Statistical Validation of a Risk-Adjusted Integral Index for Energy Public–Private Partnerships: Analysis of Variance, Multicollinearity and Structural Forecast for Uzbekistan

Composite indices are easy to build and hard to defend statistically. This article tests the PRISM index, which multiplies a weighted sum of four effectiveness components (financial-commercial, budgetary, production-technological and socio-economic) by a risk-stability coefficient, for appraising energy public–private partnership (PPP) projects. Two data sets are used: 59 energy PPP projects from the national register of Uzbekistan, divided into three mechanism types, and a 2015–2026 series (n = 12; the 2026 values are estimates) for a conditional project. Analysis of variance shows that the mechanism type explains 32% of the variance in specific investment (F(2, 56) = 13.24; p < 0.001; η2 = 0.32), and the result holds under the Welch and Kruskal–Wallis tests. In the series the components correlate with the index at |r| = 0.91–0.995 and with each other up to 0.9997, so variance inflation factors in a four-factor regression reach 44–355 and two coefficients take negative signs, which is not an economic effect. Only one regression result is stable: the risk-stability coefficient is positive in 100% of 2,000 bootstrap samples (1.430; 95% interval 1.177–1.689). Because the index is a product, its 2020–2025 growth splits exactly: 65.8% comes from the risk-stability coefficient and 34.2% from the weighted effectiveness. The structural forecast gives 0.738 in 2027 and 0.933 in 2031. The results rest on a conditional project and a short series and should be re-estimated on actual projects.