Transfer Model: Energy Intake

Module 3: Transfer Models

Why Model Energy?

Energy intake (kilocalories) is fundamental for child growth and development. Where energy intake is low, the utilization of dietary protein and micronutrients for growth is constrained, so energy adequacy conditions the interpretation of the other nutrient outcomes. By modeling energy intake from maize and non-maize sources separately, we can:

  1. Simulate biofortification scenarios — Understand how energy from maize contributes to total energy intake
  2. Preserve baseline non-maize intake — Keep other dietary sources constant when modeling interventions
  3. Contextualize nutrient adequacy — Energy intake bears on the interpretation of the other nutrient indicators
NoteRole of Energy in Stunting

Biofortification targets micronutrient content and protein quality, and energy adequacy provides the context for interpreting those nutrient impacts. Where energy intake is inadequate, the benefit a child draws from higher nutrient density in the food supply is correspondingly limited.

Modeling Approach

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

  • Positive and continuous — People consume some amount of calories 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 energy 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 using the standard Tukey method (Q3 + 1.5×IQR). The threshold suits macronutrients:

  • Energy intake distributions are more stable
  • Extreme values are consistent with measurement error
  • Energy intakes have natural biological limits

Survey Design

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

Modeling Energy Intake from Maize

Distribution Selection

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

Table 1: Distribution fit comparison for energy intake from maize
Distribution Fit Comparison. Goodness-of-fit statistics for Gamma and Lognormal distributions
Distribution Fit Comparison
Goodness-of-fit statistics for Gamma and Lognormal distributions
Distribution Log-Likelihood
Information Criteria
Goodness-of-Fit Statistics
AIC BIC Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling
Gamma −283,859.8067 567,723.6134 567,740.5594 0.0337 12.6063 79.3804
Lognormal −285,865.7090 571,735.4180 571,752.3640 0.0523 30.3720 223.4337
Four goodness-of-fit panels comparing observed energy intake from maize against a fitted Gamma distribution. Top left, a histogram of intake overlaid with the theoretical Gamma density curve. Top right, a quantile-quantile plot; bottom left, empirical versus theoretical cumulative distribution curves; bottom right, a probability-probability plot. Points and curves track the reference lines closely, indicating the Gamma distribution fits the right-skewed intake data well.
Figure 1: Distribution assessment for energy 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 energy intake from maize.

