Transfer Model: Zinc Intake

Module 3: Transfer Models

Why Model Zinc?

Zinc is essential for immune function and growth, and zinc deficiency is associated with stunting in children. In Guatemala, maize provides a substantial share of dietary zinc (see Daily Nutrient Intake by Source in Module 1) — even higher than for iron. By modeling zinc intake from maize and non-maize sources separately, we can:

  1. Simulate biofortification scenarios — Predict how higher-content maize varieties would change total zinc intake
  2. Preserve baseline non-maize intake — Keep other dietary sources constant when modeling interventions
  3. Locate the modifiable fraction — Identify where the maize-derived share of zinc intake is largest

Modeling Approach

We use survey-weighted gamma regression because zinc intake data is:

  • Positive and continuous — People consume some amount of zinc daily
  • Right-skewed — Most people have moderate intake, few have very high intake
  • Population-representative — Survey weights carry the estimates to the national level

The models predict zinc intake based on demographic and socioeconomic characteristics that are available in both ENCOVI (training data) and SIVESNU (application target).

Data Preparation

Source Data

We use the cleaned ENCOVI dataset from the previous preparation step, containing individuals with complete predictor variables and nutrient intake estimates.

Handling Extreme Values

Gamma regression requires positive values and is sensitive to extreme outliers. We apply conservative outlier detection:

TipOutlier Threshold

Upper outliers identified as values exceeding P95 + 1.5×IQR (i.e., 95th percentile plus 1.5 times the interquartile range). The threshold suits micronutrients:

  • Micronutrient intake distributions are markedly right-skewed
  • Biologically plausible high values arise from consumption of micronutrient-dense or fortified foods
  • Retaining the upper tail supports model generalizability to populations with varied dietary patterns

Survey Design

All models incorporate ENCOVI’s complex survey design (clustering and expansion weights), which places the estimates at the population level.

Modeling Zinc Intake from Maize

Distribution Selection

Before modeling, we assess which statistical distribution best fits the zinc intake data. Three candidate distributions are compared:

Table 1: Distribution fit comparison for zinc intake from maize
Distribution Fit Comparison. Goodness-of-fit statistics for Gamma, Lognormal, and Exponential distributions
Distribution Fit Comparison
Goodness-of-fit statistics for Gamma, Lognormal, and Exponential distributions
Distribution Log-Likelihood
Information Criteria
Goodness-of-Fit Statistics
AIC BIC Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling
Gamma −130,103.2506 260,210.5012 260,227.6774 0.0617 51.2549 274.8423
Lognormal −130,445.5698 260,895.1396 260,912.3158 0.0301 11.9193 103.4848
Exponential −131,268.8361 262,539.6723 262,548.2604 0.1150 207.7700 1,117.2492
Four-panel goodness-of-fit display for zinc intake from maize against a fitted gamma distribution. Top left: histogram of observed intake with the theoretical gamma density overlaid as a dashed curve. Top right: quantile-quantile plot of empirical versus theoretical quantiles. Bottom left: empirical versus theoretical cumulative distribution functions. Bottom right: probability-probability plot. Points and curves track the reference diagonals closely, indicating the right-skewed data are well described by the gamma distribution.
Figure 1: Distribution assessment for zinc intake from maize
ImportantDistribution Selection

Gamma distribution provides the best fit based on:

  • Lowest AIC/BIC (information criteria)
  • Highest Log-Likelihood

Gamma regression with log link is appropriate for positive, right-skewed continuous outcomes.

Full Model

We first train a model including all 20 candidate predictors to identify which variables significantly predict zinc intake from maize.

