Transfer Model: Digestible Protein Intake

Module 3: Transfer Models

Why Model Digestible Protein?

Protein quality, not just quantity, is an important determinant of child growth outcomes. The outcome modeled here is digestible protein (PDCAAS-adjusted): the PDCAAS (Protein Digestibility Corrected Amino Acid Score) accounts for both amino acid composition and digestibility, so the adjusted figure represents the protein fraction available for human use. By modeling digestible protein from maize and non-maize sources separately, we can:

  1. Simulate biofortification scenarios — Predict how higher-quality maize varieties would change total digestible protein intake
  2. Preserve baseline non-maize intake — Keep other dietary sources constant when modeling interventions
  3. Account for protein quality — PDCAAS is an intrinsic property of each food, enabling direct impact assessment without separate bioavailability adjustments
ImportantMethodological Note

Protein quality (PDCAAS) is incorporated at the food level during intake calculation, which allows digestible protein to be modeled directly; for micronutrients, bioavailability is applied after modeling. PDCAAS values are approximate — they vary by maize variety, processing method, and dietary context. Our analysis uses representative values for processed maize in Guatemalan diets. See how PDCAAS was computed for the source and imputation rule applied to foods without computed values.

Modeling Approach

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

  • Positive and continuous — People consume some amount of protein 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 digestible protein 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:

  • Protein intake distributions are more stable
  • Extreme values are consistent with measurement error
  • Macronutrient 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 Digestible Protein from Maize

Distribution Selection

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

Table 1: Distribution fit comparison for digestible protein 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 −124,318.2037 248,640.4073 248,657.3208 0.0337 12.2429 77.1351
Lognormal −126,285.2376 252,574.4751 252,591.3886 0.0521 29.8393 219.3095
Exponential −124,401.5241 248,805.0483 248,813.5050 0.0489 28.6618 160.1582
Four goodness-of-fit panels arranged in a 2-by-2 grid comparing observed digestible protein from maize against a fitted gamma distribution. The top-left panel overlays a dashed gamma density curve on a histogram of the data; the top-right is a quantile-quantile plot; the bottom-left compares empirical and theoretical cumulative distribution functions; the bottom-right is a probability-probability plot. Points and curves track the diagonal reference lines closely, indicating the gamma distribution provides the best fit to this positive, right-skewed intake.
Figure 1: Distribution assessment for digestible protein 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 digestible protein intake from maize.

