Transfer Model: Iron Intake

Module 3: Transfer Models

Why Model Iron?

Iron is an essential micronutrient for child development, and iron deficiency may contribute to poor growth outcomes, including stunting, particularly when combined with other forms of undernutrition. In Guatemala, maize is a substantial dietary source of iron (see Daily Nutrient Intake by Source in Module 1). By modeling iron intake from maize and non-maize sources separately, we can:

  1. Simulate biofortification scenarios — Predict how higher-content maize varieties would change total iron 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 iron intake is largest

Modeling Approach

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

  • Positive and continuous — People consume some amount of iron 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 iron 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 Iron Intake from Maize

Distribution Selection

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

Table 1: Distribution fit comparison for iron 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 −138,515.3857 277,034.7714 277,051.9536 0.0617 51.3881 275.4452
Lognormal −138,876.6997 277,757.3994 277,774.5816 0.0300 12.0083 104.2879
Exponential −139,687.8508 279,377.7015 279,386.2926 0.1151 208.6978 1,121.6871
Four-panel goodness-of-fit grid for iron intake from maize. The top-left panel overlays a histogram of intake (density on the y-axis) with a fitted gamma curve; the top-right is a quantile-quantile plot of empirical against theoretical quantiles; the bottom-left compares the empirical and theoretical cumulative distributions; and the bottom-right is a probability-probability plot. Across all panels the points and curves track the gamma reference line closely, confirming that the right-skewed intake is well described by a gamma distribution.
Figure 1: Distribution assessment for iron 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 iron intake from maize.