Table 2: Model coefficients for zinc intake from maize (full model)
Zinc Intake from Maize (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Zinc Intake from Maize (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.0732 0.2003 5.3571 <0.0001
parentescoEsposo(a) o compañero(a) 0.1486 0.0848 1.7520 0.0800
parentescoHermano(a) 0.2719 0.1482 1.8343 0.0668
parentescoHijo(a) 0.3803 0.0777 4.8935 <0.0001
parentescoJefe del hogar 0.1644 0.0816 2.0154 0.0441
parentescoNieto(a) 0.2715 0.0880 3.0848 0.0021
parentescoOtro no pariente 0.3925 0.4109 0.9552 0.3396
parentescoOtro pariente 0.3064 0.1246 2.4595 0.0140
parentescoPadre o madre 0.3368 0.0896 3.7604 0.0002
parentescoSuegro(a) 0.3453 0.1405 2.4569 0.0141
parentescoYerno o nuera 0.3299 0.1433 2.3026 0.0215
sexoMujer −0.1269 0.0190 −6.6747 <0.0001
poly(edad, 2)1 41.5762 4.4335 9.3777 <0.0001
poly(edad, 2)2 −31.9618 2.0630 −15.4927 <0.0001
departamentoEl Progreso 0.2687 0.1269 2.1171 0.0344
departamentoSacatepéquez 0.2788 0.1041 2.6788 0.0075
departamentoChimaltenango 0.4921 0.1021 4.8179 <0.0001
departamentoEscuintla 0.1588 0.1068 1.4869 0.1373
departamentoSanta Rosa 0.4403 0.1245 3.5367 0.0004
departamentoSololá 0.5975 0.1212 4.9283 <0.0001
departamentoTotonicapán 0.7248 0.1145 6.3276 <0.0001
departamentoQuetzaltenango 0.7449 0.1148 6.4875 <0.0001
departamentoSuchitepéquez 0.4631 0.0990 4.6771 <0.0001
departamentoRetalhuleu 0.5901 0.1160 5.0881 <0.0001
departamentoSan Marcos 0.6791 0.1174 5.7858 <0.0001
departamentoHuehuetenango 0.6853 0.1081 6.3400 <0.0001
departamentoQuiché 0.7955 0.1064 7.4765 <0.0001
departamentoBaja Verapaz 0.7748 0.1127 6.8737 <0.0001
departamentoAlta Verapaz 0.4866 0.1184 4.1118 <0.0001
departamentoPetén 0.6752 0.1081 6.2456 <0.0001
departamentoIzabal 0.5161 0.1183 4.3617 <0.0001
departamentoZacapa 0.1351 0.1242 1.0880 0.2768
departamentoChiquimula 0.5093 0.1277 3.9889 <0.0001
departamentoJalapa 0.7342 0.1200 6.1171 <0.0001
departamentoJutiapa 0.3740 0.1094 3.4199 0.0006
areaRural 0.1551 0.0401 3.8645 0.0001
poly(miembros_hogar, 3)1 −0.0137 3.5555 −0.0039 0.9969
poly(miembros_hogar, 3)2 −1.1755 2.9721 −0.3955 0.6925
poly(miembros_hogar, 3)3 −0.4877 3.2743 −0.1490 0.8816
propiedadPropia y pagandola a plazos −0.1395 0.1355 −1.0293 0.3035
propiedadAlquilada −0.1212 0.0749 −1.6176 0.1060
propiedadCedida o prestada −0.0053 0.0577 −0.0911 0.9274
propiedadOtro −0.3914 0.4067 −0.9626 0.3359
poly(grado_estudios_hogar, 3)1 −20.1972 4.9707 −4.0633 <0.0001
poly(grado_estudios_hogar, 3)2 0.0667 4.4799 0.0149 0.9881
poly(grado_estudios_hogar, 3)3 −3.3438 4.4585 −0.7500 0.4534
tipo_viviendaApartamento −0.3002 0.1794 −1.6731 0.0945
tipo_viviendaCuarto en casa de vecindad 0.3384 0.3106 1.0897 0.2761
tipo_viviendaRancho −1.4047 0.2720 −5.1647 <0.0001
tipo_viviendaCasa improvisada 0.1981 0.2955 0.6702 0.5028
material_paredesBlock 0.2371 0.1499 1.5822 0.1138
material_paredesConcreto 0.2862 0.2789 1.0264 0.3049
material_paredesAdobe 0.3829 0.1569 2.4401 0.0148
material_paredesMadera 0.2654 0.1655 1.6034 0.1091
material_paredesLamina metalica 0.0344 0.3357 0.1026 0.9183
material_paredesBajareque 0.6466 0.1821 3.5509 0.0004
material_paredesLepa, palo o caña 0.5482 0.2928 1.8723 0.0614
material_paredesOtro −0.0727 0.3873 −0.1878 0.8511
material_techoLamina metalica −0.0336 0.0729 −0.4603 0.6454
material_techoAsbesto cemento −0.0324 0.3307 −0.0981 0.9219
material_techoTeja −0.0113 0.0978 −0.1152 0.9083
material_techoPaja, palma o similar 1.3079 0.2740 4.7731 <0.0001
material_techoOtro −0.3447 0.4482 −0.7690 0.4420
material_pisoLadrillo de cemento −0.0051 0.0768 −0.0663 0.9472
material_pisoLadrillo de barro 0.1438 0.3803 0.3782 0.7054
material_pisoTorta de cemento 0.0469 0.0585 0.8016 0.4229
material_pisoMadera −0.0468 0.1665 −0.2808 0.7789
material_pisoTierra 0.0338 0.0649 0.5202 0.6030
poly(n_cuartos, 3)1 −6.6175 4.0246 −1.6443 0.1003
poly(n_cuartos, 3)2 −5.0198 3.6021 −1.3936 0.1637
poly(n_cuartos, 3)3 −5.3105 4.0304 −1.3176 0.1879
tipo_sanitarioUso compartido 0.1129 0.0726 1.5556 0.1200
fuente_aguaTubería fuera de la vivienda 0.1132 0.0558 2.0278 0.0428
fuente_aguaChorro publico 0.1148 0.0838 1.3703 0.1708
fuente_aguaPozo perforado 0.0763 0.0491 1.5517 0.1210
fuente_aguaRío, lago, manantial −0.0376 0.0771 −0.4883 0.6254
fuente_aguaCamion cisterna −0.1708 0.1267 −1.3475 0.1780
fuente_aguaAgua de lluvia 0.1146 0.1489 0.7695 0.4417
fuente_aguaOtro 0.0991 0.1085 0.9139 0.3609
recoleccion_basuraLa tiran en cualquier lugar −0.1716 0.0672 −2.5527 0.0108
recoleccion_basuraServicio municipal −0.3354 0.0621 −5.3973 <0.0001
recoleccion_basuraServicio privado −0.4197 0.0799 −5.2556 <0.0001
electricidadNo 0.0064 0.0461 0.1380 0.8903
televisorNo −0.0131 0.0382 −0.3417 0.7326
telefonia_celularNo −0.0270 0.0404 −0.6665 0.5052
computadoraNo 0.2205 0.0521 4.2356 <0.0001
Scatter chart of the full gamma model for zinc from maize. Observed zinc intake in milligrams per day on the x-axis, model-predicted intake on the y-axis. Points cluster along an upward diagonal, showing predictions generally track observed values across the twenty-predictor full model.
Figure 2: Observed vs predicted zinc intake from maize (full model)