Table 2: Model coefficients for energy intake from maize (full model)
Energy Intake from Maize (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Energy Intake from Maize (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 6.1117 0.1878 32.5421 <0.0001
parentescoEsposo(a) o compañero(a) 0.1283 0.0691 1.8559 0.0637
parentescoHermano(a) 0.3288 0.1507 2.1825 0.0292
parentescoHijo(a) 0.2608 0.0638 4.0853 <0.0001
parentescoJefe del hogar 0.1280 0.0675 1.8973 0.0580
parentescoNieto(a) 0.1856 0.0744 2.4935 0.0128
parentescoOtro no pariente 0.0884 0.4710 0.1877 0.8511
parentescoOtro pariente 0.2857 0.1124 2.5428 0.0111
parentescoPadre o madre 0.2310 0.0718 3.2161 0.0013
parentescoSuegro(a) 0.3480 0.1444 2.4094 0.0161
parentescoYerno o nuera 0.1264 0.1174 1.0772 0.2816
sexoMujer −0.0810 0.0162 −4.9948 <0.0001
poly(edad, 2)1 26.7738 3.9408 6.7940 <0.0001
poly(edad, 2)2 −21.1513 1.7841 −11.8555 <0.0001
departamentoEl Progreso 0.1969 0.0982 2.0047 0.0452
departamentoSacatepéquez 0.2977 0.0854 3.4867 0.0005
departamentoChimaltenango 0.4269 0.0795 5.3716 <0.0001
departamentoEscuintla 0.2095 0.0842 2.4867 0.0130
departamentoSanta Rosa 0.4275 0.0962 4.4443 <0.0001
departamentoSololá 0.6622 0.1039 6.3743 <0.0001
departamentoTotonicapán 0.5593 0.0919 6.0872 <0.0001
departamentoQuetzaltenango 0.5924 0.0945 6.2679 <0.0001
departamentoSuchitepéquez 0.4872 0.0763 6.3815 <0.0001
departamentoRetalhuleu 0.4838 0.0937 5.1644 <0.0001
departamentoSan Marcos 0.5445 0.0956 5.6986 <0.0001
departamentoHuehuetenango 0.6495 0.0967 6.7170 <0.0001
departamentoQuiché 0.6083 0.0922 6.5945 <0.0001
departamentoBaja Verapaz 0.5807 0.0938 6.1917 <0.0001
departamentoAlta Verapaz 0.4080 0.1052 3.8790 0.0001
departamentoPetén 0.5264 0.0869 6.0595 <0.0001
departamentoIzabal 0.3717 0.0974 3.8181 0.0001
departamentoZacapa 0.1734 0.1090 1.5911 0.1118
departamentoChiquimula 0.3753 0.1008 3.7248 0.0002
departamentoJalapa 0.5523 0.0926 5.9624 <0.0001
departamentoJutiapa 0.3089 0.0833 3.7069 0.0002
areaRural 0.1070 0.0331 3.2303 0.0013
poly(miembros_hogar, 3)1 10.0672 2.7434 3.6696 0.0003
poly(miembros_hogar, 3)2 1.6657 2.6761 0.6224 0.5338
poly(miembros_hogar, 3)3 −1.0326 3.2427 −0.3184 0.7502
propiedadPropia y pagandola a plazos −0.1500 0.1026 −1.4617 0.1441
propiedadAlquilada −0.0727 0.0586 −1.2410 0.2148
propiedadCedida o prestada 0.0002 0.0489 0.0050 0.9960
propiedadOtro −0.5700 0.2716 −2.0985 0.0360
poly(grado_estudios_hogar, 3)1 −11.8871 4.1326 −2.8764 0.0041
poly(grado_estudios_hogar, 3)2 −0.5885 3.8143 −0.1543 0.8774
poly(grado_estudios_hogar, 3)3 −3.5090 3.5813 −0.9798 0.3273
tipo_viviendaApartamento −0.2497 0.1506 −1.6581 0.0975
tipo_viviendaCuarto en casa de vecindad 0.3672 0.2602 1.4113 0.1584
tipo_viviendaRancho −1.4674 0.1990 −7.3741 <0.0001
tipo_viviendaCasa improvisada 0.1555 0.1771 0.8782 0.3800
material_paredesBlock 0.1301 0.1509 0.8622 0.3887
material_paredesConcreto 0.0842 0.1980 0.4251 0.6708
material_paredesAdobe 0.2159 0.1558 1.3862 0.1659
material_paredesMadera 0.1684 0.1648 1.0221 0.3069
material_paredesLamina metalica −0.0225 0.2609 −0.0863 0.9312
