# Linearization of the median income of individuals below the At Risk of Poverty Threshold

### Description

Estimation of the median income of individuals below At Risk of Poverty Threshold and computation of linearized variable for variance estimation. The At Risk of Poverty Threshold is estimated for the whole population always. The median income is estimated for the whole population or for each domain.

### Usage

1 2 3 4 |

### Arguments

`Y` |
Study variable (for example equalized disposable income). One dimensional object convertible to one-column |

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

`weight` |
Optional weight variable. One dimensional object convertible to one-column |

`sort` |
Optional variable to be used as tie-breaker for sorting. One dimensional object convertible to one-column |

`Dom` |
Optional variables used to define population domains. If supplied, linearization of the median income of persons below a poverty threshold is done for each domain. An object convertible to |

`period` |
Optional variable for survey period. If supplied, linearization of the median income of persons below a poverty threshold is done for each time period. Object convertible to |

`dataset` |
Optional survey data object convertible to |

`percentage` |
A numeric value in range
For example, to compute poverty threshold equal to 60% of some income quantile, |

`order_quant` |
A numeric value in range
For example, to compute poverty threshold equal to some percentage of median income, |

`var_name` |
A character specifying the name of the linearized variable. |

### Value

A list with two objects are returned by the function:

`value` |
A |

`lin` |
A |

### References

Working group on Statistics on Income and Living Conditions (2004) Common cross-sectional EU indicators
based on EU-SILC; the gender pay gap. *EU-SILC 131-rev/04*, Eurostat.

Guillaume Osier (2009). Variance estimation for complex indicators of poverty and inequality. *Journal of the European Survey Research Association*, Vol.3, No.3, pp. 167-195, ISSN 1864-3361, URL http://ojs.ub.uni-konstanz.de/srm/article/view/369.

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

`linarpt`

, `linrmpg`

, `varpoord`

, `vardcrospoor`

, `vardchangespoor`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | ```
data(eusilc)
dati=data.table(IDd=1:nrow(eusilc),eusilc)
# Full population
d <- linpoormed(Y = "eqIncome", id = "IDd",
weight = "rb050", Dom = NULL,
dataset = dati, percentage = 60,
order_quant = 50)
## Not run:
# Domains by location of houshold
dd <- linpoormed(Y = "eqIncome", id = "IDd",
weight = "rb050", Dom = "db040",
dataset = dati, percentage = 60,
order_quant = 50)
## End(Not run)
``` |