Variable Selection

Not all predictors contribute meaningfully to prediction. We use Wald tests to identify statistically significant variables and remove those that add complexity without improving predictions.

Table 3: Wald test results for predictor significance (zinc from maize)
Variable Significance Testing. Wald F-test results for zinc intake from maize model
Variable Significance Testing
Wald F-test results for zinc intake from maize model
variable f_statistic p_value significant
parentesco 10.61 <0.0001 *
sexo 44.55 <0.0001 *
poly(edad, 2) 147.12 <0.0001 *
departamento 6.51 <0.0001 *
area 14.93 0.0001 *
poly(miembros_hogar, 3) 0.05 0.9840
propiedad 1.11 0.3504
poly(grado_estudios_hogar, 3) 5.83 0.0006 *
tipo_vivienda 8.51 <0.0001 *
material_paredes 3.93 0.0001 *
material_techo 6.33 <0.0001 *
material_piso 0.25 0.9407
poly(n_cuartos, 3) 2.00 0.1127
tipo_sanitario 2.42 0.1200
fuente_agua 1.45 0.1826
recoleccion_basura 15.37 <0.0001 *
electricidad 0.02 0.8903
televisor 0.12 0.7326
telefonia_celular 0.44 0.5052
computadora 17.94 <0.0001 *
ImportantVariables Retained

11 predictors show significant relationships with zinc intake from maize, spanning demographic, geographic, socioeconomic, housing and asset categories. Variables that do not significantly predict zinc intake from maize after controlling for other factors are excluded from the refined model.

Refined Model

The final model is fitted on the significant predictors alone.

