Estimate Age in Months

Module 1: Nutrient Intakes

Why Estimate Age in Months?

ENCOVI 2023 records age as integer years, which creates two methodological limitations for the biofortification impact analysis:

  1. Loss of the 6-11 month population — Children reported as edad == 0 cannot be separated into those under 6 months (excluded due to exclusive breastfeeding) and those aged 6-11 months (part of the study population). Without month-level resolution, as shown in Table 4, the entire age-0 cohort must be excluded, losing the children aged 6-11 months who should be included.

  2. Imprecision in anthropometric modeling — WHO LMS growth reference tables require age in months. Using integer years introduces up to ±5.5 months of error in a range where growth curves have steep gradients, distorting height-for-age Z-score calculations.

This module resolves both limitations by generating a synthetic edad_meses variable using empirical birth distributions from the Guatemala National Statistics Institute (INE) vital statistics registry (2019-2023) (Instituto Nacional de Estadística, 2024). Each birth-year cohort is matched to the corresponding age-in-years group. Month assignment uses a greedy quota-filling algorithm that distributes children to birth months so that the survey-weighted distribution matches the observed INE proportions by department and sex.

Data Sources

The INE publishes annual vital statistics with births disaggregated by month of occurrence, department of maternal residence, and sex. Five years of data (2019-2023) are loaded and standardized to construct department- and sex-specific birth seasonality profiles.

Each birth year maps to one ENCOVI age cohort: children aged 0 years were born in 2023, aged 1 in 2022, and so on through age 4 (born 2019). This one-to-one mapping allows the INE distributions to serve as population-level reference weights for synthetic month assignment within each cohort.

NoteData Structure

The unified registry consolidates five annual INE releases (2019-2023) into a single table of births by year, month, department, and sex. Records classified as “Extranjero” or “Ignorado” are excluded from proportion calculations, as ENCOVI assigns all children to one of the 22 departments.

Table 1: INE birth registry file metadata
INE Birth Registry Source. Guatemala vital statistics, births by month, department, and sex
INE Birth Registry Source
Guatemala vital statistics, births by month, department, and sex
Year Source File Coverage
2019 ine_nacimientos_2019_2023.parquet Births by month, department, and sex
2020 ine_nacimientos_2019_2023.parquet Births by month, department, and sex
2021 ine_nacimientos_2019_2023.parquet Births by month, department, and sex
2022 ine_nacimientos_2019_2023.parquet Births by month, department, and sex
2023 ine_nacimientos_2019_2023.parquet Births by month, department, and sex

The table above documents the documentary coverage of the unified birth registry: five birth years (2019-2023), each mapping to one ENCOVI age cohort, consolidated into a single source providing births by month, department, and sex.

Table 2: Birth data loading summary by year
Birth Registry Data Summary. INE Guatemala vital statistics (2019-2023)1
Birth Registry Data Summary
INE Guatemala vital statistics (2019-2023)1
Year Records2 Departments Months Total Births
2019 528 22 12 366,448
2020 528 22 12 340,876
2021 528 22 12 344,746
2022 528 22 12 345,359
2023 528 22 12 331,510
1 Red cells indicate deviations from expected values.
2 Expected: 22 departments x 12 months x 2 sexes = 528 records per year.
TipData Completeness

All five years contain exactly 528 records (22 departments × 12 months × 2 sexes), matching the expected record grid for the vital statistics registry. Total annual births range from approximately 331,000 to 366,000 across the period.

Birth Seasonality Patterns

Before using INE birth proportions for month assignment, we verify that birth timing carries meaningful departmental and sex-specific variation beyond a uniform distribution. If births were uniformly distributed, each month would contain 8.33% (1/12) of annual births.

Table 3: Proportion sum validation by stratum
Birth Proportion Validation. Sum of monthly proportions by year (expected = 1.000 per stratum)
Birth Proportion Validation
Sum of monthly proportions by year (expected = 1.000 per stratum)
Year Strata (dept x sex) Min Sum Max Sum Mean Sum All Valid
2019 44 1.0000 1.0000 1.0000 TRUE
2020 44 1.0000 1.0000 1.0000 TRUE
2021 44 1.0000 1.0000 1.0000 TRUE
2022 44 1.0000 1.0000 1.0000 TRUE
2023 44 1.0000 1.0000 1.0000 TRUE

Within each (year × department × sex) stratum the monthly proportions sum to 1, which is the structural condition the quota-based assignment algorithm operates on.

