Transfer Model: Lysine Intake

Module 3: Transfer Models

Why Model Lysine?

Lysine is an essential amino acid that cannot be synthesized by the human body and must be obtained from the diet. It is the first limiting amino acid in maize, meaning maize protein quality is constrained by its lysine content. By modeling lysine intake from maize and non-maize sources separately, we can:

  1. Simulate biofortification scenarios — Predict how quality protein maize (QPM) with higher lysine would change total lysine intake
  2. Preserve baseline non-maize intake — Keep other dietary sources constant when modeling interventions
  3. Assess protein quality impacts — As the first limiting amino acid in maize, lysine availability can constrain the overall utilization of dietary protein
NoteWhy Lysine Matters

In maize-dependent diets, the lysine content of the grain sets a ceiling on how much of the dietary protein can be used for growth, even when total protein intake appears adequate. Quality Protein Maize (QPM) varieties carry a higher lysine content than conventional maize, which is the channel through which biofortification acts on protein quality.

Modeling Approach

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

  • Positive and continuous — People consume some amount of lysine 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 lysine 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 amino acids:

  • Amino acid intake distributions are more stable
  • Extreme values are consistent with measurement error
  • Amino acid intakes have natural biological limits tied to protein consumption

Survey Design

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

Modeling Lysine Intake from Maize

Distribution Selection

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

Table 1: Distribution fit comparison for lysine 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 −28,529.3456 57,062.6912 57,079.5986 0.0342 12.3433 77.8178
Lognormal −30,473.0113 60,950.0226 60,966.9300 0.0520 29.4518 216.7346
Exponential −28,608.8038 57,219.6076 57,228.0613 0.0490 28.3104 158.3263
Four-panel goodness-of-fit assessment for lysine intake from maize. The top-left panel overlays a right-skewed histogram of intake with a dashed gamma density curve that closely tracks the bars. The top-right quantile-quantile plot and bottom-right probability-probability plot both show points falling close to the diagonal reference line. The bottom-left panel compares the empirical and theoretical cumulative distribution functions, which nearly overlap. The close agreement across all panels supports the gamma distribution as the best fit.
Figure 1: Distribution assessment for lysine 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 lysine intake from maize.