Table 4: Model coefficients for zinc intake from maize (refined model)
Zinc Intake from Maize (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Zinc Intake from Maize (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.0315 0.1938 5.3229 <0.0001
parentescoEsposo(a) o compañero(a) 0.1760 0.0860 2.0471 0.0408
parentescoHermano(a) 0.2987 0.1538 1.9425 0.0523
parentescoHijo(a) 0.3881 0.0786 4.9400 <0.0001
parentescoJefe del hogar 0.1892 0.0844 2.2428 0.0251
parentescoNieto(a) 0.2641 0.0900 2.9344 0.0034
parentescoOtro no pariente 0.4555 0.4110 1.1084 0.2679
parentescoOtro pariente 0.3021 0.1244 2.4291 0.0153
parentescoPadre o madre 0.3227 0.0902 3.5768 0.0004
parentescoSuegro(a) 0.3645 0.1416 2.5746 0.0101
parentescoYerno o nuera 0.3313 0.1504 2.2028 0.0278
sexoMujer −0.1290 0.0203 −6.3615 <0.0001
poly(edad, 2)1 39.1664 4.5423 8.6225 <0.0001
poly(edad, 2)2 −31.2131 2.2632 −13.7914 <0.0001
departamentoEl Progreso 0.2901 0.1245 2.3312 0.0199
departamentoSacatepéquez 0.3065 0.1048 2.9253 0.0035
departamentoChimaltenango 0.5173 0.1019 5.0744 <0.0001
departamentoEscuintla 0.2041 0.1065 1.9167 0.0555
departamentoSanta Rosa 0.4708 0.1262 3.7294 0.0002
departamentoSololá 0.6202 0.1193 5.2003 <0.0001
departamentoTotonicapán 0.7454 0.1116 6.6813 <0.0001
departamentoQuetzaltenango 0.7724 0.1136 6.7986 <0.0001
departamentoSuchitepéquez 0.5063 0.0969 5.2258 <0.0001
departamentoRetalhuleu 0.6317 0.1153 5.4790 <0.0001
departamentoSan Marcos 0.7276 0.1162 6.2608 <0.0001
departamentoHuehuetenango 0.7412 0.1107 6.6947 <0.0001
departamentoQuiché 0.8287 0.1061 7.8091 <0.0001
departamentoBaja Verapaz 0.7910 0.1094 7.2282 <0.0001
departamentoAlta Verapaz 0.5370 0.1165 4.6091 <0.0001
departamentoPetén 0.7115 0.1046 6.8020 <0.0001
departamentoIzabal 0.5404 0.1178 4.5888 <0.0001
departamentoZacapa 0.1618 0.1223 1.3235 0.1859
departamentoChiquimula 0.5439 0.1293 4.2077 <0.0001
departamentoJalapa 0.7498 0.1215 6.1704 <0.0001
departamentoJutiapa 0.3934 0.1083 3.6313 0.0003
areaRural 0.1621 0.0401 4.0416 <0.0001
poly(grado_estudios_hogar, 3)1 −20.5664 4.9992 −4.1139 <0.0001
poly(grado_estudios_hogar, 3)2 −1.1251 4.4418 −0.2533 0.8001
poly(grado_estudios_hogar, 3)3 −3.6045 4.5038 −0.8003 0.4237
tipo_viviendaApartamento −0.3108 0.1864 −1.6671 0.0957
tipo_viviendaCuarto en casa de vecindad 0.4160 0.3322 1.2522 0.2107
tipo_viviendaRancho −1.4949 0.2615 −5.7165 <0.0001
tipo_viviendaCasa improvisada 0.2287 0.2961 0.7724 0.4400
material_paredesBlock 0.2278 0.1533 1.4862 0.1374
material_paredesConcreto 0.2191 0.2731 0.8023 0.4225
material_paredesAdobe 0.3880 0.1582 2.4531 0.0143
material_paredesMadera 0.2694 0.1631 1.6512 0.0989
material_paredesLamina metalica 0.0231 0.3431 0.0674 0.9463
material_paredesBajareque 0.6522 0.1807 3.6098 0.0003
material_paredesLepa, palo o caña 0.5414 0.2994 1.8081 0.0708
material_paredesOtro −0.0545 0.3918 −0.1390 0.8894
material_techoLamina metalica 0.0149 0.0700 0.2120 0.8321
material_techoAsbesto cemento −0.0428 0.3192 −0.1342 0.8933
material_techoTeja 0.0378 0.0964 0.3924 0.6948
material_techoPaja, palma o similar 1.4588 0.2657 5.4910 <0.0001
material_techoOtro −0.2718 0.4649 −0.5848 0.5588
recoleccion_basuraLa tiran en cualquier lugar −0.1694 0.0666 −2.5423 0.0111
recoleccion_basuraServicio municipal −0.3575 0.0594 −6.0226 <0.0001
recoleccion_basuraServicio privado −0.4482 0.0807 −5.5506 <0.0001
computadoraNo 0.2299 0.0536 4.2909 <0.0001
Scatter chart of the refined gamma model for zinc from maize. Observed zinc intake in milligrams per day on the x-axis, model-predicted intake on the y-axis. Points follow an upward diagonal similar to the full model, confirming that using only significant predictors preserves predictive accuracy.
Figure 3: Observed vs predicted zinc intake from maize (refined model)

Model Diagnostics

We verify the model meets statistical assumptions:

Panel of regression diagnostic plots for the refined zinc-from-maize gamma model, covering residual behaviour, leverage, and predictor collinearity. Residuals show no systematic pattern and are approximately normal, no observations exert undue leverage, and the collinearity panel plots each term's degrees-of-freedom adjusted variance inflation factor against shaded low, moderate and high reference bands.
Figure 4: Diagnostic plots for zinc from maize model
TipDiagnostic Assessment
  • Residuals: No systematic patterns, approximately normal
  • Leverage: No overly influential observations
  • Collinearity: Degrees-of-freedom adjusted variance inflation factors (VIF) reach a maximum of 10.4, with 1 of 11 terms above the conventional threshold of 5

Factors and polynomial terms contribute several columns to the model matrix, so their generalized VIF is rescaled by the term’s degrees of freedom. This places every term on the single-coefficient scale that the thresholds of 5 and 10 refer to.

