datasaem.ns | R Documentation |
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:
Set these following variables:
q = 4
r_{1} = r_{2} = r_{3} = 2, r = 6
\beta_{1} = (\beta_{11}, \beta_{12})' = (1, 1)', \beta_{2} = (\beta_{21}, \beta_{22})' = (1, 1)', \beta_{3} = (\beta_{31}, \beta_{32})' = (1, 1)'
\mu_{x1} = \mu_{x2} = \mu_{x3}
and \sigma_{x11} = 1, \sigma_{x22} = 3/2, \sigma_{x33} = 2
for k = 1, 2, \dots, q -1
and d = 1, \dots, D
, generate X_{d} = diag(x_{d1}, x_{d2}, x_{d3})_{(q-1) \times r}
, where:
x_{d1} = (x_{d11}, x_{d11})
x_{d1} = (x_{d21}, x_{d22})
x_{d1} = (x_{d31}, x_{d31})
x_{d11} = x_{d21} = x_{d31} = 1
U_{dk} \sim U(0, 1)
x_{d12} = \mu_{x1} + \sigma_{x11}^{1/2}U_{d1}
x_{d22} = \mu_{x2} + \sigma_{x22}^{1/2}U_{d2}
x_{d32} = \mu_{x3} + \sigma_{x33}^{1/2}U_{d3}
For random effects u
, u_{d} \sim N_{q-1}(0, V_{ud})
, where \theta_{1} = 1, \theta_{2} = 3/2, \theta_{3} = 2, \theta_{4} = -1/2, \theta_{5} = -1/2, \theta_{6} = 0
For sampling errors e
, e_{d} \sim N_{q-1}(0, V_{ed})
, where c = -1/4
The generated data is transformed using inverse alr transformation, so the data will be within the range of proportion.
Domain 3, 15, and 25 are set to be examples of non-sampled cases (0, 1, or NA).
c1
, c2
, and c3
are clusters performed using k-medoids algorithm with pamk
.
Auxiliary variables X_{1}, X_{2}, X_{3}
, direct estimation Y_{1}, Y_{2}, Y_{3}
, sampling variance-covariance v_{1}, v_{2}, v_{3}, v_{12}, v_{13}, v_{23}
, and cluster c1, 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.
datasaem.ns
A data frame with 30 rows and 15 columns:
Direct Estimation of Y1
Direct Estimation of Y2
Direct Estimation of Y3
Auxiliary variable of X1
Auxiliary variable of X2
Auxiliary variable of X3
Sampling Variance of Y1
Sampling Variance of Y2
Sampling Variance of Y3
Sampling Covariance of Y1 and Y2
Sampling Covariance of Y1 and Y3
Sampling Covariance of Y2 and Y3
Cluster of Y1
Cluster of Y2
Cluster of Y3
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.
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