Table 2: Model coefficients for iron intake from maize (full model)
Iron Intake from Maize (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Iron Intake from Maize (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.2745 0.1979 6.4405 <0.0001
parentescoEsposo(a) o compañero(a) 0.1573 0.0832 1.8910 0.0588
parentescoHermano(a) 0.2648 0.1470 1.8017 0.0718
parentescoHijo(a) 0.4010 0.0751 5.3392 <0.0001
parentescoJefe del hogar 0.1743 0.0789 2.2089 0.0273
parentescoNieto(a) 0.2680 0.0858 3.1220 0.0018
parentescoOtro no pariente 0.3894 0.4096 0.9507 0.3419
parentescoOtro pariente 0.3120 0.1246 2.5046 0.0124
parentescoPadre o madre 0.3523 0.0866 4.0691 <0.0001
parentescoSuegro(a) 0.3385 0.1346 2.5153 0.0120
parentescoYerno o nuera 0.3461 0.1425 2.4288 0.0153
sexoMujer −0.1276 0.0201 −6.3415 <0.0001
poly(edad, 2)1 42.6192 4.4057 9.6737 <0.0001
poly(edad, 2)2 −32.1953 2.0881 −15.4186 <0.0001
departamentoEl Progreso 0.2394 0.1253 1.9107 0.0562
departamentoSacatepéquez 0.2578 0.1024 2.5188 0.0119
departamentoChimaltenango 0.4615 0.1005 4.5934 <0.0001
departamentoEscuintla 0.1346 0.1049 1.2827 0.1998
departamentoSanta Rosa 0.4101 0.1227 3.3420 0.0009
departamentoSololá 0.5788 0.1196 4.8378 <0.0001
departamentoTotonicapán 0.7066 0.1118 6.3201 <0.0001
departamentoQuetzaltenango 0.7251 0.1132 6.4056 <0.0001
departamentoSuchitepéquez 0.4431 0.0963 4.6017 <0.0001
departamentoRetalhuleu 0.5643 0.1137 4.9632 <0.0001
departamentoSan Marcos 0.6616 0.1157 5.7172 <0.0001
departamentoHuehuetenango 0.6602 0.1062 6.2141 <0.0001
departamentoQuiché 0.7746 0.1042 7.4359 <0.0001
departamentoBaja Verapaz 0.7609 0.1108 6.8663 <0.0001
departamentoAlta Verapaz 0.4656 0.1162 4.0049 <0.0001
departamentoPetén 0.6658 0.1062 6.2701 <0.0001
departamentoIzabal 0.4848 0.1164 4.1650 <0.0001
departamentoZacapa 0.1198 0.1218 0.9836 0.3255
departamentoChiquimula 0.4809 0.1236 3.8909 0.0001
departamentoJalapa 0.7124 0.1186 6.0063 <0.0001
departamentoJutiapa 0.3609 0.1068 3.3805 0.0007
areaRural 0.1522 0.0399 3.8109 0.0001
poly(miembros_hogar, 3)1 0.5198 3.5775 0.1453 0.8845
poly(miembros_hogar, 3)2 −1.3786 3.0365 −0.4540 0.6499
poly(miembros_hogar, 3)3 −0.8687 3.3503 −0.2593 0.7954
propiedadPropia y pagandola a plazos −0.1540 0.1331 −1.1565 0.2477
propiedadAlquilada −0.1254 0.0733 −1.7109 0.0873
propiedadCedida o prestada −0.0009 0.0571 −0.0160 0.9872
propiedadOtro −0.4578 0.4050 −1.1304 0.2585
poly(grado_estudios_hogar, 3)1 −21.1350 4.9867 −4.2383 <0.0001
poly(grado_estudios_hogar, 3)2 0.5198 4.5183 0.1151 0.9084
poly(grado_estudios_hogar, 3)3 −3.3924 4.5256 −0.7496 0.4536
tipo_viviendaApartamento −0.3162 0.1797 −1.7597 0.0787
tipo_viviendaCuarto en casa de vecindad 0.3112 0.3057 1.0183 0.3087
tipo_viviendaRancho −1.3704 0.2698 −5.0797 <0.0001
tipo_viviendaCasa improvisada 0.2119 0.2971 0.7133 0.4758
material_paredesBlock 0.2445 0.1479 1.6528 0.0986
material_paredesConcreto 0.2800 0.2741 1.0216 0.3072
material_paredesAdobe 0.3877 0.1553 2.4973 0.0126
material_paredesMadera 0.2689 0.1634 1.6454 0.1001