Modeling Zinc Intake from Non-Maize Sources

Zinc from non-maize sources includes vegetables, fruits, legumes, and animal products. This component remains constant in biofortification scenarios, representing the baseline dietary zinc that would not change with maize interventions.

Distribution Selection

Table 5: Distribution fit comparison for zinc intake from non-maize sources
Distribution Fit Comparison. Goodness-of-fit statistics for Gamma, Lognormal, and Exponential distributions
Distribution Fit Comparison
Goodness-of-fit statistics for Gamma, Lognormal, and Exponential distributions
Distribution Log-Likelihood
Information Criteria
Goodness-of-Fit Statistics
AIC BIC Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling
Gamma −96,024.5252 192,053.0504 192,070.2267 0.0175 3.2288 22.7604
Lognormal −100,135.1735 200,274.3470 200,291.5232 0.0748 82.7171 519.8734
Exponential −97,613.1779 195,228.3558 195,236.9439 0.0975 128.9280 733.7516
Four-panel goodness-of-fit display for zinc intake from non-maize sources against a fitted gamma distribution. Top left: histogram of observed intake with the theoretical gamma density overlaid as a dashed curve. Top right: quantile-quantile plot of empirical versus theoretical quantiles. Bottom left: empirical versus theoretical cumulative distribution functions. Bottom right: probability-probability plot. Points and curves align with the reference diagonals, showing the gamma distribution again fits the right-skewed data well.
Figure 5: Distribution assessment for zinc intake from non-maize sources
ImportantDistribution Selection

Gamma distribution again provides the best fit for non-maize zinc intake.

