Statistical factorisation methods mine country data sets for proximity estimates of country outcomes reproduced by common underlying factors. Statistical factorisation yields explanatory variables threefold.
Systemic Factors, are multi-criteria measurements and units of account, and are generally neutral over the long run;
Deterministic Factors, establish the distributional systems of simultaneous equations that tend to reproduce covariance of country outcomes; and
Residual Factors, assign concepts in latency that are considered to reproduce variance between and among country outcomes.
Auto-regression analysis identifies the vector factorisation matrix as follows.
Table 1: Vector Factorisation Matrix
Dynamic Modeling
Dynamic modeling refers to techniques in dynamic optimisation of discrete time series data to account for empirical observations of dis-equilibrium and idiosyncratic country adjustment.
Country data sets employed in dynamic economic models (DEM) are of the generalised equation form: y(t)=f[y(t-1)]+g[(x(t),(t)], where the first term {f(~)} summarises the systemic element, and the second term {g(~)} refers to the deterministic and residual elements. Furthermore, DEM captures concepts in comparative statics analysis (CSA) through imputation of the generic formula {y(t)=g[x(t)]} to account for the persistent explanatory factor of (t) such as to denote technology, time or simply the error disturbance which is sufficient to produce a change in {y(t)} even absent any change in the variable {x(t)}. As a result, economists characteristically attribute (t) to the phenomenon of technological change such as to explain changes in the level of productivity and national economic performance.
Overall, DEM and CSA indicate that country outcomes are constituted by the conjunction of both the time path {f(t)} and the resolution of simultaneous equations constituting the transition path {g(t)}.
The statistical method of the Autologous Country Vector (ACV) 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 association with other international organisations.
Composite 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 given contour by basic themes in the sample set (see Global Indices page).
The Autologous Country Vector (ACV) is a high-level (apex) multi-dimensional composite index conforming to techniques in structural equation modelling (SEM) and linear trending such as to produce a general additive model (GAM) that derives statistical validity from uniform normalisation and independence of underlying global indices. Statistical formulation of the ACV exhibits communalities in sample factor loading and latent variables and is also consistent with ideas in ‘causal complexity’ whereby country outcomes may be construed to conform to several different combinations of complexity and logical operations.
The composite index equation for the ACV is formulated as follows:
ACV = {[v1]*[ALPHA]} + {[v2]*[(WGI+(EFWI-WGI))]} + {[V3]*[(DIPP+CPI)/2]}
Reference Indices nominated in the customisation of the ACV are summarised as follows (see Reference Indices for further information).
Table 1: ACV Key
EPRI
EGDI
PPPI
USDI
WGI
EFWI
DIPP
CPI
e-Participation Index
e-Government Development Index
GNI per capita Index (International Dollars)
GNI per capita Index (US Dollars)
World Government Index
Economic Freedom of the World Index
Political Participation Index
Corruption Perceptions Index
Estimation of country vectors is contingent to index construction processes of model selection predicated on qualitative judgments concerning input values (world domain space) and quantitative estimations for output range (country scenarios).
Formulative World Structuration
Formulative World Structuration refers to qualitative selection of world domain space (the ‘functional delimiter’) which is demarcated by principal axis of ‘freedom’, and secondary axis of ‘equality’. This is illustrated by the Alpha Matrix (see next section), which situates country alpha level according to pre-defined cluster formations of world structuration.
Alpha Analysis page
Formulative World Duration
Formulative World Duration refers to quantitative identification of country duration – a concept denoting estimated country development status {(x)} plus country growth factor {g(x)} (the ‘country scenario’) - which is stylised according to equilibrium case, prosperity case, and adversity case scenarios, subject to the projected coefficient of the deterministic component of idiosyncratic country development. This is illustrated by the Formulative World Duration Chart, which underlines the global phenomenon of uneven development between and among sovereign states.
Duration Analysis page
The ACV is a high-order structural equation model (SEM) that encapsulates a generalised hierarchical link function (GHLF) ascribing cannonical (logic) link functions embedded in the non-normal probability distributions of multivariate country datasets. Explicit processes of multi-dimensional scaling (MDS) of country data sets leads to identification of beta and gamma stimulants derived from intrinsic proximity modulation. GHLF therefore attributes ACV beta and gamma sub-components as nested second-level (β) and third-level (γ) structural components termed 'transformation indices'.
Accordingly, the ACV may be demonstrated to incorporate two distinct typologies of dis-equilibrium country transformation:
First Order Transition Dynamics
First order transition dynamics measure proximity estimates based on methodologies in advanced centering (also known as re-parameterisation) that linearly transform the country gradient (C2) variable by reference to a universal mean. The first order transition dynamic therefore formulates the Dynamism Index {β=(y-x)}, which systematically 're-parameterises' the system of simultaneous equations constituted in the country gradient component {β=(x+(y-x))/2} of the structural equation model {acv=f (α, β, γ)}.
Dynamism Index page
Second Order Transition Dynamics
Second order transition dynamics calculates proximity estimates defined by temporal delimiters and cluster structuration in the estimated density function of the country data sets that reveal differences in the country momentum (C3) variable. The second order transition dynamic thus exhibits the Momentum Index {γ=t=f(t-1)} as representing the difference equation delimiting the country momentum component {γ=(x+y)/2} of the structural equation model {acv=f (α, β, γ)}.
Consequently, transformation indices inherently capture the dis-equilibrium premium (or deficit) that accrues to nation states as a result of both (a) Organisational Transformation, such as by administrative and efficiency enhancements of the apparatus' of public administration; and (b) Cultural Transformation, as may be evidenced by explicit strategies of 'new' public management. Transformation indices therefore depict estimates of omniscient transformational value derived from the multi-collinear complex systems of nation states.
Momentum Index page
Country Transitivity refers to (a) multi-modal modulations, in the country experience (actual) or country scenario (hypothetical); conditional to (b) multi-level amplitudes, of the country vector which may also be cast for analytical purposes in terms of actual (de facto) or hypothetical.
Table 2: Country Transitivity Matrix