gtsmb {HMB}

Generalized Two-Staged Model-Based estmation

Description

Generalized Two-Staged Model-Based estmation

Usage

gtsmb(y_S, X_S, X_Sa, Z_Sa, Z_U, Omega_S, Phis_Sa)

Arguments

y_S

Response object that can be coersed into a column vector. The _S denotes that y is part of the sample S, with N_S \le N_{Sa} \le N_U.

X_S

Object of predictors variables that can be coersed into a matrix. The rows of X_S correspond to the rows of y_S.

X_Sa

Object of predictor variables that can be coresed into a matrix. The set Sa is the intermediate sample.

Z_Sa

Object of predictor variables that can be coresed into a matrix. The set Sa is the intermediate sample, and the Z-variables often some sort of auxilairy, inexpensive data. The rows of Z_Sa correspond to the rows of X_Sa

Z_U

Object of predictor variables that can be coresed into a matrix. The set U is the universal population sample.

Omega_S

The covariance structure of \boldsymbol{\epsilon}_{S}, up to a constant.

Phis_Sa

A 3D array, where the third dimension corresponds to the covariance structure of E(\boldsymbol{\xi}_{k,Sa} \boldsymbol{\xi}_{j,Sa}^T), in the order k=1, \ldots, p, j=1, \ldots k. For p = 3, the order (k,j) will thus be (1,1), (2,1), (2,2), (3,1), (3,2), (3,3).

Details

The GTSMB assumes the superpopulations

y = \boldsymbol{x} \boldsymbol{\beta} + \epsilon

x_k = \boldsymbol{z} \boldsymbol{\gamma}_k + \xi_k

\epsilon \perp \xi_k

For a sample from the superpopulation, the GTSMB assumes

E(\boldsymbol{\epsilon}) = \mathbf{0}, E(\boldsymbol{\epsilon} \boldsymbol{\epsilon}^T) = \omega^2 \boldsymbol{\Omega}

E(\boldsymbol{\xi}_k) = \mathbf{0}, E(\boldsymbol{\xi}_k \boldsymbol{\xi}_j^T) = \theta_{\Phi,k,j}^2 \boldsymbol{\Phi}_{k,j}, \theta_{\Phi,k,j}^2 \boldsymbol{\Phi}_{k,j} = \theta_{\Phi,j,k}^2 \boldsymbol{\Phi}_{j,k}

Value

A fitted object of class HMB.

References

Holm, S., Nelson, R. & Ståhl, G. (2017) Hybrid three-phase estimators for large-area forest inventory using ground plots, airborne lidar, and space lidar. Remote Sensing of Environment, 197, 85–97.

Saarela, S., Holm, S., Healey, S.P., Andersen, H.-E., Petersson, H., Prentius, W., Patterson, P.L., Næsset, E., Gregoire, T.G. & Ståhl, G. (2018). Generalized Hierarchical Model-Based Estimation for Aboveground Biomass Assessment Using GEDI and Landsat Data, Remote Sensing, 10(11), 1832.

See Also

summary, getSpec.

Examples

pop_U   = sample(nrow(HMB_data), 20000)
pop_Sa  = sample(pop_U, 500)
pop_S   = sample(pop_U, 100)

y_S     = HMB_data[pop_S, "GSV"]
X_S     = HMB_data[pop_S, c("hMAX", "h80", "CRR")]
X_Sa    = HMB_data[pop_Sa, c("hMAX", "h80", "CRR")]
Z_Sa    = HMB_data[pop_Sa, c("B20", "B30", "B50")]
Z_U     = HMB_data[pop_U, c("B20", "B30", "B50")]

Omega_S = diag(1, nrow(X_S))
Phis_Sa = array(0, c(nrow(X_Sa), nrow(X_Sa), ncol(X_Sa) * (ncol(X_Sa) + 1) / 2))
Phis_Sa[, , 1] = diag(1, nrow(X_Sa)) # Phi(1,1)
Phis_Sa[, , 2] = diag(1, nrow(X_Sa)) # Phi(2,1)
Phis_Sa[, , 3] = diag(1, nrow(X_Sa)) # Phi(2,2)
Phis_Sa[, , 4] = diag(1, nrow(X_Sa)) # Phi(3,1)
Phis_Sa[, , 5] = diag(1, nrow(X_Sa)) # Phi(3,2)
Phis_Sa[, , 6] = diag(1, nrow(X_Sa)) # Phi(3,3)

gtsmb_model = gtsmb(y_S, X_S, X_Sa, Z_Sa, Z_U, Omega_S, Phis_Sa)
gtsmb_model