Full Model

Table 6: Model coefficients for zinc intake from non-maize sources (full model)
Zinc Intake from Non-Maize Sources (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Zinc Intake from Non-Maize Sources (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.4644 0.1146 12.7748 <0.0001
parentescoEsposo(a) o compañero(a) −0.1800 0.0651 −2.7652 0.0058
parentescoHermano(a) 0.0532 0.1109 0.4794 0.6317
parentescoHijo(a) −0.0665 0.0622 −1.0694 0.2851
parentescoJefe del hogar −0.1094 0.0642 −1.7031 0.0888
parentescoNieto(a) −0.0844 0.0708 −1.1922 0.2334
parentescoOtro no pariente −0.0663 0.2444 −0.2713 0.7862
parentescoOtro pariente −0.1095 0.0743 −1.4750 0.1404
parentescoPadre o madre −0.1175 0.0698 −1.6838 0.0924
parentescoSuegro(a) 0.0008 0.0807 0.0102 0.9919
parentescoYerno o nuera 0.1381 0.0881 1.5687 0.1170
sexoMujer −0.1309 0.0103 −12.7112 <0.0001
poly(edad, 2)1 26.7136 2.8550 9.3569 <0.0001
poly(edad, 2)2 −32.8566 1.2718 −25.8342 <0.0001
departamentoEl Progreso 0.0647 0.0543 1.1917 0.2336
departamentoSacatepéquez 0.1173 0.0466 2.5163 0.0120
departamentoChimaltenango −0.0323 0.0558 −0.5789 0.5627
departamentoEscuintla 0.1001 0.0578 1.7316 0.0836
departamentoSanta Rosa 0.1473 0.0583 2.5271 0.0116
departamentoSololá 0.0267 0.0704 0.3792 0.7046
departamentoTotonicapán 0.0603 0.0655 0.9204 0.3575
departamentoQuetzaltenango 0.0283 0.0551 0.5126 0.6083
departamentoSuchitepéquez −0.0946 0.0526 −1.7993 0.0722
departamentoRetalhuleu 0.0644 0.0625 1.0312 0.3026
departamentoSan Marcos 0.1274 0.0703 1.8134 0.0700
departamentoHuehuetenango 0.1711 0.0589 2.9063 0.0037
departamentoQuiché −0.0328 0.0593 −0.5538 0.5798
departamentoBaja Verapaz −0.0227 0.0594 −0.3823 0.7023
departamentoAlta Verapaz −0.1484 0.0685 −2.1655 0.0305
departamentoPetén −0.0993 0.0622 −1.5962 0.1107
departamentoIzabal 0.0206 0.0646 0.3189 0.7499
departamentoZacapa −0.0337 0.0667 −0.5048 0.6138
departamentoChiquimula −0.0892 0.0719 −1.2413 0.2147
departamentoJalapa 0.0129 0.0574 0.2245 0.8224
departamentoJutiapa 0.1230 0.0617 1.9933 0.0464
areaRural −0.0307 0.0253 −1.2135 0.2251
poly(miembros_hogar, 3)1 −36.4278 2.9892 −12.1863 <0.0001
poly(miembros_hogar, 3)2 2.4626 3.9804 0.6187 0.5362
poly(miembros_hogar, 3)3 6.1052 4.5193 1.3509 0.1770
propiedadPropia y pagandola a plazos −0.0008 0.0520 −0.0148 0.9882
propiedadAlquilada 0.0249 0.0332 0.7497 0.4536
propiedadCedida o prestada 0.0370 0.0326 1.1329 0.2575
propiedadOtro −0.1375 0.1640 −0.8384 0.4019
poly(grado_estudios_hogar, 3)1 4.4967 1.9216 2.3401 0.0194
poly(grado_estudios_hogar, 3)2 −3.0510 1.4990 −2.0354 0.0420
poly(grado_estudios_hogar, 3)3 −0.1705 1.5241 −0.1119 0.9109
tipo_viviendaApartamento −0.0172 0.1655 −0.1041 0.9171
tipo_viviendaCuarto en casa de vecindad −0.1928 0.1080 −1.7843 0.0746
tipo_viviendaRancho 0.5913 0.2133 2.7727 0.0056
tipo_viviendaCasa improvisada −0.0219 0.2072 −0.1056 0.9159
material_paredesBlock 0.1869 0.0792 2.3600 0.0184
material_paredesConcreto 0.2354 0.0981 2.4006 0.0165
material_paredesAdobe 0.1080 0.0849 1.2715 0.2038
material_paredesMadera 0.1022 0.0885 1.1541 0.2487
material_paredesLamina metalica 0.2308 0.2256 1.0229 0.3065
material_paredesBajareque −0.0941 0.1122 −0.8390 0.4016
material_paredesLepa, palo o caña −0.0595 0.2064 −0.2882 0.7732
material_paredesOtro 0.0752 0.1407 0.5343 0.5933
material_techoLamina metalica 0.0622 0.0311 2.0025 0.0454
material_techoAsbesto cemento −0.0656 0.1205 −0.5447 0.5861
material_techoTeja 0.0449 0.0578 0.7782 0.4366
material_techoPaja, palma o similar −0.4929 0.1924 −2.5623 0.0105
material_techoOtro −0.0302 0.2048 −0.1473 0.8829
material_pisoLadrillo de cemento 0.0504 0.0413 1.2195 0.2229
material_pisoLadrillo de barro 0.0046 0.1107 0.0415 0.9669
material_pisoTorta de cemento −0.0120 0.0290 −0.4149 0.6783
material_pisoMadera 0.1562 0.1691 0.9236 0.3559
material_pisoTierra −0.0622 0.0411 −1.5130 0.1305
poly(n_cuartos, 3)1 4.8150 3.0137 1.5977 0.1103
poly(n_cuartos, 3)2 −0.6595 2.1485 −0.3070 0.7589
poly(n_cuartos, 3)3 −0.7773 2.2032 −0.3528 0.7243
tipo_sanitarioUso compartido −0.0327 0.0370 −0.8828 0.3775
fuente_aguaTubería fuera de la vivienda 0.0011 0.0372 0.0289 0.9769
fuente_aguaChorro publico −0.0088 0.0773 −0.1138 0.9094
fuente_aguaPozo perforado 0.0427 0.0405 1.0536 0.2923
fuente_aguaRío, lago, manantial −0.1905 0.0721 −2.6433 0.0083
fuente_aguaCamion cisterna 0.0702 0.0643 1.0922 0.2749
fuente_aguaAgua de lluvia −0.0211 0.0791 −0.2669 0.7896
fuente_aguaOtro −0.1156 0.0550 −2.1017 0.0358
recoleccion_basuraLa tiran en cualquier lugar −0.0208 0.0574 −0.3614 0.7179
recoleccion_basuraServicio municipal 0.0036 0.0273 0.1308 0.8960
recoleccion_basuraServicio privado 0.0423 0.0345 1.2242 0.2211
electricidadNo −0.0269 0.0381 −0.7068 0.4798
televisorNo −0.0648 0.0212 −3.0546 0.0023
telefonia_celularNo −0.0389 0.0242 −1.6061 0.1085
computadoraNo −0.0605 0.0283 −2.1393 0.0326
Scatter chart of the full gamma model for zinc from non-maize sources. Observed zinc intake in milligrams per day on the x-axis, model-predicted intake on the y-axis. Points cluster along an upward diagonal, showing predictions broadly track observed values across the full model.
Figure 6: Observed vs predicted zinc intake from non-maize sources (full model)

