
#> iteration      1
#>         1  0.351
#>         2 -1.323
#>         3  0.018
#>         4 -0.514
#>         5  0.427
#> 
#> # ... with 296 more variables
# latent abilities for new locations
newdata <- st_make_grid(ipixuna, n = c(3, 2), what = "centers")
predict(samples, newdata = newdata)
#> # A draws_array: 5 iterations, 1 chains, and 18 variables
#> , , variable = Theta[1,1]
#> 
#>          chain
#> iteration      1
#>         1  0.572
#>         2  0.239
#>         3 -0.843
#>         4 -0.588
#>         5 -0.051
#> 
#> , , variable = Theta[2,1]
#> 
#>          chain
#> iteration      1
#>         1 -0.063
#>         2 -0.823
#>         3 -0.645
#>         4 -0.652
#>         5 -0.647
#> 
#> , , variable = Theta[3,1]
#> 
#>          chain
#> iteration     1
#>         1  0.69
#>         2  0.84
#>         3 -0.61
#>         4 -1.01
#>         5 -0.58
#> 
#> , , variable = Theta[4,1]
#> 
#>          chain
#> iteration      1
#>         1  0.636
#>         2  0.062
#>         3 -0.158
#>         4 -1.590
#>         5 -1.195
#> 
#> # ... with 14 more variables

# Spifa model with predictors
samples_pred <- spifa(items ~ wealth, data = ipixuna, nfactors = nfactors, niter = 5,
  constraints = list(discrimination = A))
newdata_pred <- st_sf(wealth = rnorm(6), geometry = newdata)
predict(samples_pred, newdata = newdata_pred)
#> # A draws_array: 5 iterations, 1 chains, and 18 variables
#> , , variable = Theta[1,1]
#> 
#>          chain
#> iteration      1
#>         1  0.387
#>         2 -0.019
#>         3  2.848
#>         4 -0.752
#>         5  0.905
#> 
#> , , variable = Theta[2,1]
#> 
#>          chain
#> iteration     1
#>         1  0.27
#>         2 -1.04
#>         3  0.38
#>         4  1.84
#>         5  0.29
#> 
#> , , variable = Theta[3,1]
#> 
#>          chain
#> iteration     1
#>         1 -1.36
#>         2 -0.48
#>         3  0.98
#>         4 -1.66
#>         5 -0.28
#> 
#> , , variable = Theta[4,1]
#> 
#>          chain
#> iteration     1
#>         1 -0.30
#>         2 -0.25
#>         3 -0.64
#>         4  2.64
#>         5  0.22
#> 
#> # ... with 14 more variables
# }