# Variance estimation of the sample surveys in domain by the ultimate cluster method

### Description

Computes the variance estimation of the sample surveys in domain by the ultimate cluster method.

### Usage

1 2 3 4 5 6 7 8 9 10 |

### Arguments

`Y` |
Variables of interest. Object convertible to |

`H` |
The unit stratum variable. One dimensional object convertible to one-column |

`PSU` |
Primary sampling unit variable. One dimensional object convertible to one-column |

`w_final` |
Weight variable. One dimensional object convertible to one-column |

`id` |
Optional variable for unit ID codes. One dimensional object convertible to one-column |

`Dom` |
Optional variables used to define population domains. If supplied, variables of interest are calculated for each domain. An object convertible to |

`period` |
Optional variable for survey period. If supplied, residual estimation of calibration is done independently for each time period. One dimensional object convertible to one-column |

`PSU_sort` |
optional; if PSU_sort is defined, then variance is calculated for systematic sample. |

`N_h` |
optional data object convertible to |

`fh_zero` |
by default FALSE; fh is calculated as division of n_h and N_h in each strata, if true, fh value is zero in each strata. |

`PSU_level` |
by default TRUE; if PSU_level is true, in each strata fh is calculated as division of count of PSU in sample (n_h) and count of PSU in frame(N_h). if PSU_level is false, in each strata fh is calculated as division of count of units in sample (n_h) and count of units in frame(N_h), which calculated as sum of weights. |

`Z` |
Optional variables of denominator for ratio estimation. Object convertible to |

`X` |
Optional matrix of the auxiliary variables for the calibration estimator. Object convertible to |

`ind_gr` |
Optional variable by which divided independently X matrix of the auxiliary variables for the calibration. One dimensional object convertible to one-column |

`g` |
Optional variable of the g weights. One dimensional object convertible to one-column |

`q` |
Variable of the positive values accounting for heteroscedasticity. One dimensional object convertible to one-column |

`dataset` |
Optional survey data object convertible to |

`confidence` |
Optional positive value for confidence interval. This variable by default is 0.95. |

`percentratio` |
Positive numeric value. All linearized variables are multiplied with |

`outp_lin` |
Logical value. If |

`outp_res` |
Logical value. If |

### Details

Calculate variance estimation in domains based on book of Hansen, Hurwitz and Madow.

### Value

A list with objects is returned by the function:

`lin_out` |
A |

`res_out` |
A |

`all_result` |
A |

### References

Morris H. Hansen, William N. Hurwitz, William G. Madow, (1953), Sample survey methods and theory Volume I Methods and applications, 257-258, Wiley.

Guillaume Osier and Emilio Di Meglio. The linearisation approach implemented by Eurostat for the first wave of EU-SILC: what could be done from the second wave onwards? 2012

Guillaume Osier, Yves Berger, Tim Goedeme, (2013), Standard error estimation for the EU-SILC indicators of poverty and social exclusion, Eurostat Methodologies and Working papers, URL http://ec.europa.eu/eurostat/documents/3888793/5855973/KS-RA-13-024-EN.PDF.

Eurostat Methodologies and Working papers, Handbook on precision requirements and variance estimation for ESS household surveys, 2013, URL http://ec.europa.eu/eurostat/documents/3859598/5927001/KS-RA-13-029-EN.PDF.

Yves G. Berger, Tim Goedeme, Guillame Osier (2013). Handbook on standard error estimation and other related sampling issues in EU-SILC, URL https://ec.europa.eu/eurostat/cros/content/handbook-standard-error-estimation-and-other-related-sampling-issues-ver-29072013_en

Jean-Claude Deville (1999). Variance estimation for complex statistics and estimators: linearization and residual techniques. Survey Methodology, 25, 193-203, URL http://www5.statcan.gc.ca/bsolc/olc-cel/olc-cel?lang=eng&catno=12-001-X19990024882.

### See Also

`domain`

, `lin.ratio`

, `residual_est`

,
`vardomh`

, `var_srs`

, `variance_est`

,
`variance_othstr`

### Examples

1 2 3 4 5 6 7 8 9 | ```
data(eusilc)
dataset <- data.table(IDd=1:nrow(eusilc), eusilc)
aa <- vardom(Y="eqIncome", H="db040", PSU="db030",
w_final="rb050", id="rb030", Dom = "db040",
period = NULL, N_h = NULL, Z = NULL,
X = NULL, g = NULL, q = NULL, dataset = dataset,
confidence = .95, percentratio = 100,
outp_lin = TRUE, outp_res = TRUE)
``` |

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