Variable Selection

Table 7: Wald test results for predictor significance (zinc from non-maize)
Variable Significance Testing. Wald F-test results for zinc intake from non-maize model
Variable Significance Testing
Wald F-test results for zinc intake from non-maize model
variable f_statistic p_value significant
parentesco 10.53 <0.0001 *
sexo 161.57 <0.0001 *
poly(edad, 2) 347.33 <0.0001 *
departamento 3.61 <0.0001 *
area 1.47 0.2251
poly(miembros_hogar, 3) 120.74 <0.0001 *
propiedad 0.62 0.6502
poly(grado_estudios_hogar, 3) 2.61 0.0503
tipo_vivienda 5.33 0.0003 *
material_paredes 3.30 0.0010 *
material_techo 2.65 0.0215 *
material_piso 1.40 0.2218
poly(n_cuartos, 3) 1.22 0.3023
tipo_sanitario 0.78 0.3775
fuente_agua 1.91 0.0645
recoleccion_basura 0.66 0.5750
electricidad 0.50 0.4798
televisor 9.33 0.0023 *
telefonia_celular 2.58 0.1085
computadora 4.58 0.0326 *
ImportantVariables Retained

10 predictors significantly predict zinc intake from non-maize sources, drawing from the same set of demographic, geographic, socioeconomic and housing variables. The retained set differs from the maize model: the two outcomes are predicted by different subsets of the same candidate variables.

Refined Model

Table 8: Model coefficients for zinc intake from non-maize sources (refined model)
Zinc Intake from Non-Maize Sources (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Zinc Intake from Non-Maize Sources (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.6273 0.1108 14.6935 <0.0001
parentescoEsposo(a) o compañero(a) −0.2050 0.0671 −3.0554 0.0023
parentescoHermano(a) 0.0381 0.1088 0.3506 0.7260
parentescoHijo(a) −0.0868 0.0646 −1.3448 0.1789
parentescoJefe del hogar −0.1362 0.0666 −2.0457 0.0410
parentescoNieto(a) −0.1028 0.0732 −1.4044 0.1604
parentescoOtro no pariente −0.0191 0.2550 −0.0749 0.9403
parentescoOtro pariente −0.1193 0.0767 −1.5541 0.1204
parentescoPadre o madre −0.1329 0.0719 −1.8483 0.0648
parentescoSuegro(a) −0.0143 0.0812 −0.1766 0.8599
parentescoYerno o nuera 0.1013 0.0908 1.1147 0.2652
sexoMujer −0.1333 0.0106 −12.5344 <0.0001
poly(edad, 2)1 27.5131 2.7332 10.0663 <0.0001
poly(edad, 2)2 −33.3262 1.2846 −25.9425 <0.0001
departamentoEl Progreso 0.0261 0.0511 0.5111 0.6094
departamentoSacatepéquez 0.1034 0.0459 2.2523 0.0245
departamentoChimaltenango −0.0690 0.0533 −1.2950 0.1956
departamentoEscuintla 0.0703 0.0518 1.3580 0.1747
departamentoSanta Rosa 0.0870 0.0539 1.6156 0.1064
departamentoSololá −0.0278 0.0660 −0.4207 0.6740
departamentoTotonicapán −0.0026 0.0605 −0.0438 0.9651
departamentoQuetzaltenango −0.0304 0.0503 −0.6041 0.5459
departamentoSuchitepéquez −0.1339 0.0468 −2.8584 0.0043
departamentoRetalhuleu 0.0335 0.0567 0.5918 0.5541
departamentoSan Marcos 0.0441 0.0653 0.6746 0.5000
departamentoHuehuetenango 0.0988 0.0526 1.8801 0.0603
departamentoQuiché −0.0970 0.0538 −1.8011 0.0719
departamentoBaja Verapaz −0.0831 0.0581 −1.4322 0.1523
departamentoAlta Verapaz −0.2443 0.0627 −3.8944 0.0001
departamentoPetén −0.1472 0.0602 −2.4463 0.0146
departamentoIzabal −0.0233 0.0627 −0.3717 0.7102
departamentoZacapa −0.0906 0.0656 −1.3818 0.1673
departamentoChiquimula −0.1577 0.0692 −2.2804 0.0227
departamentoJalapa −0.0617 0.0529 −1.1679 0.2431
departamentoJutiapa 0.0751 0.0585 1.2829 0.1998
poly(miembros_hogar, 3)1 −37.0274 2.6447 −14.0006 <0.0001
poly(miembros_hogar, 3)2 1.9885 3.6923 0.5386 0.5903
poly(miembros_hogar, 3)3 6.3435 4.2467 1.4937 0.1355
tipo_viviendaApartamento −0.0168 0.1692 −0.0994 0.9208
tipo_viviendaCuarto en casa de vecindad −0.2232 0.0998 −2.2368 0.0255
tipo_viviendaRancho 0.5335 0.2142 2.4913 0.0128
tipo_viviendaCasa improvisada −0.0526 0.2061 −0.2554 0.7985
material_paredesBlock 0.1514 0.0822 1.8424 0.0656
material_paredesConcreto 0.2017 0.1002 2.0117 0.0444
material_paredesAdobe 0.0282 0.0871 0.3237 0.7462
material_paredesMadera −0.0024 0.0893 −0.0268 0.9786
material_paredesLamina metalica 0.1682 0.2263 0.7435 0.4573
material_paredesBajareque −0.1926 0.1144 −1.6831 0.0926
material_paredesLepa, palo o caña −0.1858 0.2045 −0.9083 0.3639
material_paredesOtro −0.0197 0.1392 −0.1416 0.8874
material_techoLamina metalica 0.0244 0.0271 0.8971 0.3698
material_techoAsbesto cemento −0.0519 0.1245 −0.4165 0.6771
material_techoTeja 0.0173 0.0546 0.3164 0.7517
material_techoPaja, palma o similar −0.5211 0.1921 −2.7125 0.0068
material_techoOtro −0.0952 0.2016 −0.4721 0.6369
televisorNo −0.0865 0.0215 −4.0326 <0.0001
computadoraNo −0.0935 0.0270 −3.4556 0.0006
Scatter chart of the refined gamma model for zinc from non-maize sources. Observed zinc intake in milligrams per day on the x-axis, model-predicted intake on the y-axis. Points follow an upward diagonal comparable to the full model, confirming that reducing to significant predictors retains predictive accuracy.
Figure 7: Observed vs predicted zinc intake from non-maize sources (refined model)