material_paredesLamina metalica 0.0251 0.3362 0.0747 0.9405
material_paredesBajareque 0.6497 0.1802 3.6057 0.0003
material_paredesLepa, palo o caña 0.5270 0.2909 1.8114 0.0703
material_paredesOtro −0.0716 0.3894 −0.1838 0.8542
material_techoLamina metalica −0.0247 0.0730 −0.3384 0.7351
material_techoAsbesto cemento −0.0272 0.3292 −0.0826 0.9342
material_techoTeja −0.0094 0.0977 −0.0965 0.9231
material_techoPaja, palma o similar 1.3118 0.2731 4.8040 <0.0001
material_techoOtro −0.3243 0.4478 −0.7242 0.4691
material_pisoLadrillo de cemento −0.0120 0.0758 −0.1582 0.8743
material_pisoLadrillo de barro 0.1486 0.3803 0.3908 0.6960
material_pisoTorta de cemento 0.0608 0.0592 1.0272 0.3045
material_pisoMadera −0.0544 0.1648 −0.3298 0.7416
material_pisoTierra 0.0494 0.0656 0.7529 0.4516
poly(n_cuartos, 3)1 −5.6225 4.0876 −1.3755 0.1692
poly(n_cuartos, 3)2 −3.2144 3.7737 −0.8518 0.3945
poly(n_cuartos, 3)3 −5.8370 3.9402 −1.4814 0.1387
tipo_sanitarioUso compartido 0.1036 0.0715 1.4492 0.1475
fuente_aguaTubería fuera de la vivienda 0.1107 0.0552 2.0063 0.0450
fuente_aguaChorro publico 0.1259 0.0837 1.5039 0.1329
fuente_aguaPozo perforado 0.0774 0.0486 1.5926 0.1115
fuente_aguaRío, lago, manantial −0.0287 0.0770 −0.3727 0.7094
fuente_aguaCamion cisterna −0.2027 0.1264 −1.6038 0.1090
fuente_aguaAgua de lluvia 0.1197 0.1467 0.8162 0.4146
fuente_aguaOtro 0.0958 0.1083 0.8848 0.3764
recoleccion_basuraLa tiran en cualquier lugar −0.1771 0.0672 −2.6339 0.0085
recoleccion_basuraServicio municipal −0.3359 0.0624 −5.3854 <0.0001
recoleccion_basuraServicio privado −0.3979 0.0800 −4.9732 <0.0001
electricidadNo 0.0019 0.0463 0.0418 0.9667
televisorNo −0.0167 0.0378 −0.4428 0.6580
telefonia_celularNo −0.0244 0.0401 −0.6094 0.5424
computadoraNo 0.2044 0.0527 3.8747 0.0001
Scatter plot with observed iron from maize (mg/day) on the x-axis and predicted iron from maize (mg/day) on the y-axis for the full model with all 20 candidate predictors. Points follow a positive, upward-sloping cloud, showing predictions rise with observed intake and track the data across the range.
Figure 2: Observed vs predicted iron 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 (iron from maize)
Variable Significance Testing. Wald F-test results for iron intake from maize model
Variable Significance Testing
Wald F-test results for iron intake from maize model
variable f_statistic p_value significant
parentesco 10.73 <0.0001 *
sexo 40.22 <0.0001 *
poly(edad, 2) 144.53 <0.0001 *
departamento 6.58 <0.0001 *
area 14.52 0.0001 *
poly(miembros_hogar, 3) 0.08 0.9698
propiedad 1.28 0.2758
poly(grado_estudios_hogar, 3) 6.25 0.0003 *
tipo_vivienda 8.30 <0.0001 *
material_paredes 3.87 0.0002 *
material_techo 6.26 <0.0001 *
material_piso 0.42 0.8322
poly(n_cuartos, 3) 1.54 0.2024
tipo_sanitario 2.10 0.1475
fuente_agua 1.57 0.1407
recoleccion_basura 14.78 <0.0001 *
electricidad 0.00 0.9667
televisor 0.20 0.6580
telefonia_celular 0.37 0.5424
computadora 15.01 0.0001 *
ImportantVariables Retained

