Dataset to simulate ratio benchmarking of Multivariate 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)`

.

Sampling error`e`

is generated with the following*σe11*= 0.01,*σe22*= 0.02,*σe33*= 0.03, and*ρe*= 1/2.

For random effect`u`

, we set*σu11*= 0.02,*σu22*= 0.03, and*σu33*= 0.04.

For the weight, we generate`w1, w2, w3`

by set w1, w2, w3 ~ U(10, 20)

Set beta,*β01*= 10,*β02*= 8,*β03*= 6,*β11*= -0.3,*β12*= 0.2,*β13*= 0.4,*β21*= 0.5,*β22*= -0.1, and*β23*= -0.2.

Calculate direct estimation`Y1 Y2 Y3`

where*Yi*=*Xβ+ui+ei*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

1 |

A data frame with 30 rows and 14 variables:

- Y1
Direct Estimation of Y1

- Y2
Direct Estimation of Y2

- Y3
Direct Estimation of Y3

- X1
Auxiliary variable of X1

- X2
Auxiliary variable of X2

- w1
Known proportion of units in small areas of Y1

- w2
Known proportion of units in small areas of Y2

- w3
Known proportion of units in small areas of Y3

- v1
Sampling Variance of Y1

- v12
Sampling Covariance of Y1 and Y2

- v13
Sampling Covariance of Y1 and Y3

- v2
Sampling Variance of Y2

- v23
Sampling Covariance of Y2 and Y3

- v3
Sampling Variance of Y3

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