3. Statistical Analysis

Statistical analysis and modelling of e-government readiness for biometric authentication depends on the availability of global indices computed using geometric means of normalised statistics for longitudinal country data series as provided by leading institutions of global development such as the United Nations, the World Bank, the International Monetary Fund, in conjunction with other international organisations. Global indices embody thematic indicators of world development, and are generally published annually as stylised data sets. Collectively, the indices provide comparative indicators of commonalities in the reference points and are characterised by basic themes in the sample set.

Foundational themes are: (i) universalism, a concept of universal rights both technical (moral and legal) and substantive (tangible public goods such as peacekeeping and humanitarian assistance); (ii) global commons, known as ‘the commons’ being those resources held in common by all populations (environment, cultural, intellectual property, scientific and genomic) the subject of ‘global public domain’ [46] which is an institutionalised arena for the production of global public goods such as the biometric regime; and (iii) global risk management, largely intermediated and maintained by the supranational agencies in the areas of containing global epidemics, natural disaster management and early warning systems (EWS) for market-linked financial crisis. Risk management of biometrics extend to computer security countermeasures, particularly pertaining to critical infrastructures known as SCADA vulnerabilities [47].

Composite Models which compare country performance by aggregating governance indicators [48] are increasingly recognised as a useful tool in policy analysis and public communication [49]. The customisation of a multi-dimensional composite model [50] to estimate e-government readiness for biometric authentication utilises structural equation modelling techniques in combination with linear trending to produce a Generalised Additive Model [51] that explicates communalities in factor loading and latent variables. The model is also consistent with ideas in ‘causal complexity’, whereby computations may be construed to conform to several different combinations of complexity and logical operations [52].

Figure 1: Formulating a Composite Index

3.0.1 Biometric Readiness Composite Index.

Global indices used in to construct the custom index are: (i) DERI, the Digital Economy Rankings Index produced by the Economist Intelligence Unit; (ii) eGDI, the e-Government Development Index compiled by the UN UNPAN; (iii) WGI, the World Governance Index prepared by the Forum for a New World Governance; (iv) EFWI, the Economic Freedom of the World Index, produced by the Fraser Institute; (v) eEPI, the e-Participation Index, a sub-index of the eGDI; and (vi) eCPI, the Corruption Perception Index, maintained by Transparency International. In conducting the statistical analysis, the objective function for maximum sample size was constrained by differences in total country sampling of the underlying global indices. For total world countries the BRI measures 68 reference points that capture 79% of total world population, 18% of which are OECD countries; and a representative spread of GNI per capita; nominally, 19% high income countries, 43% high-middle income countries and 38% low-middle income countries.

The Biometric Readiness Index (BRI) (shown above) is constructed as a composite index (equation a) of the generalised additive model form (equation b) which synchronises to a concept of formulative duration world model (shown at Figure 1).

Equation A

Equation B

The structural form of the BRI is nested in a matrix solution set (equation c) that is contingent to the country vector set (equation d) and which fully reconciles with the coincident theoretical framework (Table 2) premised on applied theories of Cartesian mathematics, organic process, policy articulation, and country vector.

Equation C

Equation D

Table 1 : Composite Index Components

The magnitude of country vector is given by composite index components of: C1: country level (equation e), C2: country gradient (equation f); and C3: country momentum (equation g). These components capture statistical propensities of sample dependence (country level), system of distribution functions (country gradient), and transition probability (country momentum).

Equation E

Equation F

Equation G

Transitivity within the ‘formulative duration world model’ denotes horizontal variance in the data envelopment analysis (DEA) concept [53], and invokes statistical ‘survivor models’ [54], namely, the hazard function and effect parameters of the proportional hazards model. In this direction, empirical data in the logic of complexity discerns that country experience of hazards is principally affected by the prevalence of policy entrepreneurs capable of seizing ‘windows of opportunity’, and external inter-dependencies that yield to a democratic peace ‘proposition’ [55]; as well as the possibility of a ‘switching point’ between two regimes [56]. Formulative duration may also be explained such that transitivity effectively normalises the uncertainty in Uncertainty Analysis [57] while at the same it time fully actualises the sensitivity in Sensitivity Analysis (ibid).

3.0.2 Transformation Indices

Even while e-governments pursue both (i) organisational transformation, such as administrative and efficiency enhancements; and (ii) cultural transformation, by strategies such as One-Stop-Shops, marketing and outreach programs, and high volume transaction services [58], the omniscience of country momentum persistently accrues transformational value from dynamic and systemic processes. Specifically, the BRI may be deconstructed into constituent components for determination of the nested transformation indices: (i) dynamism index, represented by the premium of economic freedom above total public sector delivery, given by the equation DYI=EFWI-eWGI; and (ii) momentum index, indicating the residual vigour of institutions, a transposition of public integrity that is the inverse of entropic processes, indicated by the formula Auti={(EPI + (1-eCPI))/2}, where Auti refers to residual autonomy, and the term 1-eCPI denotes the inverse of the corruption perception index which is itself notionally in contrariety (cf. Transformation Charts below).

General transformation (or adjustment) of the BRI exhibits the structural equation’s adaptability for standard econometric analysis, a classic example being adjustment to C1 and C3 components in order to yield the corresponding autologous country vector. As shown below, a generic country composite index (CCI) substitutes Y/G country (alpha) level, no change to country gradient, and substitution of QLI (quality of life indicators) for country momentum.

Equation H

cf. Biopolitics References

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[46] Ruggie, 2004; [47] Wilson, 2005; [48] Kaufmann et al, 1999; [49] OECD, 2008; [50] Booysen, 2002; [51] Jones & Almond, 1992; [52] Braumoeller, 2003; [53] Despotsis, 2005; [54] Cox, 1972; [55] Braumoeller, 2003; [56] Quandt, 1958; [57] Saisana, 2005; [58] OECD, 2009

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