Table 2: Model coefficients for digestible protein intake from maize (full model)
Digestible Protein Intake (PDCAAS-Adjusted) from Maize (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Digestible Protein Intake (PDCAAS-Adjusted) from Maize (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.6992 0.1881 9.0338 <0.0001
parentescoEsposo(a) o compañero(a) 0.0929 0.0756 1.2298 0.2190
parentescoHermano(a) 0.3052 0.1568 1.9460 0.0519
parentescoHijo(a) 0.2439 0.0701 3.4819 0.0005
parentescoJefe del hogar 0.1011 0.0725 1.3951 0.1632
parentescoNieto(a) 0.1559 0.0799 1.9502 0.0514
parentescoOtro no pariente 0.0539 0.5380 0.1003 0.9201
parentescoOtro pariente 0.2551 0.1173 2.1746 0.0298
parentescoPadre o madre 0.2221 0.0785 2.8309 0.0047
parentescoSuegro(a) 0.2992 0.1509 1.9833 0.0475
parentescoYerno o nuera 0.1212 0.1210 1.0020 0.3165
sexoMujer −0.0841 0.0162 −5.1965 <0.0001
poly(edad, 2)1 27.4500 3.9338 6.9780 <0.0001
poly(edad, 2)2 −20.9405 1.8166 −11.5276 <0.0001
departamentoEl Progreso 0.2007 0.0985 2.0367 0.0419
departamentoSacatepéquez 0.2638 0.0854 3.0903 0.0020
departamentoChimaltenango 0.4302 0.0806 5.3360 <0.0001
departamentoEscuintla 0.1881 0.0818 2.2983 0.0217
departamentoSanta Rosa 0.4073 0.0973 4.1869 <0.0001
departamentoSololá 0.6621 0.1051 6.2977 <0.0001
departamentoTotonicapán 0.5412 0.0945 5.7258 <0.0001
departamentoQuetzaltenango 0.5798 0.0953 6.0857 <0.0001
departamentoSuchitepéquez 0.4713 0.0774 6.0920 <0.0001
departamentoRetalhuleu 0.4660 0.0951 4.8975 <0.0001
departamentoSan Marcos 0.5257 0.0957 5.4903 <0.0001
departamentoHuehuetenango 0.6291 0.0974 6.4564 <0.0001
departamentoQuiché 0.5934 0.0932 6.3634 <0.0001
departamentoBaja Verapaz 0.5676 0.0951 5.9679 <0.0001
departamentoAlta Verapaz 0.4144 0.1061 3.9035 <0.0001
departamentoPetén 0.5104 0.0883 5.7837 <0.0001
departamentoIzabal 0.3471 0.0978 3.5506 0.0004
departamentoZacapa 0.1586 0.1084 1.4636 0.1435
departamentoChiquimula 0.3710 0.1017 3.6479 0.0003
departamentoJalapa 0.5371 0.0929 5.7804 <0.0001
departamentoJutiapa 0.2969 0.0867 3.4258 0.0006
areaRural 0.1177 0.0333 3.5405 0.0004
poly(miembros_hogar, 3)1 9.4217 2.7884 3.3789 0.0007
poly(miembros_hogar, 3)2 2.6728 2.6718 1.0004 0.3173
poly(miembros_hogar, 3)3 −1.8498 3.2231 −0.5739 0.5661
propiedadPropia y pagandola a plazos −0.1360 0.1023 −1.3288 0.1841
propiedadAlquilada −0.0683 0.0598 −1.1426 0.2534
propiedadCedida o prestada 0.0009 0.0494 0.0186 0.9851
propiedadOtro −0.5461 0.2946 −1.8535 0.0640
poly(grado_estudios_hogar, 3)1 −12.7080 4.1494 −3.0626 0.0022
poly(grado_estudios_hogar, 3)2 −2.5396 3.5443 −0.7165 0.4738
poly(grado_estudios_hogar, 3)3 −5.0661 3.0566 −1.6575 0.0977
tipo_viviendaApartamento −0.2196 0.1770 −1.2410 0.2148
tipo_viviendaCuarto en casa de vecindad 0.3592 0.2654 1.3533 0.1762
tipo_viviendaRancho −1.4624 0.1988 −7.3559 <0.0001
tipo_viviendaCasa improvisada 0.1360 0.1741 0.7811 0.4349
material_paredesBlock 0.1303 0.1530 0.8515 0.3946
material_paredesConcreto 0.0627 0.1999 0.3136 0.7539
material_paredesAdobe 0.2149 0.1575 1.3641 0.1728
material_paredesMadera 0.1682 0.1668 1.0081 0.3136