Table 2: Model coefficients for lysine intake from maize (full model)
Lysine Intake from Maize (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Lysine Intake from Maize (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) −1.0558 0.1883 −5.6083 <0.0001
parentescoEsposo(a) o compañero(a) 0.1024 0.0769 1.3312 0.1834
parentescoHermano(a) 0.3001 0.1590 1.8873 0.0593
parentescoHijo(a) 0.2533 0.0700 3.6176 0.0003
parentescoJefe del hogar 0.1002 0.0725 1.3817 0.1673
parentescoNieto(a) 0.1737 0.0802 2.1667 0.0304
parentescoOtro no pariente 0.1213 0.4774 0.2540 0.7996
parentescoOtro pariente 0.2668 0.1161 2.2977 0.0217
parentescoPadre o madre 0.2360 0.0787 2.9974 0.0028
parentescoSuegro(a) 0.2929 0.1482 1.9768 0.0483
parentescoYerno o nuera 0.1230 0.1237 0.9940 0.3204
sexoMujer −0.0852 0.0164 −5.1916 <0.0001
poly(edad, 2)1 28.4649 3.9275 7.2475 <0.0001
poly(edad, 2)2 −20.9373 1.8682 −11.2071 <0.0001
departamentoEl Progreso 0.1948 0.0986 1.9750 0.0485
departamentoSacatepéquez 0.2558 0.0847 3.0204 0.0026
departamentoChimaltenango 0.4284 0.0803 5.3360 <0.0001
departamentoEscuintla 0.1753 0.0819 2.1397 0.0326
departamentoSanta Rosa 0.3916 0.0970 4.0351 <0.0001
departamentoSololá 0.6454 0.1047 6.1616 <0.0001
departamentoTotonicapán 0.5345 0.0941 5.6819 <0.0001
departamentoQuetzaltenango 0.5756 0.0949 6.0627 <0.0001
departamentoSuchitepéquez 0.4620 0.0771 5.9915 <0.0001
departamentoRetalhuleu 0.4687 0.0950 4.9324 <0.0001
departamentoSan Marcos 0.5184 0.0961 5.3966 <0.0001
departamentoHuehuetenango 0.6218 0.0973 6.3885 <0.0001
departamentoQuiché 0.5901 0.0922 6.3999 <0.0001
departamentoBaja Verapaz 0.5595 0.0951 5.8812 <0.0001
departamentoAlta Verapaz 0.3999 0.1060 3.7711 0.0002
departamentoPetén 0.5066 0.0886 5.7157 <0.0001
departamentoIzabal 0.3360 0.0984 3.4148 0.0007
departamentoZacapa 0.1650 0.1095 1.5070 0.1320
departamentoChiquimula 0.3647 0.1027 3.5499 0.0004
departamentoJalapa 0.5257 0.0925 5.6818 <0.0001
departamentoJutiapa 0.2805 0.0854 3.2854 0.0010
areaRural 0.1144 0.0333 3.4355 0.0006
poly(miembros_hogar, 3)1 9.0382 2.7665 3.2670 0.0011
poly(miembros_hogar, 3)2 3.2438 2.6921 1.2049 0.2284
poly(miembros_hogar, 3)3 −1.9008 3.2427 −0.5862 0.5579
propiedadPropia y pagandola a plazos −0.1256 0.1042 −1.2052 0.2284
propiedadAlquilada −0.0698 0.0586 −1.1904 0.2341
propiedadCedida o prestada −0.0004 0.0487 −0.0090 0.9928
propiedadOtro −0.5551 0.2936 −1.8909 0.0588
poly(grado_estudios_hogar, 3)1 −12.0579 4.0568 −2.9723 0.0030
poly(grado_estudios_hogar, 3)2 −2.5126 3.5155 −0.7147 0.4749
poly(grado_estudios_hogar, 3)3 −5.0615 3.0400 −1.6650 0.0962
tipo_viviendaApartamento −0.2235 0.1760 −1.2698 0.2044
tipo_viviendaCuarto en casa de vecindad 0.3572 0.2662 1.3420 0.1798
tipo_viviendaRancho −1.4764 0.1990 −7.4176 <0.0001
tipo_viviendaCasa improvisada 0.1323 0.1718 0.7704 0.4412
material_paredesBlock 0.1229 0.1515 0.8116 0.4172
material_paredesConcreto 0.0644 0.2065 0.3118 0.7552
material_paredesAdobe 0.2083 0.1561 1.3345 0.1823
material_paredesMadera 0.1516 0.1654 0.9167 0.3595
