sae.fay_herriot

Fit a Fay-Herriot area-level small-area model — an Empirical Best Linear Unbiased Predictor (EBLUP) — with Fisher scoring. The target is a direct (design-based) area estimate; vardir is its known sampling variance. Writes the fitted model, which sae.fay_herriot_mse turns into per-area estimates and MSE without refitting, together with the coefficient table and goodness-of-fit statistics. Fails if the model does not converge. Use sae.all_subsets_fh instead to choose the predictors from a larger candidate pool.

Name the model with a formula (estimate ~ B20 + B25 + B30 + 0), or with a target and a features column selector.

Kind: standard
Network: no

Inputs🔗

Name	Type	Description
`data`	file (Parquet or CSV)	One row per area, with the target, predictor and sampling-variance columns.
`vardir`	string	Name of the column holding each area's sampling variance.
`formula`	string	Model formula, e.g. `estimate ~ B20 + B25 + B30 + 0`. Use instead of `target` and `features`.
`target`	string	The direct-estimate column (when no formula is given).
`features`	string	Column selector for the predictors (when no formula is given): names, globs and exclusions, e.g. `B20,B25,B30` or `B*,-B5`.
`intercept`	boolean	Include an intercept when building from `target` and `features`. Default `false`, matching the paper's `~ ... + 0` models.
`id_columns`	string	Column selector for identifier columns, never used as predictors. Default empty.
`categorical`	string	Column selector for numeric-coded predictors to treat as categorical. Default empty.
`na_action`	string	`fail` (default) or `drop`: what to do with an area that has a missing value in a model column.
`method`	string	Variance estimation method - one of `REML` (default), `ML`, or `FH`.
`max_iter`	number	Maximum Fisher-scoring iterations. Default `1000`.

Outputs🔗

Name	Type	Description
`model`	file (SpadeModel)	The fitted model (family `fay_herriot`): coefficients, their covariance, the between-area variance and its asymptotic variance and bias.
`coefficients`	file (CSV)	One row per design column: `term`, `estimate`, `std_error`, `statistic`, `p_value`.
`fit`	json	Areas used and dropped, the arguments that shaped the fit, and `metrics`: `refvar` (between-area variance), `loglike`, `aic`, `bic`, `iterations`.

Example🔗

- id: "@fit"
  name: sae.fay_herriot
  inputs:
    - "@long_data"
  args:
    target: "estimate"
    features: "B20,B25,B30"
    vardir: "var_of_estimate"
    method: "REML"