material_paredesBajareque 0.4056 0.1788 2.2679 0.0235
material_paredesLepa, palo o caña 0.1346 0.2406 0.5596 0.5758
material_paredesOtro −0.0900 0.2386 −0.3772 0.7061
material_techoLamina metalica 0.0316 0.0566 0.5587 0.5764
material_techoAsbesto cemento −0.2972 0.1396 −2.1296 0.0334
material_techoTeja 0.1089 0.0859 1.2683 0.2049
material_techoPaja, palma o similar 1.4103 0.1826 7.7230 <0.0001
material_techoOtro −0.0287 0.2472 −0.1159 0.9077
material_pisoLadrillo de cemento −0.0002 0.0662 −0.0033 0.9974
material_pisoLadrillo de barro −0.0195 0.2830 −0.0690 0.9450
material_pisoTorta de cemento 0.0710 0.0465 1.5271 0.1270
material_pisoMadera −0.1625 0.1403 −1.1578 0.2471
material_pisoTierra 0.0954 0.0555 1.7189 0.0859
poly(n_cuartos, 3)1 −5.0595 3.3773 −1.4981 0.1343
poly(n_cuartos, 3)2 −1.7630 2.9360 −0.6005 0.5483
poly(n_cuartos, 3)3 −6.4372 4.0070 −1.6065 0.1084
tipo_sanitarioUso compartido 0.0876 0.0593 1.4787 0.1395
fuente_aguaTubería fuera de la vivienda 0.1211 0.0445 2.7213 0.0066
fuente_aguaChorro publico 0.0588 0.0740 0.7941 0.4273
fuente_aguaPozo perforado 0.0405 0.0396 1.0232 0.3064
fuente_aguaRío, lago, manantial −0.0587 0.0611 −0.9618 0.3363
fuente_aguaCamion cisterna −0.1318 0.1315 −1.0021 0.3165
fuente_aguaAgua de lluvia −0.0045 0.0886 −0.0504 0.9598
fuente_aguaOtro −0.0687 0.0667 −1.0290 0.3036
recoleccion_basuraLa tiran en cualquier lugar −0.1384 0.0643 −2.1534 0.0315
recoleccion_basuraServicio municipal −0.3430 0.0511 −6.7097 <0.0001
recoleccion_basuraServicio privado −0.3804 0.0702 −5.4203 <0.0001
electricidadNo 0.0180 0.0382 0.4718 0.6372
televisorNo −0.0178 0.0342 −0.5200 0.6031
telefonia_celularNo −0.0482 0.0305 −1.5797 0.1144
computadoraNo 0.1475 0.0452 3.2657 0.0011
Scatter chart with observed energy from maize in kilocalories per day on the x-axis and model-predicted energy on the y-axis, using all 20 candidate predictors. Each point is a person. Predicted values span a narrower range than observed values, so the cloud rises gently rather than following the ideal one-to-one line, showing the model captures average intake but compresses the extremes.
Figure 2: Observed vs predicted energy 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 (energy from maize)
Variable Significance Testing. Wald F-test results for energy intake from maize model
Variable Significance Testing
Wald F-test results for energy intake from maize model
variable f_statistic p_value significant
parentesco 5.22 <0.0001 *
sexo 24.95 <0.0001 *
poly(edad, 2) 80.23 <0.0001 *
departamento 5.58 <0.0001 *
area 10.43 0.0013 *
poly(miembros_hogar, 3) 4.55 0.0035 *
propiedad 1.99 0.0937
poly(grado_estudios_hogar, 3) 3.38 0.0177 *
tipo_vivienda 20.76 <0.0001 *
material_paredes 1.83 0.0683
material_techo 15.35 <0.0001 *
material_piso 1.50 0.1857
poly(n_cuartos, 3) 1.52 0.2067
tipo_sanitario 2.19 0.1395
fuente_agua 1.93 0.0616
recoleccion_basura 18.87 <0.0001 *
electricidad 0.22 0.6372
televisor 0.27 0.6031
telefonia_celular 2.50 0.1144
computadora 10.66 0.0011 *
ImportantVariables Retained