11 predictors show significant relationships with iron intake from maize, spanning demographic, geographic, socioeconomic, housing and asset categories. Variables that do not significantly predict iron 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 iron intake from maize (refined model)
Iron Intake from Maize (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Iron Intake from Maize (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.2366 0.1923 6.4322 <0.0001
parentescoEsposo(a) o compañero(a) 0.1775 0.0836 2.1232 0.0339
parentescoHermano(a) 0.2878 0.1510 1.9061 0.0568
parentescoHijo(a) 0.4073 0.0764 5.3351 <0.0001
parentescoJefe del hogar 0.1908 0.0812 2.3508 0.0189
parentescoNieto(a) 0.2616 0.0880 2.9732 0.0030
parentescoOtro no pariente 0.4411 0.4083 1.0803 0.2802
parentescoOtro pariente 0.3028 0.1234 2.4544 0.0142
parentescoPadre o madre 0.3400 0.0877 3.8774 0.0001
parentescoSuegro(a) 0.3506 0.1359 2.5792 0.0100
parentescoYerno o nuera 0.3475 0.1497 2.3211 0.0204
sexoMujer −0.1306 0.0216 −6.0457 <0.0001
poly(edad, 2)1 40.6937 4.5551 8.9336 <0.0001
poly(edad, 2)2 −31.6591 2.2960 −13.7888 <0.0001
departamentoEl Progreso 0.2637 0.1235 2.1346 0.0330
departamentoSacatepéquez 0.2904 0.1034 2.8087 0.0050
departamentoChimaltenango 0.4912 0.1007 4.8788 <0.0001
departamentoEscuintla 0.1826 0.1050 1.7396 0.0822
departamentoSanta Rosa 0.4445 0.1249 3.5598 0.0004
departamentoSololá 0.6083 0.1181 5.1505 <0.0001
departamentoTotonicapán 0.7343 0.1094 6.7091 <0.0001
departamentoQuetzaltenango 0.7565 0.1121 6.7474 <0.0001
departamentoSuchitepéquez 0.4929 0.0946 5.2083 <0.0001
departamentoRetalhuleu 0.6084 0.1130 5.3851 <0.0001
departamentoSan Marcos 0.7166 0.1149 6.2383 <0.0001
departamentoHuehuetenango 0.7222 0.1092 6.6143 <0.0001
departamentoQuiché 0.8137 0.1038 7.8399 <0.0001
departamentoBaja Verapaz 0.7810 0.1081 7.2270 <0.0001
departamentoAlta Verapaz 0.5267 0.1143 4.6070 <0.0001
departamentoPetén 0.7058 0.1029 6.8584 <0.0001
departamentoIzabal 0.5124 0.1160 4.4182 <0.0001
departamentoZacapa 0.1509 0.1202 1.2553 0.2096
departamentoChiquimula 0.5195 0.1257 4.1321 <0.0001
departamentoJalapa 0.7343 0.1205 6.0954 <0.0001
departamentoJutiapa 0.3840 0.1063 3.6125 0.0003
areaRural 0.1598 0.0399 4.0002 <0.0001
poly(grado_estudios_hogar, 3)1 −21.6872 5.0367 −4.3059 <0.0001
poly(grado_estudios_hogar, 3)2 −0.6148 4.4627 −0.1378 0.8904
poly(grado_estudios_hogar, 3)3 −3.7338 4.5596 −0.8189 0.4130
tipo_viviendaApartamento −0.3408 0.1864 −1.8287 0.0677
tipo_viviendaCuarto en casa de vecindad 0.3872 0.3297 1.1743 0.2405
tipo_viviendaRancho −1.4776 0.2583 −5.7193 <0.0001
tipo_viviendaCasa improvisada 0.2346 0.2961 0.7921 0.4284
material_paredesBlock 0.2388 0.1521 1.5700 0.1166
material_paredesConcreto 0.2182 0.2694 0.8100 0.4181
material_paredesAdobe 0.3990 0.1570 2.5411 0.0112
material_paredesMadera 0.2780 0.1618 1.7180 0.0860
material_paredesLamina metalica 0.0303 0.3426 0.0883 0.9296
material_paredesBajareque 0.6629 0.1796 3.6905 0.0002
material_paredesLepa, palo o caña 0.5271 0.2968 1.7760 0.0759
material_paredesOtro −0.0467 0.3920 −0.1191 0.9052
material_techoLamina metalica 0.0241 0.0705 0.3413 0.7329
material_techoAsbesto cemento −0.0414 0.3154 −0.1313 0.8956
material_techoTeja 0.0408 0.0965 0.4231 0.6723
material_techoPaja, palma o similar 1.4800 0.2643 5.6001 <0.0001
material_techoOtro −0.2386 0.4681 −0.5097 0.6103
recoleccion_basuraLa tiran en cualquier lugar −0.1734 0.0669 −2.5932 0.0096
recoleccion_basuraServicio municipal −0.3591 0.0597 −6.0151 <0.0001
recoleccion_basuraServicio privado −0.4273 0.0808 −5.2885 <0.0001
computadoraNo 0.2118 0.0548 3.8664 0.0001
Scatter plot with observed iron from maize (mg/day) on the x-axis and predicted iron from maize (mg/day) on the y-axis for the refined model that keeps only the significant predictors. Points follow the same positive trend as the full model, indicating the simpler model preserves predictive accuracy.
Figure 3: Observed vs predicted iron intake from maize (refined model)