material_paredesLamina metalica −0.0121 0.2600 −0.0465 0.9629
material_paredesBajareque 0.4039 0.1798 2.2470 0.0248
material_paredesLepa, palo o caña 0.1283 0.2398 0.5349 0.5928
material_paredesOtro −0.0616 0.2408 −0.2559 0.7980
material_techoLamina metalica 0.0269 0.0584 0.4607 0.6451
material_techoAsbesto cemento −0.3556 0.1404 −2.5326 0.0114
material_techoTeja 0.1057 0.0878 1.2029 0.2292
material_techoPaja, palma o similar 1.4130 0.1823 7.7515 <0.0001
material_techoOtro −0.0334 0.2517 −0.1327 0.8945
material_pisoLadrillo de cemento −0.0256 0.0679 −0.3771 0.7062
material_pisoLadrillo de barro −0.0056 0.2742 −0.0203 0.9838
material_pisoTorta de cemento 0.0794 0.0470 1.6882 0.0916
material_pisoMadera −0.0963 0.1461 −0.6591 0.5099
material_pisoTierra 0.1089 0.0557 1.9560 0.0507
poly(n_cuartos, 3)1 −5.6747 3.3703 −1.6837 0.0925
poly(n_cuartos, 3)2 −2.0572 2.9609 −0.6948 0.4873
poly(n_cuartos, 3)3 −6.2578 4.0789 −1.5342 0.1252
tipo_sanitarioUso compartido 0.0857 0.0586 1.4644 0.1433
fuente_aguaTubería fuera de la vivienda 0.1158 0.0451 2.5690 0.0103
fuente_aguaChorro publico 0.0469 0.0739 0.6347 0.5257
fuente_aguaPozo perforado 0.0296 0.0400 0.7418 0.4583
fuente_aguaRío, lago, manantial −0.0678 0.0613 −1.1061 0.2689
fuente_aguaCamion cisterna −0.0675 0.1304 −0.5180 0.6046
fuente_aguaAgua de lluvia −0.0079 0.0886 −0.0889 0.9291
fuente_aguaOtro −0.0725 0.0673 −1.0768 0.2818
recoleccion_basuraLa tiran en cualquier lugar −0.1487 0.0648 −2.2947 0.0219
recoleccion_basuraServicio municipal −0.3368 0.0515 −6.5452 <0.0001
recoleccion_basuraServicio privado −0.3905 0.0716 −5.4503 <0.0001
electricidadNo 0.0250 0.0384 0.6509 0.5152
televisorNo −0.0196 0.0342 −0.5718 0.5676
telefonia_celularNo −0.0430 0.0303 −1.4214 0.1554
computadoraNo 0.1454 0.0452 3.2149 0.0013
Scatter chart with observed lysine intake from maize in grams per day on the x-axis and model-predicted intake in grams per day on the y-axis, for the full model with all 20 candidate predictors. Points concentrate in the lower intake range and follow a positive but dispersed trend, indicating moderate predictive accuracy.
Figure 2: Observed vs predicted lysine 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 (lysine from maize)
Variable Significance Testing. Wald F-test results for lysine intake from maize model
Variable Significance Testing
Wald F-test results for lysine intake from maize model
variable f_statistic p_value significant
parentesco 5.42 <0.0001 *
sexo 26.95 <0.0001 *
poly(edad, 2) 75.31 <0.0001 *
departamento 5.35 <0.0001 *
area 11.80 0.0006 *
poly(miembros_hogar, 3) 3.96 0.0079 *
propiedad 1.59 0.1752
poly(grado_estudios_hogar, 3) 5.31 0.0012 *
tipo_vivienda 19.84 <0.0001 *
material_paredes 1.77 0.0795
material_techo 16.28 <0.0001 *
material_piso 1.64 0.1467
poly(n_cuartos, 3) 1.64 0.1792
tipo_sanitario 2.14 0.1433
fuente_agua 1.75 0.0934
recoleccion_basura 18.74 <0.0001 *
electricidad 0.42 0.5152
televisor 0.33 0.5676
telefonia_celular 2.02 0.1554
computadora 10.34 0.0013 *
ImportantVariables Retained