material_paredesLamina metalica −0.0060 0.2622 −0.0228 0.9818
material_paredesBajareque 0.4029 0.1809 2.2267 0.0261
material_paredesLepa, palo o caña 0.1421 0.2409 0.5899 0.5553
material_paredesOtro −0.0469 0.2413 −0.1944 0.8459
material_techoLamina metalica 0.0170 0.0579 0.2926 0.7699
material_techoAsbesto cemento −0.3569 0.1403 −2.5440 0.0111
material_techoTeja 0.1022 0.0872 1.1723 0.2413
material_techoPaja, palma o similar 1.3858 0.1813 7.6431 <0.0001
material_techoOtro −0.0492 0.2501 −0.1967 0.8441
material_pisoLadrillo de cemento 0.0023 0.0674 0.0337 0.9731
material_pisoLadrillo de barro −0.0143 0.2810 −0.0508 0.9595
material_pisoTorta de cemento 0.0808 0.0467 1.7276 0.0843
material_pisoMadera −0.1541 0.1422 −1.0838 0.2786
material_pisoTierra 0.1063 0.0555 1.9155 0.0556
poly(n_cuartos, 3)1 −5.4970 3.4031 −1.6153 0.1065
poly(n_cuartos, 3)2 −2.1173 2.9805 −0.7104 0.4776
poly(n_cuartos, 3)3 −6.5387 4.1295 −1.5834 0.1136
tipo_sanitarioUso compartido 0.0845 0.0591 1.4290 0.1532
fuente_aguaTubería fuera de la vivienda 0.1156 0.0450 2.5700 0.0103
fuente_aguaChorro publico 0.0644 0.0739 0.8721 0.3833
fuente_aguaPozo perforado 0.0333 0.0397 0.8382 0.4021
fuente_aguaRío, lago, manantial −0.0574 0.0613 −0.9363 0.3493
fuente_aguaCamion cisterna −0.0766 0.1350 −0.5671 0.5707
fuente_aguaAgua de lluvia −0.0066 0.0874 −0.0755 0.9398
fuente_aguaOtro −0.0640 0.0671 −0.9541 0.3402
recoleccion_basuraLa tiran en cualquier lugar −0.1392 0.0648 −2.1464 0.0320
recoleccion_basuraServicio municipal −0.3426 0.0518 −6.6133 <0.0001
recoleccion_basuraServicio privado −0.3870 0.0715 −5.4103 <0.0001
electricidadNo 0.0142 0.0385 0.3691 0.7121
televisorNo −0.0210 0.0347 −0.6067 0.5441
telefonia_celularNo −0.0477 0.0302 −1.5800 0.1143
computadoraNo 0.1387 0.0460 3.0161 0.0026
Scatter chart with observed digestible protein from maize in grams per day along the x-axis and the full model's predicted values along the y-axis. Points cluster along an upward diagonal trend, showing predictions rise with observed intake, though scatter around the line reflects the model's limited precision for individual-level values.
Figure 2: Observed vs predicted digestible protein 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 (digestible protein from maize)
Variable Significance Testing. Wald F-test results for digestible protein intake from maize model
Variable Significance Testing
Wald F-test results for digestible protein intake from maize model
variable f_statistic p_value significant
parentesco 4.94 <0.0001 *
sexo 27.00 <0.0001 *
poly(edad, 2) 78.09 <0.0001 *
departamento 5.33 <0.0001 *
area 12.54 0.0004 *
poly(miembros_hogar, 3) 4.02 0.0073 *
propiedad 1.60 0.1706
poly(grado_estudios_hogar, 3) 5.49 0.0009 *
tipo_vivienda 19.66 <0.0001 *
material_paredes 1.71 0.0926
material_techo 15.97 <0.0001 *
material_piso 1.67 0.1385
poly(n_cuartos, 3) 1.63 0.1811
tipo_sanitario 2.04 0.1532
fuente_agua 1.67 0.1135
recoleccion_basura 18.99 <0.0001 *
electricidad 0.14 0.7121
televisor 0.37 0.5441
telefonia_celular 2.50 0.1143
computadora 9.10 0.0026 *
ImportantVariables Retained