Departmental Patterns

Faceted line chart with 22 panels, one per department, ordered by seasonal variability. Each panel plots month (January to December) on the x-axis against the proportion of annual births on the y-axis, with a dashed reference line at the uniform 8.33%. Most departments dip in November and December and peak in the first quarter, showing systematic seasonal timing that departs from a uniform distribution.
Figure 1: Monthly birth proportions by department (2019-2023 average)

All 22 departments show seasonal patterns that depart from the uniform distribution (dashed green line), with most departments exhibiting a trough in November-December and peaks in the first quarter of the year. The month assignment therefore draws on department-specific empirical proportions.

Sex Differential

Lollipop chart with points and vertical stems for each month from January to December on the x-axis and the male-to-female birth ratio on the y-axis, zoomed to a range of 0.99 to 1.06 with a dashed reference line at parity (1.0). Every month sits above parity, between about 1.02 and 1.05, reflecting the biological excess of male births.
Figure 2: Male-to-female birth ratio by month (national average 2019-2023)

The male-to-female birth ratio exceeds parity in every month (range: 1.02-1.05), consistent with the documented global biological excess of male births. This sex differential, combined with departmental seasonality, is why the month assignment is conditioned on both department and sex.

ENCOVI Children and Cohort Mapping

Target Population

ENCOVI 2023 contains 4,725 children aged 0-4 years, distributed across five single-year age groups. These children form the population requiring synthetic month assignment.

Table 4: Age distribution of children 0-4 years before month assignment
Children Aged 0-4 Years in ENCOVI 2023. Distribution by age (integer years) and sex before month assignment (sampled children, unweighted)
Children Aged 0-4 Years in ENCOVI 2023
Distribution by age (integer years) and sex before month assignment (sampled children, unweighted)
Age (years) Male Female Total
0 480 446 926
1 446 435 881
2 488 453 941
3 458 433 891
4 559 527 1,086
Total — 2,431 2,294 4,725

Cohort Mapping Logic

Each integer age maps to a single birth-year cohort. A child aged n years was born in 2023 - n. Within each cohort, the 12 possible birth months define a 12-month age range.

Table 5: Age-to-cohort mapping for synthetic month assignment
Cohort Mapping: ENCOVI Age to INE Birth Year. Each integer age maps to a birth year and 12-month range
Cohort Mapping: ENCOVI Age to INE Birth Year
Each integer age maps to a birth year and 12-month range
Age (years) Birth Year Month Offset Age Range (months)
0 2023 0 0-11
1 2022 12 12-23
2 2021 24 24-35
3 2020 36 36-47
4 2019 48 48-59
NoteCohort Assignment Assumption

This mapping assumes children were interviewed during 2023 and that their reported age reflects completed years. For children interviewed near their birthday, the resulting imprecision is bounded at ±1 month within the cohort.

Synthetic Month Assignment

Assignment Algorithm

Within each stratum (birth year × department × sex), the algorithm distributes children to birth months using a greedy quota-filling approach:

  1. Calculate target population per month from INE proportions and total survey-weighted population in the stratum.
  2. Sort children by survey weight (descending), with random tie-breaking.
  3. Assign each child to the month with the largest remaining quota, subtracting the child’s weight from that month’s quota.

The survey-weighted (population-represented) distribution of assigned months therefore follows the INE reference proportions.

A child assigned birth month m within a given birth year receives edad_meses = month_offset + (12 - m), mapping January births to the oldest position within the cohort and December births to the youngest.

ImportantPopulation-Level Quota Matching

The algorithm operates on survey-weighted quotas. A department with 50 sampled children representing 5,000 individuals therefore produces a weighted distribution that follows INE proportions at the population level — the level at which results are reported. The greedy approach is quasi-deterministic: stochasticity is limited to tie-breaking among children with identical survey weights.

