Dataset to simulate ratio benchmarking of Multivariate non sampled area in Fay-Herriot model
This data is generated based on multivariate Fay-Herriot model by these following steps:
Generate explanatory variables X1 and X2. X1 ~ N(10, 1) and X2 ~ U(9.5, 10.5).
Cluster is generated discrete uniform distribution with a = 1 and b = 2.
Sampling error e is generated with the following \(\sigma_{e11}\) = 0.01, \(\sigma_{e22}\) = 0.02, \(\sigma_{e33}\) = 0.03, and \(\rho_{e}\) = 1/2.
For random effect u, we set \(\sigma_{u11}\)= 0.02, \(\sigma_{u22}\)= 0.03, and \(\sigma_{u33}\)= 0.04.
For the weight, we generate w1, w2, w3 by set w1, w2, w3 ~ U(10, 20)
Set beta, \(\beta01\) = 10, \(\beta02\) = 8, \(\beta03\) = 6, \(\beta11\) = -0.3, \(\beta12\) = 0.2, \(\beta13\) = 0.4, \(\beta21\) = 0.5, \(\beta22\) = -0.1, and \(\beta23\) = -0.2.
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, weight w1 w2 w3, and sampling varians covarians v1 v12 v13 v2 v23 v3 in a dataframe then named as datamsaeRB
datamsaeRBnsA data frame with 30 rows and 17 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
Cluster for Y1
Cluster for Y2
Cluster for Y3