11 predictors show significant relationships with digestible protein intake from maize, spanning demographic, geographic, socioeconomic, housing and asset categories. Variables that do not significantly predict digestible protein 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 digestible protein intake from maize (refined model)
Digestible Protein Intake (PDCAAS-Adjusted) from Maize (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Digestible Protein Intake (PDCAAS-Adjusted) from Maize (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 1.7931 0.1069 16.7749 <0.0001
parentescoEsposo(a) o compañero(a) 0.0999 0.0759 1.3159 0.1884
parentescoHermano(a) 0.2976 0.1631 1.8240 0.0684
parentescoHijo(a) 0.2336 0.0701 3.3347 0.0009
parentescoJefe del hogar 0.1048 0.0730 1.4366 0.1510
parentescoNieto(a) 0.1527 0.0805 1.8955 0.0582
parentescoOtro no pariente 0.1060 0.5387 0.1968 0.8440
parentescoOtro pariente 0.2314 0.1155 2.0042 0.0452
parentescoPadre o madre 0.1983 0.0779 2.5465 0.0110
parentescoSuegro(a) 0.2845 0.1410 2.0183 0.0438
parentescoYerno o nuera 0.0970 0.1259 0.7706 0.4411
sexoMujer −0.0880 0.0163 −5.4026 <0.0001
poly(edad, 2)1 25.7392 3.8580 6.6717 <0.0001
poly(edad, 2)2 −20.1727 1.8080 −11.1574 <0.0001
departamentoEl Progreso 0.2538 0.0993 2.5565 0.0107
departamentoSacatepéquez 0.2933 0.0860 3.4119 0.0007
departamentoChimaltenango 0.4474 0.0800 5.5957 <0.0001
departamentoEscuintla 0.2058 0.0813 2.5312 0.0115
departamentoSanta Rosa 0.4389 0.0955 4.5954 <0.0001
departamentoSololá 0.6985 0.1059 6.5965 <0.0001
departamentoTotonicapán 0.6086 0.0922 6.5993 <0.0001
departamentoQuetzaltenango 0.6143 0.0953 6.4432 <0.0001
departamentoSuchitepéquez 0.5110 0.0774 6.6034 <0.0001
departamentoRetalhuleu 0.5019 0.0952 5.2697 <0.0001
departamentoSan Marcos 0.5754 0.0965 5.9649 <0.0001
departamentoHuehuetenango 0.6953 0.0937 7.4227 <0.0001
departamentoQuiché 0.6600 0.0909 7.2631 <0.0001
departamentoBaja Verapaz 0.6145 0.0912 6.7391 <0.0001
departamentoAlta Verapaz 0.4704 0.0960 4.9016 <0.0001
departamentoPetén 0.5415 0.0846 6.4026 <0.0001
departamentoIzabal 0.3695 0.0950 3.8879 0.0001
departamentoZacapa 0.2596 0.1099 2.3629 0.0183
departamentoChiquimula 0.4730 0.1036 4.5660 <0.0001
departamentoJalapa 0.5886 0.0916 6.4281 <0.0001
departamentoJutiapa 0.3258 0.0853 3.8221 0.0001
areaRural 0.1246 0.0335 3.7215 0.0002
poly(miembros_hogar, 3)1 9.3339 2.6949 3.4635 0.0005
poly(miembros_hogar, 3)2 2.4615 2.7645 0.8904 0.3734
poly(miembros_hogar, 3)3 −2.2873 3.4159 −0.6696 0.5032
poly(grado_estudios_hogar, 3)1 −13.6729 4.2255 −3.2358 0.0012
poly(grado_estudios_hogar, 3)2 −3.0877 3.4977 −0.8828 0.3775
poly(grado_estudios_hogar, 3)3 −5.8023 3.1227 −1.8581 0.0634
tipo_viviendaApartamento −0.2188 0.1782 −1.2273 0.2199
tipo_viviendaCuarto en casa de vecindad 0.4829 0.2870 1.6828 0.0926
tipo_viviendaRancho −1.4944 0.1188 −12.5837 <0.0001
tipo_viviendaCasa improvisada 0.0446 0.0739 0.6038 0.5461
material_techoLamina metalica 0.0970 0.0590 1.6425 0.1007
material_techoAsbesto cemento −0.3465 0.1456 −2.3802 0.0174
material_techoTeja 0.2244 0.0872 2.5748 0.0101
material_techoPaja, palma o similar 1.5622 0.1012 15.4388 <0.0001
material_techoOtro 0.0627 0.2677 0.2343 0.8147
recoleccion_basuraLa tiran en cualquier lugar −0.1342 0.0651 −2.0617 0.0394
recoleccion_basuraServicio municipal −0.3797 0.0501 −7.5818 <0.0001
recoleccion_basuraServicio privado −0.4195 0.0703 −5.9663 <0.0001
computadoraNo 0.1555 0.0467 3.3306 0.0009
Scatter chart with observed digestible protein from maize in grams per day along the x-axis and the refined model's predicted values along the y-axis. Points follow the same upward diagonal trend as the full model, confirming that dropping non-significant predictors preserves predictive accuracy while simplifying the model.
Figure 3: Observed vs predicted digestible protein intake from maize (refined model)

