hmb {HMB}

Hierarchical Model-Based estmation

Description

Hierarchical Model-Based estmation

Usage

hmb(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 HMB assumes two models

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

\boldsymbol{x} \boldsymbol{\beta} = \boldsymbol{z} \boldsymbol{\alpha} + u

\epsilon \perp u

For a sample from the superpopulation, the HMB assumes

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

E(\boldsymbol{u}) = \mathbf{0}, E(\boldsymbol{u} \boldsymbol{u}^T) = \sigma^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.

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, 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")]

hmb_model = hmb(y_S, X_S, X_Sa, Z_Sa, Z_U)
hmb_model