11 predictors show significant relationships with lysine intake from maize, spanning demographic, geographic, socioeconomic, housing and asset categories. Variables that do not significantly predict lysine 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 lysine intake from maize (refined model)
Lysine Intake from Maize (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Lysine Intake from Maize (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) −0.9711 0.1067 −9.0989 <0.0001
parentescoEsposo(a) o compañero(a) 0.1104 0.0771 1.4317 0.1525
parentescoHermano(a) 0.2957 0.1644 1.7983 0.0724
parentescoHijo(a) 0.2417 0.0700 3.4540 0.0006
parentescoJefe del hogar 0.1045 0.0730 1.4315 0.1525
parentescoNieto(a) 0.1700 0.0808 2.1034 0.0356
parentescoOtro no pariente 0.1694 0.4781 0.3543 0.7232
parentescoOtro pariente 0.2440 0.1146 2.1293 0.0334
parentescoPadre o madre 0.2104 0.0781 2.6946 0.0071
parentescoSuegro(a) 0.2839 0.1404 2.0219 0.0434
parentescoYerno o nuera 0.1011 0.1287 0.7855 0.4323
sexoMujer −0.0900 0.0165 −5.4576 <0.0001
poly(edad, 2)1 26.4773 3.8640 6.8524 <0.0001
poly(edad, 2)2 −20.1537 1.8546 −10.8670 <0.0001
departamentoEl Progreso 0.2507 0.0990 2.5329 0.0114
departamentoSacatepéquez 0.2882 0.0849 3.3931 0.0007
departamentoChimaltenango 0.4446 0.0793 5.6102 <0.0001
departamentoEscuintla 0.1935 0.0814 2.3788 0.0175
departamentoSanta Rosa 0.4243 0.0951 4.4622 <0.0001
departamentoSololá 0.6834 0.1053 6.4900 <0.0001
departamentoTotonicapán 0.6042 0.0916 6.5980 <0.0001
departamentoQuetzaltenango 0.6106 0.0946 6.4543 <0.0001
departamentoSuchitepéquez 0.5023 0.0769 6.5307 <0.0001
departamentoRetalhuleu 0.5047 0.0948 5.3234 <0.0001
departamentoSan Marcos 0.5707 0.0966 5.9069 <0.0001
departamentoHuehuetenango 0.6891 0.0932 7.3940 <0.0001
departamentoQuiché 0.6575 0.0897 7.3342 <0.0001
departamentoBaja Verapaz 0.6075 0.0910 6.6768 <0.0001
departamentoAlta Verapaz 0.4575 0.0958 4.7763 <0.0001
departamentoPetén 0.5365 0.0845 6.3495 <0.0001
departamentoIzabal 0.3605 0.0956 3.7711 0.0002
departamentoZacapa 0.2676 0.1104 2.4233 0.0155
departamentoChiquimula 0.4678 0.1046 4.4739 <0.0001
departamentoJalapa 0.5803 0.0905 6.4096 <0.0001
departamentoJutiapa 0.3098 0.0838 3.6951 0.0002
areaRural 0.1224 0.0334 3.6598 0.0003
poly(miembros_hogar, 3)1 8.9724 2.6819 3.3456 0.0008
poly(miembros_hogar, 3)2 3.0148 2.7977 1.0776 0.2814
poly(miembros_hogar, 3)3 −2.4002 3.4454 −0.6966 0.4861
poly(grado_estudios_hogar, 3)1 −13.0856 4.1250 −3.1723 0.0015
poly(grado_estudios_hogar, 3)2 −3.0151 3.4750 −0.8677 0.3857
poly(grado_estudios_hogar, 3)3 −5.7451 3.1024 −1.8519 0.0643
tipo_viviendaApartamento −0.2327 0.1773 −1.3126 0.1895
tipo_viviendaCuarto en casa de vecindad 0.4801 0.2889 1.6620 0.0967
tipo_viviendaRancho −1.4890 0.1193 −12.4771 <0.0001
tipo_viviendaCasa improvisada 0.0480 0.0731 0.6562 0.5118
material_techoLamina metalica 0.1079 0.0589 1.8319 0.0672
material_techoAsbesto cemento −0.3451 0.1457 −2.3688 0.0180
material_techoTeja 0.2297 0.0871 2.6375 0.0084
material_techoPaja, palma o similar 1.5750 0.1020 15.4398 <0.0001
material_techoOtro 0.0707 0.2677 0.2642 0.7917
recoleccion_basuraLa tiran en cualquier lugar −0.1456 0.0650 −2.2399 0.0253
recoleccion_basuraServicio municipal −0.3755 0.0497 −7.5557 <0.0001
recoleccion_basuraServicio privado −0.4218 0.0703 −6.0023 <0.0001
computadoraNo 0.1622 0.0460 3.5263 0.0004
Scatter chart with observed lysine intake from maize in grams per day on the x-axis and predicted intake in grams per day on the y-axis, for the refined model using only significant predictors. The positive, dispersed pattern closely matches the full-model plot, showing that dropping non-significant predictors preserves predictive accuracy.
Figure 3: Observed vs predicted lysine intake from maize (refined model)