11 predictors show significant relationships with energy intake from maize, spanning demographic, geographic, socioeconomic, housing and asset categories. Variables that do not significantly predict energy 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 energy intake from maize (refined model)
Energy Intake from Maize (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Energy Intake from Maize (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 6.2053 0.1023 60.6521 <0.0001
parentescoEsposo(a) o compañero(a) 0.1346 0.0692 1.9445 0.0520
parentescoHermano(a) 0.3204 0.1553 2.0634 0.0393
parentescoHijo(a) 0.2518 0.0644 3.9104 <0.0001
parentescoJefe del hogar 0.1301 0.0677 1.9228 0.0547
parentescoNieto(a) 0.1828 0.0753 2.4286 0.0153
parentescoOtro no pariente 0.1435 0.4719 0.3042 0.7610
parentescoOtro pariente 0.2650 0.1098 2.4132 0.0159
parentescoPadre o madre 0.2093 0.0723 2.8970 0.0038
parentescoSuegro(a) 0.3354 0.1366 2.4556 0.0142
parentescoYerno o nuera 0.1020 0.1224 0.8336 0.4047
sexoMujer −0.0850 0.0164 −5.1731 <0.0001
poly(edad, 2)1 25.3299 3.8571 6.5671 <0.0001
poly(edad, 2)2 −20.3602 1.7698 −11.5039 <0.0001
departamentoEl Progreso 0.2491 0.0988 2.5225 0.0118
departamentoSacatepéquez 0.3263 0.0853 3.8255 0.0001
departamentoChimaltenango 0.4478 0.0789 5.6738 <0.0001
departamentoEscuintla 0.2309 0.0826 2.7964 0.0052
departamentoSanta Rosa 0.4599 0.0941 4.8879 <0.0001
departamentoSololá 0.7014 0.1046 6.7060 <0.0001
departamentoTotonicapán 0.6291 0.0898 7.0092 <0.0001
departamentoQuetzaltenango 0.6276 0.0945 6.6404 <0.0001
departamentoSuchitepéquez 0.5294 0.0759 6.9759 <0.0001
departamentoRetalhuleu 0.5212 0.0936 5.5663 <0.0001
departamentoSan Marcos 0.5956 0.0960 6.2027 <0.0001
departamentoHuehuetenango 0.7183 0.0928 7.7412 <0.0001
departamentoQuiché 0.6773 0.0897 7.5477 <0.0001
departamentoBaja Verapaz 0.6270 0.0901 6.9567 <0.0001
departamentoAlta Verapaz 0.4672 0.0948 4.9287 <0.0001
departamentoPetén 0.5609 0.0830 6.7610 <0.0001
departamentoIzabal 0.3938 0.0943 4.1781 <0.0001
departamentoZacapa 0.2736 0.1096 2.4967 0.0127
departamentoChiquimula 0.4774 0.1028 4.6436 <0.0001
departamentoJalapa 0.6047 0.0905 6.6837 <0.0001
departamentoJutiapa 0.3386 0.0812 4.1716 <0.0001
areaRural 0.1156 0.0333 3.4694 0.0005
poly(miembros_hogar, 3)1 10.0573 2.6384 3.8119 0.0001
poly(miembros_hogar, 3)2 1.4797 2.7533 0.5374 0.5911
poly(miembros_hogar, 3)3 −1.4542 3.4228 −0.4248 0.6710
poly(grado_estudios_hogar, 3)1 −12.8836 4.2176 −3.0547 0.0023
poly(grado_estudios_hogar, 3)2 −1.2567 3.7834 −0.3322 0.7398
poly(grado_estudios_hogar, 3)3 −4.3134 3.6316 −1.1877 0.2351
tipo_viviendaApartamento −0.2458 0.1506 −1.6321 0.1029
tipo_viviendaCuarto en casa de vecindad 0.4879 0.2824 1.7280 0.0842
tipo_viviendaRancho −1.4740 0.1194 −12.3485 <0.0001
tipo_viviendaCasa improvisada 0.0457 0.0726 0.6295 0.5291
material_techoLamina metalica 0.1050 0.0579 1.8143 0.0699
material_techoAsbesto cemento −0.2890 0.1442 −2.0043 0.0452
material_techoTeja 0.2244 0.0860 2.6098 0.0092
material_techoPaja, palma o similar 1.5561 0.1030 15.1017 <0.0001
material_techoOtro 0.0778 0.2638 0.2951 0.7679
recoleccion_basuraLa tiran en cualquier lugar −0.1332 0.0644 −2.0698 0.0387
recoleccion_basuraServicio municipal −0.3811 0.0494 −7.7139 <0.0001
recoleccion_basuraServicio privado −0.4141 0.0689 −6.0145 <0.0001
computadoraNo 0.1623 0.0457 3.5470 0.0004
Scatter chart with observed energy from maize in kilocalories per day on the x-axis and model-predicted energy on the y-axis, using only the significant predictors retained after variable selection. Each point is a person. The pattern closely mirrors the full model, confirming that dropping non-significant variables preserves predictive accuracy while simplifying the model.
Figure 3: Observed vs predicted energy intake from maize (refined model)

