TheilU.RdCalculate Theil's U index of inequality.
TheilU(a, p, type = c(2, 1), na.rm = FALSE)a numeric vector with the actual observed values.
a numeric vector containing the predictions.
defining the type of Theil's two U measures, see Details. Default is 2.
logical, indicating whether NA values should be stripped before the computation proceeds. If set to TRUE complete cases of cbind(x, y) will be used. Defaults to FALSE.
Theil proposed two error measures, but at different times and under the same symbol U, which has caused some confusion.
U type = 1 is taken from Theil (1958, pp. 31-42). The argument a represents the actual observations and p the corresponding predictions. He left it open whether a and p should be used as absolute values or as observed and predicted changes.
Theil (1966, chapter 2) proposed U type = 2 as a measure of forecast quality: "...where \(A_i\) and \(P_i\) stand for a pair of predicted and observed changes. ..."
As \(U_1\) has some serious disadvantages (see Bliemel 1973) it is recommended to use \(U_2\).
Theil, H. (1958): Economic Forecasts and Policy. Amsterdam: North Holland.
Thiel, H. (1966): Applied Economic Forecasting. Chicago: Rand McNally.
Bliemel, F. (1973): Theil's Forecast Accuracy Coefficient: A Clarification, Journal of Marketing Research Vol. 10, No. 4 (Nov., 1973), pp. 444-446
TheilU(1:10, 2:11, type=1)
#> [1] 0.0751
TheilU(1:10, 2:11, type=2)
#> [1] 0.161