Model Diagnostics

We verify the model meets statistical assumptions:

Grid of regression diagnostic panels for the gamma model of lysine intake from maize. The panels show residuals plotted against fitted values with no systematic pattern, residual quantiles that fall approximately along the normal reference line, a leverage plot with no overly influential observations, and degrees-of-freedom adjusted variance inflation factors plotted against shaded low, moderate and high reference bands.
Figure 4: Diagnostic plots for lysine 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 5.8, 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 Lysine Intake from Non-Maize Sources

NoteLysine in Non-Maize Foods

Non-maize sources (especially animal products and legumes) are typically lysine-rich. This model captures the higher-quality protein component of the diet that complements maize-based nutrition.

Distribution Selection

Table 5: Distribution fit comparison for lysine 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 −49,053.2991 98,110.5983 98,127.5056 0.0328 12.8655 89.3496
Lognormal −54,299.8336 108,603.6673 108,620.5746 0.0938 118.8248 751.3135
Exponential −50,863.5733 101,729.1466 101,737.6003 0.1162 173.6004 946.1863
Four-panel goodness-of-fit assessment for lysine intake from non-maize sources. The top-left panel overlays a right-skewed histogram of intake with a dashed gamma density curve that closely tracks the bars. The top-right quantile-quantile plot and bottom-right probability-probability plot both show points falling close to the diagonal reference line. The bottom-left panel compares the empirical and theoretical cumulative distribution functions, which nearly overlap. The close agreement across all panels again supports the gamma distribution as the best fit.
Figure 5: Distribution assessment for lysine intake from non-maize sources
ImportantDistribution Selection