Model Diagnostics

We verify the model meets statistical assumptions:

Grid of regression diagnostic panels for the refined maize gamma model, covering residuals, leverage, and 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 bands.
Figure 4: Diagnostic plots for digestible protein 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 5.7, 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 Digestible Protein from Non-Maize Sources

Digestible protein from non-maize sources includes animal products, legumes, and other plant proteins. This component remains constant in biofortification scenarios, representing the baseline dietary protein that would not change with maize interventions.

Distribution Selection

Table 5: Distribution fit comparison for digestible protein 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 −134,925.9878 269,855.9757 269,872.8891 0.0236 7.8470 57.4781
Lognormal −139,518.6712 279,041.3423 279,058.2557 0.0811 94.1587 601.2007
Exponential −136,995.0846 273,992.1693 274,000.6260 0.1130 172.3479 963.0685
Four goodness-of-fit panels arranged in a 2-by-2 grid comparing observed digestible protein from non-maize sources against a fitted gamma distribution. The panels show a histogram with an overlaid dashed gamma density curve, a quantile-quantile plot, an empirical versus theoretical cumulative distribution function plot, and a probability-probability plot. Points and curves align closely with the diagonal reference lines, confirming the gamma distribution again fits best.
Figure 5: Distribution assessment for digestible protein intake from non-maize sources
ImportantDistribution Selection

