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IGOR — Individuals Grouped Over Ratios

IGOR is an Iterative Proportional Fitting (IPF) method that disaggregates gridded total population (ARDECO) into narrow 5-year sex–age groups, constrained simultaneously to:

• cell-level sex and broad-age shares from ESTAT 1 km rasters, and
• region-level (LAU) population pyramids from census microdata.

The result is a set of population grids at 1 km resolution, one per SexAgeGroup combination (currently 36 classes: 18 age bands × 2 sexes).

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Pages

• Algorithm — IPF procedure, formulas, convergence
• Data — Input datasets, spatial domains, fallback logic, outputs
• Implementation — GeoDMS containers, parameters, how to run

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Index notation

Symbol	GeoDMS name	Description
$a$	SexAgeClasses	Narrow age group (5-yr band)
$b(a)$	SexAgeClasses/BroadClasses_rel	Broad age group containing $a$: LT15, 15–64, GE65
$s(a)$	SexAgeClasses/Sex_rel	Sex of class $a$: M or F
$i$	domain	IPF unit (grouping of 100 m cells sharing a LAU region)
$r(i)$	i/r_rel	LAU region that cell $i$ belongs to
$e(i)$	i/e_rel	1 km ESTAT cell that contains cell $i$

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Input fields

Symbol	GeoDMS name	Description
$P_i$	P_i	Total population per IPF unit $i$ (aggregated from ARDECO 100 m)
$E_{i,s}$	E_is/M, E_is/F	Sex share at 1 km cell $e(i)$ (from ESTAT; fallback: LAU share)
$E_{i,b}$	E_ib/LT15 etc.	Broad-age share at 1 km cell $e(i)$ (from ESTAT; fallback: LAU share)
$Q_{asr}$	Q_asr/<name>	Census population per LAU region $r$, per SexAgeClass $a$ (fallback: NUTS3 share × $P_r$)

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Core formula

For each iteration the population per SexAgeClass $a$ in cell $i$ is:

$$X_{ai} = E_{i,s(a)} \cdot E_{i,b(a)} \cdot A_i \cdot B_{a,r(i)}$$

Cell balancing factor $A_i$ ensures $\sum_a X_{ai} = P_i$:

$$A_i = \frac{P_i}{\displaystyle\sum_{a} E_{i,s(a)} \cdot E_{i,b(a)} \cdot B_{a,r(i)}}$$

Region balancing factor $B_{ar}$ ensures $\sum_{i:, r(i)=r} X_{ai} \approx Q_{ar}$. Updated each iteration as:

$$\tilde{B}_{ar}^{(t)} = B_{ar}^{(t-1)} \cdot \frac{Q_{ar}}{\displaystyle\sum_{i:, r(i)=r} X_{ai}^{(t)}}$$

Then normalized within each region to prevent unbounded growth:

$$B_{ar}^{(t)} = \frac{\tilde{B}_{ar}^{(t)}}{\max_{a'} \tilde{B}_{a'r}^{(t)}}$$

Initialization: $B_{ar}^{(0)} = 1\ \forall, a, r$

Convergence: 10 iterations by default — see Algorithm for details.

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Quick links

Topic	Page
How the IPF loop works	Algorithm
What data goes in and out	Data
How to run the model	Implementation