Model Diagnostics

We verify the model meets statistical assumptions:

Grid of regression diagnostic plots for the refined gamma model of iron from maize, including residuals versus fitted values, a normal quantile-quantile plot of the residuals, and leverage and collinearity checks. The residuals scatter without any systematic pattern and fall close to the reference line, no observations stand out as high-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 iron 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 10.5, 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 Iron Intake from Non-Maize Sources

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

Distribution Selection

Table 5: Distribution fit comparison for iron 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 −126,317.1061 252,638.2123 252,655.3945 0.0245 6.6475 43.6880
Lognormal −130,785.5689 261,575.1378 261,592.3201 0.0787 94.3826 585.8780
Exponential −129,148.5596 258,299.1192 258,307.7104 0.1299 235.0764 1,294.3827
Four-panel goodness-of-fit grid for iron intake from non-maize sources. The top-left panel overlays a histogram of intake (density on the y-axis) with a fitted gamma curve; the top-right is a quantile-quantile plot of empirical against theoretical quantiles; the bottom-left compares the empirical and theoretical cumulative distributions; and the bottom-right is a probability-probability plot. The points and curves again follow the gamma reference line closely, confirming a gamma distribution best fits this right-skewed intake.
Figure 5: Distribution assessment for iron intake from non-maize sources
ImportantDistribution Selection