Biological Plausibility Correction

Within households containing multiple children aged 0-4 years, independent stratum-based assignment can produce age-in-months values that are biologically implausible for siblings. Two children from the same mother cannot be born less than 9 months apart unless they are twins (age difference of exactly 0 months).

The post-assignment correction identifies all sibling pairs where the assigned age separation falls in the invalid range (1-8 months) and reassigns the child with the smaller survey weight to the valid birth month with the largest remaining INE quota in that child’s stratum. The correction is iterative: after each reassignment, all sibling pairs within the household are re-evaluated.

Assignment Results

Table 6: Age in months assignment summary
Synthetic Age-in-Months Assignment Summary. ENCOVI 2023 individual dataset
Synthetic Age-in-Months Assignment Summary
ENCOVI 2023 individual dataset
Category N
Total individuals in ENCOVI 46,017
Children 0-4 years (synthetic assignment) 4,725
Children under 1 year 926
Children 6-11 months (synthetic assignment) 434
Children 0-5 months (excluded, exclusive breastfeeding assumption) 492
Adults and older children (simple conversion) 41,292
TipStudy Population Recovery

The synthetic month assignment identifies 434 children aged 6-11 months, who cannot be separated from infants under 6 months on integer age alone (both report edad == 0). This extends the study population to the intended 6-59 month range, covering the complementary feeding window.

Validation

Distributional Match to INE Proportions

The primary validation compares the survey-weighted distribution of assigned birth months against the INE reference proportions for each cohort. Grey segments show the deviation between observed (blue dots) and expected (green crosses) proportions.

Faceted chart with one panel per cohort. Each panel plots birth month (January to December) on the x-axis against proportion on the y-axis. Blue dots mark the observed survey-weighted proportions, a green dashed line with crosses marks the INE expected proportions, and grey vertical segments connect them to show the deviation. Observed and expected values track closely across cohorts, indicating the synthetic month assignment reproduces the reference distribution.
Figure 3: Synthetic assignment vs INE expected birth proportions by cohort

Age Distribution in Study Population

Histogram of synthetic age in months (0 to 59) on the x-axis against count of children on the y-axis, using one-month bins. A dashed vertical line at 5.5 months marks the boundary between the excluded under-6-months group and the 6-59 months study population. The bars are roughly uniform across the full range, consistent with comparable birth cohort sizes in ENCOVI.
Figure 4: Distribution of edad_meses for children 0-59 months

The histogram shows a relatively uniform distribution of age in months across the 0-59 range, consistent with approximately equal birth cohort sizes in ENCOVI. The 6-month boundary (dashed red line) clearly separates the excluded breastfeeding population from the study population.

Departmental Age Distribution

Horizontal box-and-whisker chart with one box per department, ordered by median. Department runs along the y-axis and synthetic age in months (6 to 59) along the x-axis. Medians cluster around 30 to 40 months with comparable interquartile ranges and no department showing distributional anomalies, indicating no systematic assignment bias.
Figure 5: Synthetic edad_meses distribution by department for children 6-59 months

Departmental boxplots confirm that the synthetic age distribution is well-behaved across all 22 departments, with median ages centered around 30-40 months and comparable interquartile ranges. No department shows distributional anomalies that would suggest systematic assignment bias.

Weighted Deviation from INE Proportions

The primary quality metric quantifies the departure of the synthetic assignment from the target INE birth proportions. For each department, the mean and maximum absolute deviation are calculated across all cohort-month strata.

