datasaem.ns {sae.prop}R Documentation

Data generated based on Multivariate Fay Herriot Model with Additive Logistic Transformation with Non-Sampled Cases

Description

This data is generated based on multivariate Fay-Herriot model and then transformed by using inverse Additive Logistic Transformation (alr). Then some domain would be edited to be non-sampled. The steps are as follows:

  1. Set these following variables:

    • q=4q = 4

    • r1=r2=r3=2,r=6r_{1} = r_{2} = r_{3} = 2, r = 6

    • β1=(β11,β12)=(1,1),β2=(β21,β22)=(1,1),β3=(β31,β32)=(1,1)\beta_{1} = (\beta_{11}, \beta_{12})' = (1, 1)', \beta_{2} = (\beta_{21}, \beta_{22})' = (1, 1)', \beta_{3} = (\beta_{31}, \beta_{32})' = (1, 1)'

    • μx1=μx2=μx3\mu_{x1} = \mu_{x2} = \mu_{x3} and σx11=1,σx22=3/2,σx33=2\sigma_{x11} = 1, \sigma_{x22} = 3/2, \sigma_{x33} = 2

    • for k=1,2,,q1k = 1, 2, \dots, q -1 and d=1,,Dd = 1, \dots, D, generate Xd=diag(xd1,xd2,xd3)(q1)×rX_{d} = diag(x_{d1}, x_{d2}, x_{d3})_{(q-1) \times r}, where:

      • xd1=(xd11,xd11)x_{d1} = (x_{d11}, x_{d11})

      • xd1=(xd21,xd22)x_{d1} = (x_{d21}, x_{d22})

      • xd1=(xd31,xd31)x_{d1} = (x_{d31}, x_{d31})

      • xd11=xd21=xd31=1x_{d11} = x_{d21} = x_{d31} = 1

      • UdkU(0,1)U_{dk} \sim U(0, 1)

      • xd12=μx1+σx111/2Ud1x_{d12} = \mu_{x1} + \sigma_{x11}^{1/2}U_{d1}

      • xd22=μx2+σx221/2Ud2x_{d22} = \mu_{x2} + \sigma_{x22}^{1/2}U_{d2}

      • xd32=μx3+σx331/2Ud3x_{d32} = \mu_{x3} + \sigma_{x33}^{1/2}U_{d3}

  2. For random effects uu, udNq1(0,Vud)u_{d} \sim N_{q-1}(0, V_{ud}), where θ1=1,θ2=3/2,θ3=2,θ4=1/2,θ5=1/2,θ6=0\theta_{1} = 1, \theta_{2} = 3/2, \theta_{3} = 2, \theta_{4} = -1/2, \theta_{5} = -1/2, \theta_{6} = 0

  3. For sampling errors ee, edNq1(0,Ved)e_{d} \sim N_{q-1}(0, V_{ed}), where c=1/4c = -1/4

  4. The generated data is transformed using inverse alr transformation, so the data will be within the range of proportion.

  5. Domain 3, 15, and 25 are set to be examples of non-sampled cases (0, 1, or NA).

  6. c1c1, c2c2, and c3c3 are clusters performed using k-medoids algorithm with pamk.

Auxiliary variables X1,X2,X3X_{1}, X_{2}, X_{3}, direct estimation Y1,Y2,Y3Y_{1}, Y_{2}, Y_{3}, sampling variance-covariance v1,v2,v3,v12,v13,v23v_{1}, v_{2}, v_{3}, v_{12}, v_{13}, v_{23}, and cluster c1,c2,c3c1, c2, c3 are combined into a data frame called datasaem.ns. For more details about the structure of covariance matrix, it is available in supplementary materials of Reference.

Usage

datasaem.ns

Format

A data frame with 30 rows and 15 columns:

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

X3

Auxiliary variable of X3

v1

Sampling Variance of Y1

v2

Sampling Variance of Y2

v3

Sampling Variance of Y3

v12

Sampling Covariance of Y1 and Y2

v13

Sampling Covariance of Y1 and Y3

v23

Sampling Covariance of Y2 and Y3

c1

Cluster of Y1

c2

Cluster of Y2

c3

Cluster of Y3

Reference

Esteban, M. D., Lombardía, M. J., López-Vizcaíno, E., Morales, D., & Pérez, A. (2020). Small area estimation of proportions under area-level compositional mixed models. Test, 29(3), 793–818. https://doi.org/10.1007/s11749-019-00688-w.


[Package sae.prop version 0.1.2 Index]