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

Full Model

Table 6: Model coefficients for iron intake from non-maize sources (full model)
Iron Intake from Non-Maize Sources (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Iron 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) 2.2223 0.1106 20.0866 <0.0001
parentescoEsposo(a) o compañero(a) −0.2169 0.0661 −3.2827 0.0011
parentescoHermano(a) −0.0422 0.1103 −0.3824 0.7022
parentescoHijo(a) −0.0864 0.0646 −1.3376 0.1813
parentescoJefe del hogar −0.1560 0.0652 −2.3928 0.0169
parentescoNieto(a) −0.1239 0.0711 −1.7417 0.0818
parentescoOtro no pariente −0.1395 0.2306 −0.6049 0.5453
parentescoOtro pariente −0.1218 0.0782 −1.5570 0.1197
parentescoPadre o madre −0.1313 0.0714 −1.8394 0.0661
parentescoSuegro(a) −0.0051 0.0787 −0.0644 0.9487
parentescoYerno o nuera 0.0626 0.0846 0.7409 0.4589
sexoMujer −0.1423 0.0105 −13.5315 <0.0001
poly(edad, 2)1 30.0468 2.7841 10.7922 <0.0001
poly(edad, 2)2 −33.9647 1.2391 −27.4114 <0.0001
departamentoEl Progreso 0.0710 0.0485 1.4628 0.1438
departamentoSacatepéquez 0.1023 0.0412 2.4846 0.0131
departamentoChimaltenango −0.0108 0.0467 −0.2323 0.8164
departamentoEscuintla 0.0872 0.0519 1.6820 0.0928
departamentoSanta Rosa 0.1021 0.0530 1.9265 0.0542
departamentoSololá 0.0111 0.0670 0.1655 0.8685
departamentoTotonicapán −0.0012 0.0582 −0.0206 0.9836
departamentoQuetzaltenango 0.0127 0.0526 0.2412 0.8094
departamentoSuchitepéquez −0.0301 0.0467 −0.6443 0.5195
departamentoRetalhuleu 0.0475 0.0602 0.7896 0.4299
departamentoSan Marcos 0.0874 0.0680 1.2852 0.1989
departamentoHuehuetenango 0.1883 0.0584 3.2273 0.0013
departamentoQuiché −0.0104 0.0564 −0.1848 0.8534
departamentoBaja Verapaz −0.0719 0.0562 −1.2784 0.2013
departamentoAlta Verapaz −0.1898 0.0669 −2.8347 0.0047
departamentoPetén −0.1216 0.0575 −2.1148 0.0346
departamentoIzabal −0.0435 0.0598 −0.7279 0.4668
departamentoZacapa −0.0897 0.0571 −1.5708 0.1165
departamentoChiquimula −0.1221 0.0633 −1.9299 0.0538
departamentoJalapa 0.0197 0.0570 0.3459 0.7295
departamentoJutiapa 0.0753 0.0566 1.3319 0.1831
areaRural −0.0014 0.0238 −0.0570 0.9545
poly(miembros_hogar, 3)1 −36.7121 2.1553 −17.0337 <0.0001
poly(miembros_hogar, 3)2 0.5748 2.3651 0.2430 0.8080
poly(miembros_hogar, 3)3 4.3754 2.7318 1.6016 0.1095
propiedadPropia y pagandola a plazos −0.0318 0.0506 −0.6286 0.5297
propiedadAlquilada 0.0127 0.0309 0.4107 0.6813
propiedadCedida o prestada 0.0500 0.0288 1.7363 0.0827
propiedadOtro −0.2177 0.1561 −1.3947 0.1633
poly(grado_estudios_hogar, 3)1 0.5136 1.8665 0.2752 0.7832
poly(grado_estudios_hogar, 3)2 −2.7750 1.4116 −1.9659 0.0495
