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:
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
andd = 1, \dots, D
, generateX_{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})
, wherec = -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
, andc3
are clusters performed using k-medoids algorithm withpamk
.
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.
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.