ghmb: Generalized Hierarchical Model-Based estimation method

In HMB: Hierarchical Model-Based Estimation Approach

Description

Generalized Hierarchical Model-Based estimation method

Usage

ghmb(y_S, X_S, X_Sa, Z_Sa, Z_U, Omega_S, Sigma_Sa)

Arguments

y_S	Response object that can be coerced into a column vector. The _S denotes that y is part of the sample S, with N_S ≤ N_Sa ≤ N_U.
X_S	Object of predictors variables that can be coerced into a matrix. The rows of X_S correspond to the rows of y_S.
X_Sa	Object of predictor variables that can be coerced into a matrix. The set Sa is the intermediate sample.
Z_Sa	Object of predictor variables that can be coerced 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 coerced into a matrix. The set U is the universal population sample.
Omega_S	The covariance structure of ε_S, up to a constant.
Sigma_Sa	The covariance structure of u_Sa, up to a constant.

Details

The GHMB assumes two models

y = x β + ε

x β = z α + u

ε indep. u

For a sample from the superpopulation, the GHMB assumes

E(ε) = 0, E(ε ε') = ω^2 Ω

E(u) = 0, E(u u') = σ^2 Σ

Value

A fitted object of class HMB.

References

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, 2500)
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")]

Omega_S  = diag(1, nrow(X_S))
Sigma_Sa = diag(1, nrow(Z_Sa))

ghmb_model = ghmb(
  y_S, X_S, X_Sa, Z_Sa, Z_U, Omega_S, Sigma_Sa)
ghmb_model

Example output

Attaching package: ‘HMB’

The following object is masked from ‘package:base’:

    summary

Estimated population mean: 103.3294 
Estimated variance: 9.860915 

HMB documentation built on July 8, 2020, 7:34 p.m.