datasae1 {msae}

Data generated based on Multivariate Fay Herriot Model (Model 1)

Description

This data is generated based on multivariate Fay-Herriot model (model 1) by these following steps:

1. Generate sampling error e, random effect u, and auxiliary variables X1 X2.

   • For sampling error e, we set e_{d} ~ N_{3}(0, V_{ed}) , where V_{ed} = (\sigma_{dij})_{i,j=1,2,3}, with \sigma_{11} ~ InvGamma(11, 1), \sigma_{22} ~ InvGamma(11, 2), \sigma_{33} ~ InvGamma(11, 3), and \rho_{e} = 0.5.

   • For random effect u, we set u ~ N_{3}(0, V_{u}) , where \sigma_{u11} = 0.2 , \sigma_{u22} = 0.4 , and \sigma_{u33} = 1.2.

   • For auxiliary variables X1 and X2, we set X1 ~ N(5, 0.1) and X2 ~ N(10, 0.2).

2. Calculate direct estimation Y1 Y2 and Y3 , where Y_{i} = X * \beta + u_{i} + e_{i}. We take \beta_{1} = 5 and \beta_{2} = 10.

Auxiliary variables X1 X2, direct estimation Y1 Y2 Y3, and sampling variance-covariance v1 v2 v3 v12 v13 v23 are combined into a dataframe called datasae1.

Usage

datasae1

Format

A data frame with 50 rows and 11 variables:

X1

Auxiliary variable of X1

X2

Auxiliary variable of X2

Y1

Direct Estimation of Y1

Y2

Direct Estimation of Y2

Y3

Direct Estimation 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

Reference

Benavent, Roberto & Morales, Domingo. (2015). Multivariate Fay-Herriot models for small area estimation. Computational Statistics & Data Analysis. 100. 372-390. DOI: 10.1016/j.csda.2015.07.013.