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# This function helps the "two phase" estimator function when the first phase sample size goes to infinity.
# This corresponds to the situation where wall2wall info is known for post-stratification
# The external and g-weight variances are calulated
# INPUTS:
# formula = model formula
# data = data.frame
# exhaustive = the vector of auxiliary variable means known exhaustively (should ideally be weighted mean adjusted for proportion of pixels in interpretation are in the forest)
#
# OUTPUTS:
# estimate = point estimate
# ext_variance = external variance
# g_variance = g-weight variance
# n1 = Inf
# n2 = sample size
# r.squared = R squared of model
global_exhaustive2p <- function(formula, data, exhaustive){
model.object <- lm(formula, data=data, x=TRUE, y=TRUE)
design_matrix.s2 <- model.object$x
n1 <- Inf
n2 <- nrow(design_matrix.s2)
As2inv <- solve( t(design_matrix.s2)%*%design_matrix.s2/n2 )
g <- exhaustive %*% As2inv %*% t(design_matrix.s2)
resid <- model.object$residuals
estimate <- mean(g*model.object$y)
ext_variance <- var(resid)/n2
g_variance <- (1/n2^2)*sum((g^2)*(resid^2))
## ------- create outputs ------------------------------------------------- ##
# summarize sample size info:
samplesizes<- data.frame(cbind (n1, n2))
colnames(samplesizes)<- c("n1", "n2")
rownames(samplesizes)<- "plots"
estimation<- data.frame(estimate=estimate, ext_variance=ext_variance, g_variance=g_variance,
n1=samplesizes$n1, n2=samplesizes$n2, r.squared=summary(model.object)$r.squared)
# ... to store inputs used:
inputs<- list()
inputs[["data"]]<- data
inputs[["formula"]]<- formula
inputs[["boundary_weights"]]<- NA
inputs[["method"]]<- "exhaustive"
inputs[["cluster"]]<- FALSE
inputs[["exhaustive"]]<- TRUE
# save warning-messages:
warn.messages<- NA
result<- list(input=inputs,
estimation=estimation,
samplesizes=samplesizes,
coefficients=coef(model.object),
cov_coef=NA,
Z_bar_1=NA,
cov_Z_bar_1G=NA,
Rc_x_hat=resid,
mean_Rc_x_hat=mean(resid),
warn.messages=warn.messages)
class(result)<- c("global", "twophase")
return(result)
}
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