testTIP: Test for TIP dominance
In AngelBerihuete/rtip: Inequality, Welfare and Poverty Indices and Curves using the EU-SILC Data

Description Usage Arguments Details Value Author(s) References See Also Examples

Statistical test procedure given by Xu and Osberg (1998) to study TIP dominance from sample TIP curve estimates.

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testTIP(dataset1, dataset2, ipuc = "ipuc", hhcsw = "DB090",
  hhsize = "HX040", pz = 0.6, same.arpt.value = NULL, norm = FALSE,
  samplesize = 50, alpha = 0.05)

`dataset1`	a data.frame containing the variables.
`dataset2`	a data.frame containing the variables.
`ipuc`	a character string indicating the variable name of the income per unit of consumption. Default is "ipuc".
`hhcsw`	a character string indicating the variable name of the household cross-sectional weight. Default is "DB090".
`hhsize`	a character string indicating the variable name of the household size. Default is "HX040".
`pz`	a number between 0 and 1 which represents the percentage to be used to calculate the at-risk-of-poverty threshold. The default is 0.6.
`same.arpt.value`	a number that will be used as a common poverty threshold. If NULL, poverty thresholds will be calculated from each datasets (see arpt).
`norm`	logical; if TRUE, the normalised TIP curve ordinates are computed using the normalised poverty gaps (poverty gaps divided by the poverty threshold).
`samplesize`	an integer which represents the number of TIP curve ordinates to be estimated. The default is 50.
`alpha`	a scalar indicating the significance level. Default is 0.05.

Because the TIP curve becomes horizontal at the arpr value, it is only necessary to have the test implemented over the interval (0, max {arpr1, arpr2}). For that reason both TIP curves are truncated at the same value equal to max{arpr1, arpr2} and ordinates are only compared at points p_i = i/samplesize, where i=1, …, k in the interval (0, max { arpr1, arpr2}) (see arpr function).

The null hypothesis to be tested is that the TIP curve calculated from dataset1 dominates the one calculated from dataset2.

A list with the following components:

Tvalue, the value of the test-statistic.
p.value, simulated p-value of the test-statistic Tvalue (Wolak, 1989). It is calculated only when the Tvalue falls into an inconclusive region.
decision, if the Tvalue is less than the lower-bound of the critical value at the alpha significance level the decision is "Do not reject null hypothesis". If the Tvalue is greater than the upper-bound of the critical value at the alpha significance level the decision is "Reject null hypothesis". Lower and upper-bounds critical values are obtained from Kodde and Palm (1986). If Tvalue falls into an inconclusive region (between the lower- and upper-bounds) the p-value will be estimated following Wolak (1989).

A. Berihuete, C.D. Ramos and M.A. Sordo

C. M. Beach and S. F. Kaliski (1986) Curve inference with sample weights: and application to the distribution of unemployment experience, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 35, No. 1, 38–45.

D.A. Kodde and F.C. Palm (1986) Wald criteria for jointly testing equality and inequality restrictions, Econometrica, 50, 1243–1248.

F.A. Wolak (1989), Testing inequality constrains in linear econometric models, Journal of Econometrics, 41, 205–235.

K. Xu and L. Osberg (1998) A distribution-free test for deprivation dominance, Econometric Reviews, 17, 415–429.

OmegaTIP, setupDataset, arpt, arpr

data(eusilc2)
ATdataset <- setupDataset(eusilc2, country = "AT")
ATdataset1 <- setupDataset(eusilc2, country = "AT", region = "Burgenland")
ATdataset2 <- setupDataset(eusilc2, country = "AT", region = "Carinthia")
testTIP(ATdataset1, ATdataset2, same.arpt.value = arpt(ATdataset), samplesize = 50, alpha = 0.05)