Agriculture Reference
In-Depth Information
$fit$method
[1] "REML"
$fit$convergence
[1] TRUE
$fit$iterations
[1] 7
$fit$estcoef
beta std.error tvalue pvalue
auxFH 1.957471 0.04275585 45.78253 0
$fit$refvar
[1] 21.73859
$fit$goodness
loglike AIC BIC
-28.39482 60.78965 61.18409
The command lines for the MSE estimates of the EBLUP estimates are as follows.
> domFH < - mseFH(yobs ~ auxFH - 1, vardir¼var, data¼datFH)
> domFH$mse
[1] 15.6488295 12.9263352 18.0321732 15.1425798 0.6581343 13.8323691
12.4330856 18.5129038 14.9496946
Note that in the function eblupFH, the default option is method¼"REML".
If we want to use the ML estimator, the option is method¼"ML". Furthermore, it
is worth noting that the direct estimate obtained using the survey package (i.e.,
yobs) is used as an object of the function. Finally, we have used a model without
intercepts because we consider it more appropriate for this study (i.e., yobs ~
auxFH - 1).
The following produces a graph that compares the estimate of the variance of the
direct estimator with the MSE estimate of the EBLUP estimator (see Fig. 11.2 ).
> plot(datFH$var,domFH$mse,axes ¼ T,cex ¼ 0.5,pch ¼ 19,xlab ¼ "Variance
Direct", ylab ¼ "MSE EBLUP", xlim ¼ c(0,34),ylim ¼ c(0,20))
> abline(a ¼ 0, b ¼ 1)
In this section, we have provided details about the EBLUP estimator using the
basic area level model. For EBLUP under the unit level model see Rao ( 2003 ).
However, we now also present an agricultural case study concerning small area
model at the unit level, based on the data set used by Battese et al. ( 1988 , see Sect.
11.3.2).
The data set is provided in the sae package. It concerns survey and satellite
data for corn and soy beans in 12 Iowa counties, obtained from the 1978 June
Enumerative Survey of the US Department of Agriculture and from land observa-
tory satellites (LANDSAT) during the 1978 growing season. The preliminary
instructions are as follows.
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