Model Diagnostics

We verify the model meets statistical assumptions:

A grid of regression diagnostic panels for the refined Gamma model of energy from maize, covering residual behaviour, influential observations, and predictor collinearity. Residuals scatter around their reference line with no systematic pattern, no points exert excessive leverage, and the collinearity panel plots each term's degrees-of-freedom adjusted variance inflation factor against shaded low, moderate and high bands.
Figure 4: Diagnostic plots for energy 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 5.6, 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 Energy Intake from Non-Maize Sources

NoteNon-Maize Energy Sources

Non-maize energy sources contribute to dietary diversity and often provide additional protein and fat alongside energy. This model captures the portion of energy intake that may reflect economic access to a more varied diet.

Distribution Selection

Table 5: Distribution fit comparison for energy intake from non-maize sources
Distribution Fit Comparison. Goodness-of-fit statistics for Gamma and Lognormal distributions
Distribution Fit Comparison
Goodness-of-fit statistics for Gamma and Lognormal distributions
Distribution Log-Likelihood
Information Criteria
Goodness-of-Fit Statistics
AIC BIC Kolmogorov-Smirnov Cramer-von Mises Anderson-Darling
Gamma −271,293.2011 542,590.4021 542,607.3481 0.0278 9.9915 66.5808
Lognormal −275,384.4923 550,772.9845 550,789.9304 0.0785 86.9901 549.6540
Four goodness-of-fit panels comparing observed energy intake from non-maize sources against a fitted Gamma distribution. Top left, a histogram of intake overlaid with the theoretical Gamma density curve. Top right, a quantile-quantile plot; bottom left, empirical versus theoretical cumulative distribution curves; bottom right, a probability-probability plot. Points and curves stay close to the reference lines, confirming the Gamma distribution again fits the right-skewed intake data well.
Figure 5: Distribution assessment for energy intake from non-maize sources
ImportantDistribution Selection

