Numeric vector with non-negative values (strictly positive
when epsilon=1).
z
Factor who determines the subgroups.
w
Numeric vector of sampling weigths (optional).
epsilon
Parameter of the Atkinson index (must be strictly positive).
decomp
Character string specifying the decomposition. It must be one of "BDA"
for the Blackorby and alii (1985) decomposition or "DP" for the
Das and Parikh (1982) decomposition.
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 Atk (value of inequality index)
and epsilon (value of parameter).
decomp
a list with components within (value of within-group
inequality), between (value of between-group inequality),
residual (value of residual inequality) and, if ELMO is
TRUE, betweenELMO (value of maximum between-group inequality).
intra
a list with component AtkGroups (the subgroup values of
inequality index).
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
Atkinson A.B. (1970) On the Measurement of Inequality. Journal of
Economic Theory, 2, pp. 244-263.
Blackorby C., Donaldson D., Auersperg M. (1981) A new procedure for the
measurement of inequality within and among population subgroups. Canadian
Journal of Economics, 14, pp. 665-685.
Das T., Parikh A. (1982) Decomposition of Inequality Measures and a
Comparative Analysis. Empirical Economics, 7(1-2), pp. 23-48.
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> library(IC2)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/IC2/decompAtkinson.Rd_%03d_medium.png", width=480, height=480)
> ### Name: decompAtkinson
> ### Title: Decomposition by Groups for Atkinson Index
> ### Aliases: decompAtkinson
>
> ### ** Examples
>
> data(hhbudgets)
>
> decompAtkinson(hhbudgets[,"ingreso"], hhbudgets[,"estructura"], epsilon=3)
$ineq
$ineq$index
Atk
0.6053387
$ineq$parameter
epsilon
3
$decomp
$decomp$within
[1] 0.5954879
$decomp$between
[1] 0.02435238
$decomp$cross
[1] 0.01450155
$decomp$betweenELMO
[1] 0.5457692
$intra
$intra$AtkGroups
unipersonal nuclear ampliado compuesto coresidente
0.6143927 0.6166800 0.5014218 0.5729412 0.2584896
$ws
$ws$wIntra
unipersonal nuclear ampliado compuesto coresidente
0.114476790 0.614083399 0.263965382 0.003540519 0.003933910
$ws$sIntra
unipersonal nuclear ampliado compuesto coresidente
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"
> summary(hhbudgets[,"tenencia"]) # 35 NA's
rentada prestada propia_pagando propia litigio
501 432 159 1343 63
otra NA's
9 35
> summary(decompAtkinson(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], decomp="DP", ELMO=FALSE))
Length Class Mode
0 NULL NULL
> summary(decompAtkinson(x=hhbudgets[,"transporte"], z=hhbudgets[,"tenencia"], w=hhbudgets[,"factor"], decomp="DP", epsilon=0.25))
Atk epsilon
0.11435 0.25000
Decomposition (DP):
within between residual
1.1128e-01 3.0111e-03 6.5006e-05
betweenELMO
0.093282
>
>
>
>
>
> dev.off()
null device
1
>