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

Full Model

Table 6: Model coefficients for lysine intake from non-maize sources (full model)
Lysine Intake from Non-Maize Sources (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Lysine 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) 0.4803 0.1193 4.0246 <0.0001
parentescoEsposo(a) o compañero(a) −0.1425 0.0676 −2.1063 0.0354
parentescoHermano(a) 0.0348 0.1236 0.2818 0.7782
parentescoHijo(a) −0.0314 0.0672 −0.4683 0.6397
parentescoJefe del hogar −0.1034 0.0675 −1.5320 0.1257
parentescoNieto(a) −0.0175 0.0757 −0.2308 0.8175
parentescoOtro no pariente −0.2052 0.3143 −0.6530 0.5139
parentescoOtro pariente −0.0611 0.0822 −0.7435 0.4573
parentescoPadre o madre −0.0419 0.0737 −0.5677 0.5703
parentescoSuegro(a) 0.0021 0.0860 0.0244 0.9805
parentescoYerno o nuera 0.1212 0.0848 1.4289 0.1533
sexoMujer −0.1129 0.0099 −11.3819 <0.0001
poly(edad, 2)1 27.7594 2.6931 10.3074 <0.0001
poly(edad, 2)2 −29.0911 1.2061 −24.1200 <0.0001
departamentoEl Progreso 0.0378 0.0452 0.8362 0.4032
departamentoSacatepéquez 0.0413 0.0460 0.8969 0.3700
departamentoChimaltenango −0.0007 0.0485 −0.0149 0.9881
departamentoEscuintla 0.1062 0.0480 2.2130 0.0271
departamentoSanta Rosa 0.0777 0.0504 1.5412 0.1235
departamentoSololá −0.0311 0.0729 −0.4264 0.6699
departamentoTotonicapán −0.0502 0.0625 −0.8039 0.4216
departamentoQuetzaltenango −0.0946 0.0496 −1.9068 0.0568
departamentoSuchitepéquez −0.0484 0.0468 −1.0337 0.3014
departamentoRetalhuleu 0.0935 0.0588 1.5902 0.1120
departamentoSan Marcos 0.0997 0.0661 1.5079 0.1318
departamentoHuehuetenango 0.1160 0.0531 2.1848 0.0291
departamentoQuiché −0.0273 0.0602 −0.4540 0.6499
departamentoBaja Verapaz −0.1067 0.0597 −1.7855 0.0744
departamentoAlta Verapaz −0.1347 0.0666 −2.0224 0.0433
departamentoPetén −0.0496 0.0561 −0.8831 0.3773
departamentoIzabal 0.0389 0.0589 0.6603 0.5092
departamentoZacapa 0.0253 0.0536 0.4732 0.6362
departamentoChiquimula −0.0737 0.0675 −1.0918 0.2751
departamentoJalapa −0.0313 0.0584 −0.5371 0.5913
departamentoJutiapa 0.0706 0.0532 1.3263 0.1850
areaRural −0.0571 0.0246 −2.3266 0.0201
poly(miembros_hogar, 3)1 −28.4383 2.1855 −13.0124 <0.0001
poly(miembros_hogar, 3)2 −1.4769 2.3904 −0.6178 0.5368
poly(miembros_hogar, 3)3 4.6177 2.3946 1.9284 0.0540
propiedadPropia y pagandola a plazos 0.0756 0.0514 1.4717 0.1413
propiedadAlquilada 0.0221 0.0344 0.6406 0.5219
propiedadCedida o prestada 0.0258 0.0285 0.9061 0.3650
propiedadOtro −0.0354 0.1702 −0.2077 0.8355
poly(grado_estudios_hogar, 3)1 6.4703 1.7370 3.7250 0.0002
poly(grado_estudios_hogar, 3)2 −2.7694 1.4558 −1.9023 0.0573