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

Full Model

Table 6: Model coefficients for energy intake from non-maize sources (full model)
Energy Intake from Non-Maize Sources (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Energy 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) 6.8372 0.1021 66.9438 <0.0001
parentescoEsposo(a) o compañero(a) −0.2016 0.0567 −3.5553 0.0004
parentescoHermano(a) −0.0021 0.1039 −0.0206 0.9836
parentescoHijo(a) −0.0648 0.0558 −1.1614 0.2457
parentescoJefe del hogar −0.1630 0.0560 −2.9113 0.0037
parentescoNieto(a) −0.0669 0.0630 −1.0623 0.2883
parentescoOtro no pariente −0.4116 0.2766 −1.4882 0.1369
parentescoOtro pariente −0.1306 0.0710 −1.8390 0.0661
parentescoPadre o madre −0.0903 0.0632 −1.4280 0.1535
parentescoSuegro(a) −0.0088 0.0733 −0.1206 0.9040
parentescoYerno o nuera 0.0711 0.0754 0.9426 0.3461
sexoMujer −0.1231 0.0091 −13.4781 <0.0001
poly(edad, 2)1 30.2250 2.2939 13.1764 <0.0001
poly(edad, 2)2 −30.8917 1.1187 −27.6138 <0.0001
departamentoEl Progreso 0.0678 0.0435 1.5581 0.1194
departamentoSacatepéquez 0.0879 0.0384 2.2867 0.0224
departamentoChimaltenango −0.0688 0.0506 −1.3602 0.1740
departamentoEscuintla 0.0499 0.0478 1.0442 0.2966
departamentoSanta Rosa 0.0587 0.0445 1.3183 0.1876
departamentoSololá −0.1057 0.0645 −1.6402 0.1012
departamentoTotonicapán −0.0584 0.0576 −1.0151 0.3103
departamentoQuetzaltenango −0.0872 0.0453 −1.9252 0.0544
departamentoSuchitepéquez −0.0342 0.0436 −0.7842 0.4330
departamentoRetalhuleu 0.0024 0.0536 0.0453 0.9639
departamentoSan Marcos 0.0397 0.0619 0.6414 0.5214
departamentoHuehuetenango 0.0219 0.0514 0.4251 0.6709
departamentoQuiché −0.1636 0.0557 −2.9376 0.0034
departamentoBaja Verapaz −0.1846 0.0631 −2.9244 0.0035
departamentoAlta Verapaz −0.2001 0.0589 −3.3951 0.0007
departamentoPetén −0.1435 0.0510 −2.8127 0.0050
departamentoIzabal −0.0117 0.0548 −0.2142 0.8304
departamentoZacapa −0.0808 0.0541 −1.4929 0.1357
departamentoChiquimula −0.1674 0.0568 −2.9461 0.0033
departamentoJalapa −0.0466 0.0528 −0.8830 0.3774
departamentoJutiapa 0.0146 0.0534 0.2733 0.7846
areaRural −0.0323 0.0228 −1.4139 0.1576
poly(miembros_hogar, 3)1 −31.0662 2.1246 −14.6221 <0.0001
poly(miembros_hogar, 3)2 0.0661 2.5583 0.0258 0.9794
poly(miembros_hogar, 3)3 8.1094 2.8125 2.8833 0.0040
propiedadPropia y pagandola a plazos −0.0168 0.0446 −0.3766 0.7065
propiedadAlquilada 0.0159 0.0272 0.5830 0.5600
propiedadCedida o prestada 0.0337 0.0250 1.3474 0.1781
propiedadOtro 0.1105 0.2840 0.3890 0.6973
poly(grado_estudios_hogar, 3)1 4.1556 1.6470 2.5231 0.0117
poly(grado_estudios_hogar, 3)2 −2.9893 1.3246 −2.2567 0.0242
poly(grado_estudios_hogar, 3)3 0.6538 1.2760 0.5124 0.6085
tipo_viviendaApartamento −0.0576 0.1501 −0.3836 0.7013
tipo_viviendaCuarto en casa de vecindad −0.1771 0.0865 −2.0480 0.0408
tipo_viviendaRancho 0.8904 0.1681 5.2985 <0.0001
tipo_viviendaCasa improvisada 0.0856 0.1742 0.4915 0.6232
material_paredesBlock 0.1735 0.0771 2.2504 0.0246
material_paredesConcreto 0.2411 0.0869 2.7741 0.0056
material_paredesAdobe 0.0578 0.0807 0.7160 0.4741
material_paredesMadera 0.1240 0.0827 1.4993 0.1340
material_paredesLamina metalica 0.1223 0.1925 0.6352 0.5254
material_paredesBajareque −0.0683 0.1035 −0.6598 0.5095
material_paredesLepa, palo o caña −0.2040 0.1788 −1.1409 0.2541
material_paredesOtro 0.1790 0.1278 1.4008 0.1615
material_techoLamina metalica 0.0975 0.0275 3.5410 0.0004
material_techoAsbesto cemento −0.1051 0.1168 −0.8997 0.3685
material_techoTeja 0.1137 0.0557 2.0413 0.0414
material_techoPaja, palma o similar −0.6315 0.1517 −4.1622 <0.0001
material_techoOtro 0.3026 0.2093 1.4456 0.1485
material_pisoLadrillo de cemento 0.0321 0.0367 0.8755 0.3814
material_pisoLadrillo de barro −0.0629 0.1323 −0.4751 0.6348
material_pisoTorta de cemento 0.0127 0.0248 0.5144 0.6071
material_pisoMadera 0.0443 0.1028 0.4312 0.6664
material_pisoTierra −0.0149 0.0361 −0.4120 0.6804
poly(n_cuartos, 3)1 3.2417 2.1726 1.4921 0.1359
poly(n_cuartos, 3)2 −1.8684 1.8308 −1.0205 0.3077
poly(n_cuartos, 3)3 −0.3222 1.7725 −0.1817 0.8558
tipo_sanitarioUso compartido −0.0140 0.0298 −0.4708 0.6378
fuente_aguaTubería fuera de la vivienda −0.0071 0.0299 −0.2384 0.8116
fuente_aguaChorro publico 0.0242 0.0620 0.3895 0.6970
fuente_aguaPozo perforado 0.0062 0.0330 0.1892 0.8499
fuente_aguaRío, lago, manantial −0.1772 0.0569 −3.1131 0.0019
fuente_aguaCamion cisterna 0.0720 0.0690 1.0446 0.2964
fuente_aguaAgua de lluvia −0.0072 0.0670 −0.1072 0.9147
fuente_aguaOtro −0.0392 0.0481 −0.8148 0.4153
recoleccion_basuraLa tiran en cualquier lugar −0.0895 0.0488 −1.8343 0.0668
recoleccion_basuraServicio municipal −0.0204 0.0242 −0.8459 0.3978
recoleccion_basuraServicio privado −0.0005 0.0302 −0.0175 0.9860
electricidadNo −0.0636 0.0323 −1.9662 0.0495
televisorNo −0.0453 0.0172 −2.6288 0.0087
telefonia_celularNo −0.0439 0.0207 −2.1187 0.0343
computadoraNo −0.0527 0.0237 −2.2257 0.0262
Scatter chart with observed energy from non-maize sources in kilocalories per day on the x-axis and model-predicted energy on the y-axis, using all candidate predictors. Each point is a person. Predictions span a narrower range than the observed spread, reflecting the greater heterogeneity of non-maize food sources and a weaker fit than the maize model.
Figure 6: Observed vs predicted energy intake from non-maize sources (full model)

