tsmb {HMB}

Two-staged Model-Based estmation

Description

Two-staged Model-Based estmation

Usage

tsmb(y_S, X_S, X_Sa, Z_Sa, Z_U)

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.

Details

The TSMB assumes the superpopulations

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

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

\epsilon \perp \xi_k

For a sample from the superpopulation, the TSMB assumes

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

E(\boldsymbol{\xi}_k) = \mathbf{0}, E(\boldsymbol{\xi}_k \boldsymbol{\xi}_j^T) = \phi_{k,j}^2 \mathbf{I}

Value

A fitted object of class HMB.

References

Saarela, S., Holm, S., Grafström, A., Schnell, S., Næsset, E., Gregoire, T.G., Nelson, R.F. & Ståhl, G. (2016). Hierarchical model-based inference for forest inventory utilizing three sources of information. Annals of Forest Science, 73(4), 895-910.

See Also

summary, getSpec.

Examples

pop_U  = sample(nrow(HMB_data), 20000)
pop_Sa = sample(pop_U, 5000)
pop_S  = sample(pop_U, 300)

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

tsmb_model = tsmb(y_S, X_S, X_Sa, Z_Sa, Z_U)
tsmb_model