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

Full Model

Table 6: Model coefficients for digestible protein intake from non-maize sources (full model)
Digestible Protein Intake (PDCAAS-Adjusted) from Non-Maize Sources (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Digestible Protein Intake (PDCAAS-Adjusted) from Non-Maize Sources (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 2.9894 0.1143 26.1655 <0.0001
parentescoEsposo(a) o compañero(a) −0.1415 0.0651 −2.1727 0.0300
parentescoHermano(a) 0.0494 0.1203 0.4109 0.6812
parentescoHijo(a) −0.0342 0.0651 −0.5246 0.6000
parentescoJefe del hogar −0.1000 0.0649 −1.5405 0.1237
parentescoNieto(a) −0.0335 0.0725 −0.4617 0.6443
parentescoOtro no pariente −0.3960 0.3649 −1.0852 0.2780
parentescoOtro pariente −0.0579 0.0783 −0.7401 0.4594
parentescoPadre o madre −0.0613 0.0723 −0.8481 0.3965
parentescoSuegro(a) 0.0394 0.0842 0.4683 0.6397
parentescoYerno o nuera 0.1580 0.0866 1.8240 0.0684
sexoMujer −0.1163 0.0102 −11.3941 <0.0001
poly(edad, 2)1 26.2474 2.6853 9.7744 <0.0001
poly(edad, 2)2 −28.8209 1.1845 −24.3319 <0.0001
departamentoEl Progreso 0.0089 0.0474 0.1879 0.8509
departamentoSacatepéquez 0.0386 0.0441 0.8762 0.3811
departamentoChimaltenango −0.0532 0.0501 −1.0616 0.2886
departamentoEscuintla 0.0560 0.0493 1.1349 0.2566
departamentoSanta Rosa 0.0541 0.0506 1.0695 0.2850
departamentoSololá −0.0342 0.0701 −0.4872 0.6262
departamentoTotonicapán −0.0143 0.0616 −0.2318 0.8167
departamentoQuetzaltenango −0.0578 0.0499 −1.1584 0.2469
departamentoSuchitepéquez −0.0817 0.0477 −1.7117 0.0872
departamentoRetalhuleu 0.0770 0.0576 1.3360 0.1818
departamentoSan Marcos 0.0826 0.0663 1.2459 0.2130
departamentoHuehuetenango 0.1039 0.0547 1.8995 0.0577
departamentoQuiché −0.0463 0.0614 −0.7539 0.4510
departamentoBaja Verapaz −0.1292 0.0604 −2.1387 0.0326
departamentoAlta Verapaz −0.2014 0.0691 −2.9159 0.0036
departamentoPetén −0.1095 0.0565 −1.9397 0.0526
departamentoIzabal 0.0127 0.0616 0.2063 0.8366
departamentoZacapa −0.0693 0.0606 −1.1420 0.2537
departamentoChiquimula −0.1686 0.0735 −2.2927 0.0220
departamentoJalapa −0.0947 0.0562 −1.6853 0.0922
departamentoJutiapa 0.0159 0.0543 0.2931 0.7695
areaRural −0.0567 0.0246 −2.3070 0.0212
poly(miembros_hogar, 3)1 −28.1839 2.4921 −11.3094 <0.0001
poly(miembros_hogar, 3)2 0.3814 3.0469 0.1252 0.9004
poly(miembros_hogar, 3)3 7.4126 3.2039 2.3136 0.0208
propiedadPropia y pagandola a plazos 0.0420 0.0539 0.7785 0.4364
propiedadAlquilada 0.0136 0.0337 0.4017 0.6880
propiedadCedida o prestada 0.0111 0.0287 0.3866 0.6991
propiedadOtro −0.0636 0.1687 −0.3772 0.7061
poly(grado_estudios_hogar, 3)1 6.4369 1.7520 3.6741 0.0002
poly(grado_estudios_hogar, 3)2 −2.9687 1.4252 −2.0830 0.0374
poly(grado_estudios_hogar, 3)3 1.6283 1.3619 1.1957 0.2320
tipo_viviendaApartamento −0.1164 0.2014 −0.5782 0.5632
tipo_viviendaCuarto en casa de vecindad −0.0968 0.1005 −0.9628 0.3358
tipo_viviendaRancho −0.0532 0.2144 −0.2483 0.8039
tipo_viviendaCasa improvisada −0.0064 0.2080 −0.0306 0.9756
material_paredesBlock 0.1807 0.0809 2.2331 0.0257
material_paredesConcreto 0.2597 0.0969 2.6805 0.0074
material_paredesAdobe 0.0698 0.0857 0.8143 0.4156
material_paredesMadera 0.1244 0.0905 1.3746 0.1695
material_paredesLamina metalica 0.2298 0.2251 1.0205 0.3076
material_paredesBajareque −0.1421 0.1151 −1.2346 0.2172
material_paredesLepa, palo o caña −0.0492 0.2047 −0.2404 0.8101
material_paredesOtro 0.2120 0.1297 1.6344 0.1024
material_techoLamina metalica 0.0694 0.0287 2.4173 0.0158
material_techoAsbesto cemento −0.0168 0.1066 −0.1574 0.8749
material_techoTeja 0.1094 0.0576 1.8986 0.0578
material_techoPaja, palma o similar 0.2683 0.1906 1.4076 0.1595
material_techoOtro 0.2462 0.1855 1.3271 0.1847
material_pisoLadrillo de cemento 0.0112 0.0405 0.2755 0.7830
material_pisoLadrillo de barro −0.0164 0.1224 −0.1338 0.8936
material_pisoTorta de cemento −0.0326 0.0260 −1.2548 0.2098
material_pisoMadera −0.0508 0.1287 −0.3943 0.6934
material_pisoTierra −0.1126 0.0397 −2.8337 0.0047
poly(n_cuartos, 3)1 7.8302 2.5664 3.0510 0.0023
poly(n_cuartos, 3)2 0.5734 2.0430 0.2807 0.7790
poly(n_cuartos, 3)3 0.4077 1.9278 0.2115 0.8325
tipo_sanitarioUso compartido −0.0409 0.0339 −1.2083 0.2272
fuente_aguaTubería fuera de la vivienda −0.0074 0.0357 −0.2062 0.8367
fuente_aguaChorro publico 0.0390 0.0692 0.5635 0.5732
fuente_aguaPozo perforado 0.0286 0.0378 0.7569 0.4493
fuente_aguaRío, lago, manantial −0.1764 0.0654 −2.6979 0.0071
fuente_aguaCamion cisterna 0.1336 0.0709 1.8830 0.0599
fuente_aguaAgua de lluvia −0.0069 0.0888 −0.0780 0.9378
fuente_aguaOtro −0.1078 0.0548 −1.9672 0.0494
recoleccion_basuraLa tiran en cualquier lugar −0.0614 0.0531 −1.1562 0.2478
recoleccion_basuraServicio municipal 0.0315 0.0263 1.2002 0.2303
recoleccion_basuraServicio privado 0.0668 0.0327 2.0444 0.0411
electricidadNo −0.0509 0.0378 −1.3468 0.1783
televisorNo −0.0609 0.0201 −3.0337 0.0025
telefonia_celularNo −0.0359 0.0234 −1.5386 0.1241
computadoraNo −0.0743 0.0261 −2.8498 0.0044
Scatter chart with observed digestible protein from non-maize sources in grams per day along the x-axis and the full model's predicted values along the y-axis. Points cluster along an upward diagonal trend, showing predictions increase with observed intake, with scatter around the line reflecting individual-level variability the model does not capture.
Figure 6: Observed vs predicted digestible protein intake from non-maize sources (full model)

