# decompGEI: Decomposition by Groups for GEI In IC2: Inequality and Concentration Indices and Curves

## Description

Decomposes by population subgroups a generalized entropy inequality measure within a vector.

## Usage

 `1` ```decompGEI(x, z, w = NULL, alpha = 1, ELMO = TRUE) ```

## Arguments

 `x` Numeric vector with non-negative values (strictly positive when `alpha`=0 or `alpha`=1). `z` Factor who determines the subgroups. `w` Numeric vector of sampling weigths (optional). `alpha` Parameter of the generalized entropy index. Theil index (TT) is calculated for `alpha`=1, the mean log deviation (TL) for `alpha`=0. `ELMO` When `ELMO` is `TRUE`, a "maximum" between-group inequality index is estimated using the Elbers and alii method (2005).

## Value

A list of class `"ICI"` with components:

 `ineq` a list with components `GEI` (value of inequality index) and `alpha` (value of parameter). `decomp` a list with components `within` (value of within-group inequality), `between` (value of between-group inequality) and, if `ELMO` is `TRUE`, `betweenELMO` (value of maximum between-group inequality). `intra` a list with components `GEIGroups` (the subgroup values of inequality index) and `contribGEIGroups` (the contribution of each subgroup to the total within-groups inequality). `ws` a list with components `wIntra` (the subgroup weights) and `sIntra` (the subgroup shares of `x`). `nas` a list with `NA` counts, including components `xNA`, `zNA`, `wNA` and `totalNA`.

## References

Cowell F.A. (2000) Measurement of Inequality. In Atkinson A.B., Bourguignon F. (Eds.) Handbook of Income Distribution. Elsevier, Vol. 1, pp. 87-166.

Elbers C., Lanjouw P., Mistiaen J.A., Ozler B. (2005) Re-Interpreting Sub-Group Inequality Decompositions. World Bank, World Bank Policy Research Working Paper 3687, 42 p.

`calcGEI`

## Examples

 ```1 2 3 4 5 6``` ```data(hhbudgets) decompGEI(hhbudgets[,"ingreso"], hhbudgets[,"estructura"], alpha=4) summary(hhbudgets[,"tenencia"]) #35 NA's decompGEI(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], ELMO=FALSE) summary(decompGEI(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], alpha=1.5)) ```

### Example output

```\$ineq
\$ineq\$index
GEI
128.0722

\$ineq\$parameter
alpha
4

\$decomp
\$decomp\$within
[1] 128.0624

\$decomp\$between
[1] 0.00984258

\$decomp\$betweenELMO
[1] 23.42324

\$intra
\$intra\$GEIGroups
3.9893931 181.5403932   4.8945765   0.7425743   0.1760261

\$intra\$contribGEIGroups
0.12572964 126.50647452   1.39971064   0.01596111   0.01448319

\$ws
\$ws\$wIntra
0.114476790 0.614083399 0.263965382 0.003540519 0.003933910

\$ws\$sIntra
0.082922195 0.633804602 0.269302892 0.005557520 0.008412791

\$nas
\$nas\$xNA
[1] 0

\$nas\$zNA
[1] 0

\$nas\$wNA
NULL

\$nas\$totalNA
[1] 0

attr(,"class")
[1] "ICI"
501            432            159           1343             63
otra           NA's
9             35
NULL
GEI          alpha
0.61155        1.50000

Decomposition:
within   between
0.599633  0.011912
betweenELMO
0.42559
```

IC2 documentation built on May 29, 2017, 10:05 a.m.