FayHerriot: area-level EBLUP
\(\theta_d = x_d'\beta + \gamma_d (y_d - x_d'\beta)\),
\(\gamma_d = A / (A + D_d)\), with known sampling variances vardir;
\(A\) by Fisher scoring from median(vardir) ("REML",
"ML" or the "FH" moment equation), truncated at 0, stopping
at relative change tol; MSE \(g_1 + g_2 + 2 g_3\) (Prasad-Rao;
ML and FH add the Datta-Lahiri and Datta-Rao-Smith bias terms), as
sae::eblupFH and mseFH. BhfEblup: unit-level
nested-error EBLUP of area means,
\(f_d \bar y_d + (\bar X_d - f_d \bar x_d)'\beta + (1 - f_d) u_d\),
variance components by REML or ML from the analytic profile score in
\(\log(\sigma_u^2 / \sigma_e^2)\) (bisection; a non-positive score at
the lower end gives \(\sigma_u^2 = 0\)), as sae::eblupBHF.
Identical to the Python arm morie.fn.smallarea (Fay and Herriot
1979; Battese, Harter and Fuller 1988; Datta, Rao and Smith 2005).
Usage
FayHerriot(y, X, vardir, method = "REML", maxiter = 100L, tol = 1e-10)
BhfEblup(y, X, area, xbar_pop, areas = NULL, popsize = NULL, method = "REML")Arguments
- y
Direct estimates (
FayHerriot) or unit responses.- X
Design matrix including the intercept column.
- vardir
Sampling variances.
- method
"REML","ML"or (FayHerriot)"FH".- maxiter
Maximum scoring iterations.
- tol
Relative convergence tolerance.
- area
Area label of every unit.
- xbar_pop
Matrix of population means, one row per area.
- areas
Area labels in the row order of
xbar_pop.- popsize
Population sizes (sampling fraction 0 when
NULL).
References
Fay, R. E. and Herriot, R. A. (1979). Estimates of income for small places: an application of James-Stein procedures to census data. Journal of the American Statistical Association 74, 269-277.
Battese, G. E., Harter, R. M. and Fuller, W. A. (1988). An error-components model for prediction of county crop areas using survey and satellite data. Journal of the American Statistical Association 83, 28-36.
Datta, G. S., Rao, J. N. K. and Smith, D. D. (2005). On measuring the variability of small area estimators under a basic area level model. Biometrika 92, 183-196.