poly(grado_estudios_hogar, 3)3 0.8979 1.3937 0.6443 0.5195
tipo_viviendaApartamento −0.1121 0.2255 −0.4973 0.6191
tipo_viviendaCuarto en casa de vecindad −0.0741 0.0992 −0.7463 0.4556
tipo_viviendaRancho 0.1192 0.2085 0.5720 0.5674
tipo_viviendaCasa improvisada 0.0076 0.2039 0.0371 0.9704
material_paredesBlock 0.1757 0.0870 2.0210 0.0435
material_paredesConcreto 0.2576 0.1006 2.5607 0.0106
material_paredesAdobe 0.0663 0.0911 0.7271 0.4673
material_paredesMadera 0.1100 0.0953 1.1542 0.2486
material_paredesLamina metalica 0.2134 0.2237 0.9542 0.3402
material_paredesBajareque −0.0744 0.1142 −0.6517 0.5147
material_paredesLepa, palo o caña −0.0517 0.2056 −0.2513 0.8016
material_paredesOtro 0.1802 0.1317 1.3682 0.1715
material_techoLamina metalica 0.0782 0.0289 2.7050 0.0069
material_techoAsbesto cemento 0.0083 0.1128 0.0732 0.9417
material_techoTeja 0.1458 0.0569 2.5617 0.0105
material_techoPaja, palma o similar 0.1406 0.1851 0.7593 0.4478
material_techoOtro 0.0667 0.1705 0.3911 0.6958
material_pisoLadrillo de cemento 0.0032 0.0422 0.0748 0.9404
material_pisoLadrillo de barro 0.0831 0.1234 0.6737 0.5006
material_pisoTorta de cemento −0.0405 0.0260 −1.5563 0.1199
material_pisoMadera −0.0610 0.1441 −0.4235 0.6720
material_pisoTierra −0.1083 0.0383 −2.8243 0.0048
poly(n_cuartos, 3)1 9.2479 2.3872 3.8740 0.0001
poly(n_cuartos, 3)2 1.1456 2.0727 0.5527 0.5806
poly(n_cuartos, 3)3 0.1486 1.8813 0.0790 0.9370
tipo_sanitarioUso compartido −0.0447 0.0345 −1.2963 0.1951
fuente_aguaTubería fuera de la vivienda −0.0167 0.0364 −0.4601 0.6455
fuente_aguaChorro publico 0.0344 0.0719 0.4787 0.6322
fuente_aguaPozo perforado 0.0170 0.0352 0.4850 0.6278
fuente_aguaRío, lago, manantial −0.1710 0.0620 −2.7586 0.0059
fuente_aguaCamion cisterna 0.1629 0.0730 2.2325 0.0257
fuente_aguaAgua de lluvia 0.0324 0.0886 0.3656 0.7147
fuente_aguaOtro −0.0793 0.0574 −1.3810 0.1675
recoleccion_basuraLa tiran en cualquier lugar −0.0558 0.0505 −1.1051 0.2693
recoleccion_basuraServicio municipal 0.0184 0.0263 0.6997 0.4842
recoleccion_basuraServicio privado 0.0430 0.0333 1.2888 0.1977
electricidadNo −0.0452 0.0372 −1.2177 0.2235
televisorNo −0.0528 0.0202 −2.6161 0.0090
telefonia_celularNo −0.0308 0.0227 −1.3564 0.1752
computadoraNo −0.0716 0.0263 −2.7219 0.0066
Scatter chart with observed lysine intake from non-maize sources in grams per day on the x-axis and model-predicted intake in grams per day on the y-axis, for the full model with all candidate predictors. Points follow a positive but dispersed trend, indicating moderate predictive accuracy.
Figure 6: Observed vs predicted lysine intake from non-maize sources (full model)