poly(grado_estudios_hogar, 3)3 −1.1041 1.4306 −0.7718 0.4404
tipo_viviendaApartamento 0.0023 0.1663 0.0135 0.9892
tipo_viviendaCuarto en casa de vecindad −0.1512 0.1166 −1.2974 0.1947
tipo_viviendaRancho 0.6636 0.2025 3.2775 0.0011
tipo_viviendaCasa improvisada 0.0364 0.1941 0.1876 0.8512
material_paredesBlock 0.2097 0.0768 2.7295 0.0064
material_paredesConcreto 0.2422 0.0902 2.6847 0.0073
material_paredesAdobe 0.1464 0.0818 1.7900 0.0737
material_paredesMadera 0.1291 0.0847 1.5246 0.1276
material_paredesLamina metalica 0.2423 0.2123 1.1417 0.2538
material_paredesBajareque −0.0212 0.1010 −0.2102 0.8335
material_paredesLepa, palo o caña 0.0978 0.1902 0.5139 0.6074
material_paredesOtro 0.1028 0.1404 0.7322 0.4642
material_techoLamina metalica 0.0707 0.0291 2.4308 0.0152
material_techoAsbesto cemento −0.1022 0.1160 −0.8818 0.3780
material_techoTeja 0.0503 0.0533 0.9435 0.3456
material_techoPaja, palma o similar −0.5252 0.1813 −2.8975 0.0038
material_techoOtro 0.1179 0.1989 0.5929 0.5533
material_pisoLadrillo de cemento 0.0600 0.0392 1.5309 0.1260
material_pisoLadrillo de barro 0.0136 0.1268 0.1069 0.9148
material_pisoTorta de cemento 0.0052 0.0275 0.1877 0.8511
material_pisoMadera 0.1312 0.1550 0.8461 0.3977
material_pisoTierra −0.0116 0.0385 −0.3030 0.7620
poly(n_cuartos, 3)1 2.6246 2.4032 1.0921 0.2750
poly(n_cuartos, 3)2 −1.6400 2.0035 −0.8186 0.4132
poly(n_cuartos, 3)3 0.2101 1.7831 0.1178 0.9062
tipo_sanitarioUso compartido −0.0347 0.0328 −1.0571 0.2907
fuente_aguaTubería fuera de la vivienda 0.0132 0.0319 0.4155 0.6779
fuente_aguaChorro publico −0.0518 0.0800 −0.6466 0.5180
fuente_aguaPozo perforado 0.0207 0.0326 0.6341 0.5261
fuente_aguaRío, lago, manantial −0.1859 0.0655 −2.8397 0.0046
fuente_aguaCamion cisterna 0.0443 0.0572 0.7751 0.4384
fuente_aguaAgua de lluvia −0.0136 0.0814 −0.1675 0.8670
fuente_aguaOtro −0.0688 0.0534 −1.2898 0.1974
recoleccion_basuraLa tiran en cualquier lugar −0.0262 0.0527 −0.4969 0.6193
recoleccion_basuraServicio municipal −0.0185 0.0283 −0.6563 0.5117
recoleccion_basuraServicio privado 0.0177 0.0338 0.5232 0.6009
electricidadNo −0.0345 0.0345 −0.9995 0.3177
televisorNo −0.0509 0.0200 −2.5432 0.0111
telefonia_celularNo −0.0496 0.0226 −2.1919 0.0286
computadoraNo −0.0407 0.0272 −1.4967 0.1347
Scatter plot with observed iron from non-maize sources (mg/day) on the x-axis and predicted iron from non-maize sources (mg/day) on the y-axis for the full model with all candidate predictors. Points form a positive, upward-sloping cloud, showing predictions increase with observed intake across the range.
Figure 6: Observed vs predicted iron intake from non-maize sources (full model)