Variable Selection

Table 7: Wald test results for predictor significance (energy from non-maize)
Variable Significance Testing. Wald F-test results for energy intake from non-maize model
Variable Significance Testing
Wald F-test results for energy intake from non-maize model
variable f_statistic p_value significant
parentesco 14.50 <0.0001 *
sexo 181.66 <0.0001 *
poly(edad, 2) 421.09 <0.0001 *
departamento 4.56 <0.0001 *
area 2.00 0.1576
poly(miembros_hogar, 3) 127.92 <0.0001 *
propiedad 0.61 0.6530
poly(grado_estudios_hogar, 3) 3.04 0.0280 *
tipo_vivienda 13.86 <0.0001 *
material_paredes 4.46 <0.0001 *
material_techo 9.54 <0.0001 *
material_piso 0.48 0.7905
poly(n_cuartos, 3) 1.38 0.2462
tipo_sanitario 0.22 0.6378
fuente_agua 1.83 0.0776
recoleccion_basura 1.37 0.2508
electricidad 3.87 0.0495 *
televisor 6.91 0.0087 *
telefonia_celular 4.49 0.0343 *
computadora 4.95 0.0262 *
ImportantVariables Retained

13 predictors significantly predict energy 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 energy intake from non-maize sources (refined model)
Energy Intake from Non-Maize Sources (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Energy 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) 6.8876 0.1012 68.0516 <0.0001
parentescoEsposo(a) o compañero(a) −0.2231 0.0575 −3.8792 0.0001
parentescoHermano(a) −0.0207 0.1036 −0.1995 0.8419
parentescoHijo(a) −0.0749 0.0568 −1.3180 0.1877
parentescoJefe del hogar −0.1844 0.0568 −3.2462 0.0012
parentescoNieto(a) −0.0729 0.0642 −1.1353 0.2564
parentescoOtro no pariente −0.4249 0.2776 −1.5307 0.1261
parentescoOtro pariente −0.1408 0.0722 −1.9506 0.0513
parentescoPadre o madre −0.0911 0.0641 −1.4210 0.1555
parentescoSuegro(a) −0.0336 0.0739 −0.4553 0.6490
parentescoYerno o nuera 0.0593 0.0767 0.7731 0.4396
sexoMujer −0.1222 0.0092 −13.3244 <0.0001
poly(edad, 2)1 31.6992 2.2460 14.1139 <0.0001
poly(edad, 2)2 −31.1733 1.1270 −27.6593 <0.0001
departamentoEl Progreso 0.0534 0.0423 1.2615 0.2074
departamentoSacatepéquez 0.0745 0.0372 2.0015 0.0455
departamentoChimaltenango −0.0894 0.0494 −1.8085 0.0707
departamentoEscuintla 0.0349 0.0438 0.7972 0.4255
departamentoSanta Rosa 0.0368 0.0423 0.8707 0.3840
departamentoSololá −0.1294 0.0612 −2.1155 0.0346
departamentoTotonicapán −0.0813 0.0549 −1.4814 0.1387
departamentoQuetzaltenango −0.1141 0.0423 −2.6971 0.0071
departamentoSuchitepéquez −0.0532 0.0398 −1.3367 0.1815
departamentoRetalhuleu −0.0137 0.0494 −0.2772 0.7817
departamentoSan Marcos 0.0062 0.0598 0.1044 0.9168
departamentoHuehuetenango −0.0059 0.0481 −0.1234 0.9018
departamentoQuiché −0.1808 0.0523 −3.4544 0.0006
departamentoBaja Verapaz −0.2038 0.0635 −3.2114 0.0014
departamentoAlta Verapaz −0.2364 0.0564 −4.1908 <0.0001
departamentoPetén −0.1598 0.0494 −3.2351 0.0012
departamentoIzabal −0.0246 0.0547 −0.4508 0.6522
departamentoZacapa −0.1023 0.0528 −1.9389 0.0527
departamentoChiquimula −0.1990 0.0560 −3.5547 0.0004
departamentoJalapa −0.0715 0.0523 −1.3659 0.1722
departamentoJutiapa 0.0013 0.0512 0.0262 0.9791
poly(miembros_hogar, 3)1 −30.9578 1.9318 −16.0250 <0.0001
poly(miembros_hogar, 3)2 −0.1052 2.4339 −0.0432 0.9655
poly(miembros_hogar, 3)3 7.8703 2.7329 2.8798 0.0040