Model Diagnostics

Panel of regression diagnostic plots for the refined zinc-from-non-maize gamma model, covering residual behaviour, leverage, and predictor collinearity. Residuals show no systematic pattern and are approximately normal, no observations are unduly influential, and the collinearity panel plots each term's degrees-of-freedom adjusted variance inflation factor against shaded low, moderate and high reference bands.
Figure 8: Diagnostic plots for zinc from non-maize sources model

Summary

Final Model Performance

Table 9: Final refined model performance metrics
Final Model Performance. Refined gamma regression with log link
Final Model Performance
Refined gamma regression with log link
Metric Zinc from maize Zinc from non-maize
N observations 39,661 39,661
N predictors 59 56
Pseudo-R² (McFadden)1 0.191 0.155
Pseudo-R² (Cragg-Uhler)2 0.332 0.207
AIC 53,434 25,395
Dispersion 1.653 0.548
1 Pseudo-R² (McFadden) = 1 − (residual deviance / null deviance). Conservative measure; values above 0.2 are conventionally considered good for GLMs.
2 Pseudo-R² (Cragg-Uhler), also known as Nagelkerke's R², is normalized to a [0, 1] range and generally yields higher values than McFadden. Both measures are reported for transparency.

Model Comparison

Outcome Final Predictors Retained predictors (examples)
Zinc from maize 11 variables Age, department, education, area, garbage collection
Zinc from non-maize 10 variables Age, household size, dwelling type, wall materials

Key Findings

  1. Higher maize share for zinc: The proportion of zinc intake from maize is higher than for iron (see Daily Nutrient Intake by Source in Module 1), which makes a larger fraction of zinc intake biofortification-modifiable

  2. Geographic variation: Department is retained in both models, consistent with regional variation in dietary patterns

  3. Differential role of area: Urban/rural area is retained in the maize model and not in the non-maize model, so it carries predictive power for one intake source and not the other

  4. Service and asset variables: Garbage collection and computer ownership are retained in the maize model, television and computer ownership in the non-maize model

Application

These models will be applied to SIVESNU 2018 children to predict their zinc intake profiles based on their demographic and socioeconomic characteristics. The predicted values enable linking nutritional status to stunting outcomes.

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