Table 7: Weighted deviation from INE proportions by department
Weighted Deviation from INE Birth Proportions. By department, across all cohorts and months
Weighted Deviation from INE Birth Proportions
By department, across all cohorts and months
Department N Children (sample) Strata (cohort x month) Mean |Deviation|1 Max |Deviation|
Santa Rosa 135 120 0.0157 0.0849
Quetzaltenango 204 120 0.0135 0.0664
Zacapa 175 120 0.0129 0.0423
Sololá 164 120 0.0129 0.0793
El Progreso 161 120 0.0122 0.1071
Retalhuleu 158 120 0.0116 0.0544
Jutiapa 191 120 0.0115 0.0611
Chimaltenango 234 120 0.0103 0.0509
Huehuetenango 238 120 0.0103 0.0412
Chiquimula 176 120 0.0100 0.0531
Baja Verapaz 226 120 0.0099 0.0505
Escuintla 237 120 0.0098 0.0455
Totonicapán 231 120 0.0096 0.0341
Sacatepéquez 186 120 0.0095 0.0576
Izabal 218 120 0.0091 0.0430
Jalapa 222 120 0.0086 0.0464
Petén 223 120 0.0086 0.0580
San Marcos 233 120 0.0078 0.0406
Suchitepéquez 251 120 0.0072 0.0397
Alta Verapaz 328 120 0.0071 0.0430
Guatemala 222 120 0.0070 0.0415
Quiché 312 120 0.0065 0.0257
1 Green = mean deviation <= 2pp. Red = exceeds 2pp. Higher deviations correlate with smaller sample sizes and the discrete nature of the assignment algorithm. Max deviation captures the worst individual stratum (single month x cohort combination).
TipAssignment Quality

All 22 departments achieve mean absolute deviations below 1.6 percentage points from the INE target proportions. The departments with the highest deviations are those with smaller sample sizes where the discrete nature of the assignment algorithm has a proportionally larger impact.

Sibling Age Separation

Sibling age separations are reported after the biological plausibility correction. Valid sibling pairs have an age difference of exactly 0 months (twins) or at least 9 months (minimum full gestation period).

Table 8: Sibling age separation diagnostic after biological plausibility correction
Sibling Age Separation Distribution. All sibling pairs in households with 2+ children aged 0-4 years, after biological plausibility correction
Sibling Age Separation Distribution
All sibling pairs in households with 2+ children aged 0-4 years, after biological plausibility correction
Separation Category N Pairs Proportion
Twins (0 months) 71 6.0%
9-12 months 135 11.3%
13-24 months 370 31.0%
>24 months 617 51.7%
TipBiological Plausibility

After the correction, as shown in Table 8, no sibling pairs remain in the invalid 1-8 month separation range. The majority of pairs are separated by more than 24 months, consistent with typical inter-birth intervals in Guatemala. Approximately 71 pairs (6%) are classified as twins (0-month separation), inferred from the algorithm output rather than directly observed (ENCOVI does not record twin status).

Summary

Key Findings

  1. Study population coverage: The synthetic month assignment identifies 434 children aged 6-11 months, extending the study population to the specified 6-59 month range.

  2. Distributional accuracy: Survey-weighted month distributions track INE birth proportions with mean deviations below 1.6 percentage points in each of the 22 departments.

  3. Biological consistency: As documented in Table 8, no sibling pair remains in the impossible 1-8 month separation range after the plausibility correction.

  4. Seasonal information carried through: The assignment reproduces departmental and sex-specific birth seasonality.

WarningLimitations

  1. Interview timing assumption — The lack of individual-level interview dates means cohort assignment is approximate. A child whose household was interviewed near the child’s birthday may be misclassified by one cohort. This ambiguity affects approximately 1/12 of children at each boundary.

  2. Residual stochasticity — The assignment is quasi-deterministic, with a random component limited to tie-breaking among children with identical survey weights. Individual-level assignments are synthetic and should not be interpreted as observed values.

  3. Twin identification — The pairs classified as twins (0-month separation, see Table 8) are inferred rather than observed, as ENCOVI does not record twin status.

Application

This dataset provides month-level age resolution for all ENCOVI 2023 individuals, enabling precise WHO LMS Z-score calculations in downstream anthropometric modeling. The synthetic edad_meses variable is used by subsequent scripts in both the Covariate prediction pathway (individual consumption allocation) and the Meta-analysis (Gunaratna) pathway (height-for-age Z-score computation).

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References

Instituto Nacional de Estadística. (2024). Estadísticas Vitales — Nacimientos. Bases de Datos Anuales 2019–2023 [Dataset]. Instituto Nacional de Estadística. https://www.ine.gob.gt/vitales/