Dataset to simulate difference benchmarking of Multivariate Fay Herriot model
This data is generated base on multivariate Fay Herriot model by these following steps:
Generate explanatory variables X1 and X2
. Take \(\mu_{X1}\) = \(\mu_{X1}\) = 10, \(\sigma_{X11}\)=1, \(\sigma_{X2}\)=2, and \(\rho_{x}\)= 1/2.
Sampling error e
is generated with the following \(\sigma_{e11}\) = 0.15, \(\sigma_{e22}\) = 0.25, \(\sigma_{e33}\) = 0.35, and \(\rho_{e}\) = 1/2.
For random effect u
, we set \(\sigma_{u11}\)= 0.2, \(\sigma_{u22}\)= 0.6, and \(\sigma_{u33}\)= 1.8.
For the weight we generate w1 w2 w3
by set the w1 ~ U(25,30)
, w2 ~ U(25,30)
, w3 ~ U(25,30)
Calculate direct estimation Y1 Y2 Y3
where \(Y_{i}\) = \(X * \beta + u_{i} + e_{i}\)
Then combine the direct estimations Y1 Y2 Y3
, explanatory variables X1 X2
, weights w1 w2 w3
, and sampling varians covarians v1 v12 v13 v2 v23 v3
in a dataframe then named as datamsaeDB
datamsaeDB
A data frame with 30 rows and 14 variables:
Direct Estimation of Y1
Direct Estimation of Y2
Direct Estimation of Y3
Auxiliary variable of X1
Auxiliary variable of X2
Known proportion of units in small areas of Y1
Known proportion of units in small areas of Y2
Known proportion of units in small areas of Y3
Sampling Variance of Y1
Sampling Covariance of Y1 and Y2
Sampling Covariance of Y1 and Y3
Sampling Variance of Y2
Sampling Covariance of Y2 and Y3
Sampling Variance of Y3