Variable Selection

Table 7: Wald test results for predictor significance (digestible protein from non-maize)
Variable Significance Testing. Wald F-test results for digestible protein intake from non-maize model
Variable Significance Testing
Wald F-test results for digestible protein intake from non-maize model
variable f_statistic p_value significant
parentesco 8.52 <0.0001 *
sexo 129.82 <0.0001 *
poly(edad, 2) 307.79 <0.0001 *
departamento 3.20 <0.0001 *
area 5.32 0.0212 *
poly(miembros_hogar, 3) 79.79 <0.0001 *
propiedad 0.23 0.9194
poly(grado_estudios_hogar, 3) 4.88 0.0022 *
tipo_vivienda 0.36 0.8340
material_paredes 3.72 0.0003 *
material_techo 1.78 0.1136
material_piso 1.90 0.0910
poly(n_cuartos, 3) 3.20 0.0226 *
tipo_sanitario 1.46 0.2272
fuente_agua 2.38 0.0204 *
recoleccion_basura 2.29 0.0771
electricidad 1.81 0.1783
televisor 9.20 0.0025 *
telefonia_celular 2.37 0.1241
computadora 8.12 0.0044 *
ImportantVariables Retained

12 predictors significantly predict digestible protein 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 digestible protein intake from non-maize sources (refined model)
Digestible Protein Intake (PDCAAS-Adjusted) from Non-Maize Sources (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Digestible Protein Intake (PDCAAS-Adjusted) from Non-Maize Sources (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) 3.0610 0.1076 28.4549 <0.0001
parentescoEsposo(a) o compañero(a) −0.1470 0.0661 −2.2222 0.0264
parentescoHermano(a) 0.0482 0.1210 0.3981 0.6906
parentescoHijo(a) −0.0329 0.0658 −0.4994 0.6176
parentescoJefe del hogar −0.1062 0.0660 −1.6092 0.1078
parentescoNieto(a) −0.0346 0.0731 −0.4738 0.6357
parentescoOtro no pariente −0.4053 0.3668 −1.1048 0.2694
parentescoOtro pariente −0.0614 0.0797 −0.7701 0.4414
parentescoPadre o madre −0.0526 0.0725 −0.7258 0.4681
parentescoSuegro(a) 0.0312 0.0852 0.3665 0.7140
parentescoYerno o nuera 0.1462 0.0888 1.6460 0.1000
sexoMujer −0.1156 0.0101 −11.4663 <0.0001
poly(edad, 2)1 27.0721 2.6524 10.2068 <0.0001
poly(edad, 2)2 −29.0010 1.1924 −24.3219 <0.0001
departamentoEl Progreso 0.0035 0.0460 0.0763 0.9392
departamentoSacatepéquez 0.0350 0.0430 0.8136 0.4160
departamentoChimaltenango −0.0695 0.0488 −1.4238 0.1547
departamentoEscuintla 0.0469 0.0485 0.9674 0.3335
departamentoSanta Rosa 0.0363 0.0492 0.7381 0.4606
departamentoSololá −0.0601 0.0660 −0.9116 0.3621
departamentoTotonicapán −0.0492 0.0588 −0.8363 0.4031
departamentoQuetzaltenango −0.0843 0.0466 −1.8080 0.0708
departamentoSuchitepéquez −0.0978 0.0452 −2.1607 0.0309
departamentoRetalhuleu 0.0561 0.0541 1.0373 0.2998
departamentoSan Marcos 0.0545 0.0648 0.8422 0.3998
departamentoHuehuetenango 0.0727 0.0523 1.3900 0.1648
departamentoQuiché −0.0797 0.0596 −1.3385 0.1810
departamentoBaja Verapaz −0.1403 0.0599 −2.3434 0.0193
departamentoAlta Verapaz −0.2371 0.0667 −3.5533 0.0004
departamentoPetén −0.1083 0.0546 −1.9840 0.0475
departamentoIzabal 0.0170 0.0606 0.2798 0.7796
departamentoZacapa −0.0907 0.0609 −1.4910 0.1362
departamentoChiquimula −0.1861 0.0734 −2.5359 0.0113
departamentoJalapa −0.1370 0.0549 −2.4939 0.0128
departamentoJutiapa 0.0033 0.0534 0.0616 0.9509
areaRural −0.0723 0.0233 −3.0982 0.0020