Variable Selection

Table 7: Wald test results for predictor significance (iron from non-maize)
Variable Significance Testing. Wald F-test results for iron intake from non-maize model
Variable Significance Testing
Wald F-test results for iron intake from non-maize model
variable f_statistic p_value significant
parentesco 12.52 <0.0001 *
sexo 183.10 <0.0001 *
poly(edad, 2) 384.79 <0.0001 *
departamento 3.93 <0.0001 *
area 0.00 0.9545
poly(miembros_hogar, 3) 139.52 <0.0001 *
propiedad 1.48 0.2071
poly(grado_estudios_hogar, 3) 2.12 0.0963
tipo_vivienda 5.51 0.0002 *
material_paredes 3.04 0.0022 *
material_techo 4.29 0.0007 *
material_piso 0.78 0.5634
poly(n_cuartos, 3) 0.69 0.5597
tipo_sanitario 1.12 0.2907
fuente_agua 1.58 0.1370
recoleccion_basura 0.51 0.6756
electricidad 1.00 0.3177
televisor 6.47 0.0111 *
telefonia_celular 4.80 0.0286 *
computadora 2.24 0.1347
ImportantVariables Retained

10 predictors significantly predict iron 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 iron intake from non-maize sources (refined model)
Iron Intake from Non-Maize Sources (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Iron 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) 2.2722 0.1054 21.5567 <0.0001
parentescoEsposo(a) o compañero(a) −0.2342 0.0673 −3.4819 0.0005
parentescoHermano(a) −0.0425 0.1113 −0.3813 0.7030
parentescoHijo(a) −0.0951 0.0658 −1.4466 0.1482
parentescoJefe del hogar −0.1735 0.0667 −2.6005 0.0094
parentescoNieto(a) −0.1309 0.0724 −1.8088 0.0707
parentescoOtro no pariente −0.1345 0.2423 −0.5554 0.5787
parentescoOtro pariente −0.1322 0.0795 −1.6620 0.0967
parentescoPadre o madre −0.1342 0.0726 −1.8493 0.0646
parentescoSuegro(a) −0.0220 0.0792 −0.2782 0.7809
parentescoYerno o nuera 0.0430 0.0851 0.5045 0.6140
sexoMujer −0.1426 0.0109 −13.0350 <0.0001
poly(edad, 2)1 31.2017 2.8050 11.1234 <0.0001
poly(edad, 2)2 −34.3036 1.2683 −27.0478 <0.0001
departamentoEl Progreso 0.0446 0.0483 0.9248 0.3553
departamentoSacatepéquez 0.0789 0.0415 1.9002 0.0576
departamentoChimaltenango −0.0312 0.0454 −0.6864 0.4926
departamentoEscuintla 0.0677 0.0492 1.3760 0.1690
departamentoSanta Rosa 0.0724 0.0508 1.4266 0.1539
departamentoSololá −0.0234 0.0649 −0.3599 0.7189
departamentoTotonicapán −0.0295 0.0549 −0.5371 0.5913
departamentoQuetzaltenango −0.0184 0.0504 −0.3657 0.7146
departamentoSuchitepéquez −0.0502 0.0433 −1.1593 0.2465
departamentoRetalhuleu 0.0342 0.0564 0.6059 0.5447
departamentoSan Marcos 0.0434 0.0647 0.6716 0.5019
departamentoHuehuetenango 0.1475 0.0525 2.8098 0.0050
departamentoQuiché −0.0419 0.0527 −0.7941 0.4273
departamentoBaja Verapaz −0.1138 0.0555 −2.0509 0.0405
departamentoAlta Verapaz −0.2508 0.0616 −4.0737 <0.0001
departamentoPetén −0.1441 0.0561 −2.5667 0.0104
departamentoIzabal −0.0570 0.0587 −0.9698 0.3323
departamentoZacapa −0.1223 0.0562 −2.1753 0.0298
departamentoChiquimula −0.1606 0.0614 −2.6151 0.0090
departamentoJalapa −0.0168 0.0545 −0.3090 0.7574
departamentoJutiapa 0.0528 0.0538 0.9809 0.3268
poly(miembros_hogar, 3)1 −36.8301 2.0651 −17.8342 <0.0001
poly(miembros_hogar, 3)2 0.2132 2.2969 0.0928 0.9260
poly(miembros_hogar, 3)3 4.5470 2.7134 1.6757 0.0940
tipo_viviendaApartamento 0.0033 0.1781 0.0187 0.9851
tipo_viviendaCuarto en casa de vecindad −0.1761 0.1115 −1.5794 0.1145
tipo_viviendaRancho 0.5942 0.2047 2.9031 0.0038
tipo_viviendaCasa improvisada 0.0005 0.1947 0.0023 0.9981
material_paredesBlock 0.1912 0.0795 2.4058 0.0163
material_paredesConcreto 0.2084 0.0916 2.2739 0.0231
material_paredesAdobe 0.1067 0.0841 1.2685 0.2048
material_paredesMadera 0.0704 0.0863 0.8156 0.4149
material_paredesLamina metalica 0.2278 0.2146 1.0612 0.2888
material_paredesBajareque −0.0788 0.1021 −0.7713 0.4407
material_paredesLepa, palo o caña 0.0358 0.1884 0.1901 0.8493
material_paredesOtro 0.0630 0.1369 0.4605 0.6452
material_techoLamina metalica 0.0611 0.0265 2.3047 0.0213
material_techoAsbesto cemento −0.0914 0.1193 −0.7665 0.4435
material_techoTeja 0.0432 0.0508 0.8507 0.3951
material_techoPaja, palma o similar −0.5044 0.1838 −2.7442 0.0061
material_techoOtro 0.0899 0.1971 0.4562 0.6483
televisorNo −0.0704 0.0200 −3.5217 0.0004
telefonia_celularNo −0.0495 0.0232 −2.1350 0.0329
Scatter plot with observed iron from non-maize sources (mg/day) on the x-axis and predicted iron from non-maize sources (mg/day) on the y-axis for the refined model that keeps only the significant predictors. Points follow the same positive trend as the full model, showing the simpler model retains predictive accuracy.
Figure 7: Observed vs predicted iron intake from non-maize sources (refined model)

Model Diagnostics

Grid of regression diagnostic plots for the refined gamma model of iron from non-maize sources, including residuals versus fitted values, a normal quantile-quantile plot of the residuals, and leverage and collinearity checks. The residuals scatter without systematic pattern and stay close to the reference line, with no high-leverage points, 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 iron 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 Iron from maize Iron from non-maize
N observations 39,780 39,780
N predictors 59 56
Pseudo-R² (McFadden)1 0.187 0.161
Pseudo-R² (Cragg-Uhler)2 0.326 0.207
AIC 53,823 21,706
Dispersion 1.660 0.463
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)
Iron from maize 11 variables Age, department, education, area
Iron from non-maize 10 variables Age, household size, dwelling type

Key Findings

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

  2. 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

  3. Household size: Household size is retained in the non-maize model only

Application

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

Back to top