poly(grado_estudios_hogar, 3)1 4.8439 1.6130 3.0031 0.0027
poly(grado_estudios_hogar, 3)2 −3.2181 1.3163 −2.4447 0.0146
poly(grado_estudios_hogar, 3)3 0.6955 1.2992 0.5353 0.5925
tipo_viviendaApartamento −0.0437 0.1539 −0.2842 0.7763
tipo_viviendaCuarto en casa de vecindad −0.1937 0.0806 −2.4018 0.0164
tipo_viviendaRancho 0.8525 0.1653 5.1589 <0.0001
tipo_viviendaCasa improvisada 0.0728 0.1741 0.4182 0.6759
material_paredesBlock 0.1608 0.0795 2.0233 0.0432
material_paredesConcreto 0.2200 0.0898 2.4505 0.0144
material_paredesAdobe 0.0230 0.0829 0.2779 0.7811
material_paredesMadera 0.0790 0.0846 0.9336 0.3507
material_paredesLamina metalica 0.0988 0.1925 0.5134 0.6078
material_paredesBajareque −0.0997 0.1042 −0.9571 0.3387
material_paredesLepa, palo o caña −0.2511 0.1747 −1.4371 0.1509
material_paredesOtro 0.1458 0.1234 1.1816 0.2376
material_techoLamina metalica 0.0961 0.0248 3.8686 0.0001
material_techoAsbesto cemento −0.1010 0.1185 −0.8521 0.3943
material_techoTeja 0.1192 0.0566 2.1062 0.0354
material_techoPaja, palma o similar −0.6447 0.1494 −4.3158 <0.0001
material_techoOtro 0.3347 0.2183 1.5336 0.1254
electricidadNo −0.0917 0.0312 −2.9399 0.0033
televisorNo −0.0506 0.0172 −2.9331 0.0034
telefonia_celularNo −0.0447 0.0208 −2.1477 0.0319
computadoraNo −0.0632 0.0227 −2.7851 0.0054
Scatter chart with observed energy from non-maize sources in kilocalories per day on the x-axis and model-predicted energy on the y-axis, using only the significant predictors retained after variable selection. Each point is a person. The pattern matches the full model, confirming that the simpler refined model retains its predictive accuracy.
Figure 7: Observed vs predicted energy intake from non-maize sources (refined model)

Model Diagnostics

A grid of regression diagnostic panels for the refined Gamma model of energy from non-maize sources, covering residual behaviour, influential observations, and predictor collinearity. Residuals scatter around their reference line without systematic pattern, no observations show excessive leverage, and the collinearity panel plots each term's degrees-of-freedom adjusted variance inflation factor against shaded low, moderate and high bands.
Figure 8: Diagnostic plots for energy 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 Energy from maize Energy from non-maize
N observations 35,347 35,347
N predictors 54 61
Pseudo-R² (McFadden)1 0.174 0.192
Pseudo-R² (Cragg-Uhler)2 0.278 0.237
AIC 38,884 15,916
Dispersion 1.094 0.350
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)
Energy from maize 11 variables Age, department, area, household size
Energy from non-maize 13 variables Age, electricity, roof materials, household size

Key Findings

  1. Largest retained set of the module: The non-maize energy model retains 13 predictors, the widest set across the six nutrient models

  2. Infrastructure variables: Electricity and roof materials are retained in the non-maize model and not in the maize model

  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

Application

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

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