poly(miembros_hogar, 3)1 −28.8285 2.4391 −11.8193 <0.0001
poly(miembros_hogar, 3)2 −0.0210 2.9936 −0.0070 0.9944
poly(miembros_hogar, 3)3 7.4466 3.1534 2.3614 0.0183
poly(grado_estudios_hogar, 3)1 7.2686 1.7544 4.1431 <0.0001
poly(grado_estudios_hogar, 3)2 −3.1445 1.4576 −2.1574 0.0311
poly(grado_estudios_hogar, 3)3 1.5521 1.3794 1.1252 0.2607
material_paredesBlock 0.1848 0.0800 2.3116 0.0209
material_paredesConcreto 0.2493 0.0959 2.5996 0.0094
material_paredesAdobe 0.0558 0.0837 0.6672 0.5047
material_paredesMadera 0.0873 0.0883 0.9892 0.3227
material_paredesLamina metalica 0.1922 0.0881 2.1805 0.0294
material_paredesBajareque −0.1578 0.1155 −1.3663 0.1721
material_paredesLepa, palo o caña −0.1017 0.1912 −0.5320 0.5948
material_paredesOtro 0.1891 0.1254 1.5076 0.1319
poly(n_cuartos, 3)1 9.3209 2.3974 3.8880 0.0001
poly(n_cuartos, 3)2 −0.0389 2.0385 −0.0191 0.9848
poly(n_cuartos, 3)3 0.4055 1.9378 0.2093 0.8343
fuente_aguaTubería fuera de la vivienda −0.0200 0.0361 −0.5546 0.5792
fuente_aguaChorro publico 0.0284 0.0673 0.4217 0.6733
fuente_aguaPozo perforado 0.0181 0.0369 0.4911 0.6234
fuente_aguaRío, lago, manantial −0.1978 0.0639 −3.0953 0.0020
fuente_aguaCamion cisterna 0.1286 0.0685 1.8765 0.0608
fuente_aguaAgua de lluvia −0.0373 0.0869 −0.4300 0.6673
fuente_aguaOtro −0.1294 0.0538 −2.4065 0.0162
televisorNo −0.0757 0.0201 −3.7740 0.0002
computadoraNo −0.0812 0.0263 −3.0845 0.0021
Scatter chart with observed digestible protein from non-maize sources in grams per day along the x-axis and the refined model's predicted values along the y-axis. Points follow the same upward diagonal trend as the full model, showing that restricting to significant predictors retains predictive accuracy while simplifying the model.
Figure 7: Observed vs predicted digestible protein intake from non-maize sources (refined model)

Model Diagnostics

Grid of regression diagnostic panels for the refined non-maize gamma model, covering residuals, leverage, and collinearity. Residuals show no systematic pattern and are approximately normal, no observations are overly influential, 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 digestible protein 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 Digestible protein from maize Digestible protein from non-maize
N observations 34,777 34,777
N predictors 54 61
Pseudo-R² (McFadden)1 0.173 0.175
Pseudo-R² (Cragg-Uhler)2 0.278 0.228
AIC 38,271 20,005
Dispersion 1.094 0.454
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)
Digestible protein from maize 11 variables Age, department, household size, area
Digestible protein from non-maize 12 variables Age, household size, area, education, wall materials

Key Findings

  1. More predictors for non-maize: The non-maize model retains 12 predictors against 11 in the maize model, drawing more of the housing and service variables into the retained set

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

  3. Shared socioeconomic predictors: Age, household size, area and mean household education are retained in both models, so the same socioeconomic axis carries predictive power for maize and non-maize digestible protein

Application

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

Back to top