# Variance estimation for sample surveys in domain for two stage surveys by the ultimate cluster method

### Description

Computes the variance estimation in domain for ID_level1.

### Usage

1 2 3 4 5 6 7 8 9 10 | ```
vardomh(Y, H, PSU, w_final, ID_level1,
ID_level2 = NULL, Dom = NULL, period = NULL,
N_h = NULL, PSU_sort = NULL,
fh_zero = FALSE, PSU_level = TRUE,
Z = NULL, dataset = NULL,
X = NULL, periodX = NULL, X_ID_level1 = NULL,
ind_gr = NULL, g = NULL, q = NULL,
datasetX = NULL, confidence = .95,
percentratio = 1, outp_lin = FALSE,
outp_res = FALSE)
``` |

### 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_level1` |
Variable for level1 ID codes. One dimensional object convertible to one-column |

`ID_level2` |
Optional variable for unit ID codes. One dimensional object convertible to one-column |

`period` |
Optional variable for the survey periods. If supplied, the values for each period are computed independently. Object convertible to |

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

`N_h` |
optional data object convertible to |

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

`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 |

`dataset` |
Optional survey data object convertible to |

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

`periodX` |
Optional variable of the survey periods. If supplied, residual estimation of calibration is done independently for each time period. Object convertible to |

`X_ID_level1` |
Variable for level1 ID codes. One dimensional object convertible to one-column |

`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 |

`datasetX` |
Optional survey data object in level1 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 for household surveys based on book of Hansen, Hurwitz and Madow.

### Value

A list with objects are 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`

,
`var_srs`

, `variance_est`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 | ```
data(eusilc)
dataset <- data.table(IDd = 1 : nrow(eusilc), eusilc)
aa <- vardomh(Y = "eqIncome", H = "db040", PSU = "db030",
w_final = "rb050", ID_level1 = "db030",
ID_level2 = "rb030", Dom = "db040", period = NULL,
N_h = NULL, Z = NULL, dataset = dataset, X = NULL,
X_ID_level1 = NULL, g = NULL, q = NULL,
datasetX = NULL, confidence = 0.95, percentratio = 1,
outp_lin = TRUE, outp_res = TRUE)
## Not run:
dataset2 <- copy(dataset)
dataset$period <- 1
dataset2$period <- 2
dataset <- data.table(rbind(dataset, dataset2))
# by default without using fh_zero (finite population correction)
aa2 <- vardomh(Y = "eqIncome", H = "db040", PSU = "db030",
w_final = "rb050", ID_level1 = "db030",
ID_level2 = "rb030", Dom = "db040", period = "period",
N_h = NULL, Z = NULL, dataset = dataset,
X = NULL, X_ID_level1 = NULL,
g = NULL, q = NULL, datasetX = NULL,
confidence = .95, percentratio = 1,
outp_lin = TRUE, outp_res = TRUE)
aa2
# without using fh_zero (finite population correction)
aa3 <- vardomh(Y = "eqIncome", H = "db040", PSU = "db030",
w_final = "rb050", ID_level1 = "db030",
ID_level2 = "rb030", Dom = "db040",
period = "period", N_h = NULL, fh_zero=FALSE,
Z = NULL, dataset = dataset, X = NULL,
X_ID_level1 = NULL, g = NULL, q = NULL,
datasetX = NULL, confidence = .95,
percentratio = 1, outp_lin = TRUE,
outp_res = TRUE)
aa3
# with using fh_zero (finite population correction)
aa4 <- vardomh(Y="eqIncome", H="db040", PSU="db030", w_final="rb050",
ID_level1="db030", ID_level2="rb030", Dom = "db040",
period = "period", N_h = NULL, fh_zero=TRUE,
Z = NULL, dataset = dataset,
X = NULL, X_ID_level1 = NULL,
g = NULL, q = NULL, datasetX = NULL,
confidence = .95, percentratio = 1,
outp_lin = TRUE, outp_res = TRUE)
aa4
## End(Not run)
``` |