Variable Selection

Table 7: Wald test results for predictor significance (lysine from non-maize)
Variable Significance Testing. Wald F-test results for lysine intake from non-maize model
Variable Significance Testing
Wald F-test results for lysine intake from non-maize model
variable f_statistic p_value significant
parentesco 7.20 <0.0001 *
sexo 129.55 <0.0001 *
poly(edad, 2) 304.97 <0.0001 *
departamento 2.90 <0.0001 *
area 5.41 0.0201 *
poly(miembros_hogar, 3) 76.50 <0.0001 *
propiedad 0.71 0.5869
poly(grado_estudios_hogar, 3) 4.79 0.0025 *
tipo_vivienda 0.36 0.8395
material_paredes 3.27 0.0011 *
material_techo 2.12 0.0611
material_piso 1.97 0.0810
poly(n_cuartos, 3) 5.06 0.0017 *
tipo_sanitario 1.68 0.1951
fuente_agua 2.33 0.0227 *
recoleccion_basura 1.17 0.3198
electricidad 1.48 0.2235
televisor 6.84 0.0090 *
telefonia_celular 1.84 0.1752
computadora 7.41 0.0066 *
ImportantVariables Retained

12 predictors significantly predict lysine 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 lysine intake from non-maize sources (refined model)
Lysine Intake from Non-Maize Sources (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Lysine 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) 0.5370 0.1148 4.6789 <0.0001
parentescoEsposo(a) o compañero(a) −0.1460 0.0685 −2.1333 0.0331
parentescoHermano(a) 0.0362 0.1230 0.2941 0.7688
parentescoHijo(a) −0.0289 0.0678 −0.4271 0.6694
parentescoJefe del hogar −0.1065 0.0683 −1.5587 0.1193
parentescoNieto(a) −0.0197 0.0761 −0.2591 0.7956
parentescoOtro no pariente −0.2078 0.3155 −0.6585 0.5103
parentescoOtro pariente −0.0632 0.0832 −0.7592 0.4478
parentescoPadre o madre −0.0356 0.0740 −0.4805 0.6310
parentescoSuegro(a) −0.0040 0.0866 −0.0465 0.9629
parentescoYerno o nuera 0.1123 0.0868 1.2942 0.1958
sexoMujer −0.1114 0.0098 −11.3266 <0.0001
poly(edad, 2)1 28.3432 2.6774 10.5859 <0.0001
poly(edad, 2)2 −29.2353 1.2241 −23.8840 <0.0001
departamentoEl Progreso 0.0349 0.0440 0.7950 0.4268
departamentoSacatepéquez 0.0347 0.0455 0.7643 0.4448
departamentoChimaltenango −0.0175 0.0471 −0.3724 0.7097
departamentoEscuintla 0.1033 0.0474 2.1787 0.0295
departamentoSanta Rosa 0.0694 0.0494 1.4041 0.1605
departamentoSololá −0.0541 0.0691 −0.7833 0.4336
departamentoTotonicapán −0.0740 0.0598 −1.2375 0.2161
departamentoQuetzaltenango −0.1140 0.0471 −2.4218 0.0156
departamentoSuchitepéquez −0.0580 0.0448 −1.2961 0.1952
departamentoRetalhuleu 0.0826 0.0555 1.4882 0.1369
departamentoSan Marcos 0.0774 0.0652 1.1861 0.2358
departamentoHuehuetenango 0.0909 0.0518 1.7563 0.0793
departamentoQuiché −0.0538 0.0584 −0.9217 0.3568
departamentoBaja Verapaz −0.1090 0.0603 −1.8070 0.0710
departamentoAlta Verapaz −0.1636 0.0651 −2.5140 0.0121
departamentoPetén −0.0429 0.0546 −0.7872 0.4313
departamentoIzabal 0.0525 0.0583 0.8998 0.3684
departamentoZacapa 0.0057 0.0529 0.1081 0.9139
departamentoChiquimula −0.0854 0.0681 −1.2537 0.2102
departamentoJalapa −0.0646 0.0579 −1.1148 0.2651
departamentoJutiapa 0.0656 0.0523 1.2543 0.2100
areaRural −0.0663 0.0232 −2.8554 0.0044
poly(miembros_hogar, 3)1 −28.9402 2.1402 −13.5223 <0.0001
poly(miembros_hogar, 3)2 −1.8146 2.3362 −0.7768 0.4374
poly(miembros_hogar, 3)3 4.7187 2.3556 2.0032 0.0454
poly(grado_estudios_hogar, 3)1 7.1983 1.7406 4.1355 <0.0001
poly(grado_estudios_hogar, 3)2 −2.9301 1.5008 −1.9523 0.0511
poly(grado_estudios_hogar, 3)3 0.7992 1.3849 0.5771 0.5640
material_paredesBlock 0.1816 0.0859 2.1148 0.0346
material_paredesConcreto 0.2541 0.0992 2.5621 0.0105
material_paredesAdobe 0.0653 0.0892 0.7322 0.4642
material_paredesMadera 0.0839 0.0932 0.9002 0.3682
material_paredesLamina metalica 0.1969 0.0937 2.1019 0.0357
material_paredesBajareque −0.0767 0.1135 −0.6757 0.4993
material_paredesLepa, palo o caña −0.0726 0.1861 −0.3899 0.6967
material_paredesOtro 0.1702 0.1265 1.3459 0.1785
poly(n_cuartos, 3)1 10.4255 2.2572 4.6187 <0.0001
poly(n_cuartos, 3)2 0.5251 2.0599 0.2549 0.7988
poly(n_cuartos, 3)3 0.1450 1.8878 0.0768 0.9388
fuente_aguaTubería fuera de la vivienda −0.0274 0.0366 −0.7486 0.4542
fuente_aguaChorro publico 0.0308 0.0694 0.4446 0.6567
fuente_aguaPozo perforado 0.0100 0.0346 0.2887 0.7729
fuente_aguaRío, lago, manantial −0.1875 0.0614 −3.0552 0.0023
fuente_aguaCamion cisterna 0.1584 0.0705 2.2475 0.0248
fuente_aguaAgua de lluvia 0.0030 0.0863 0.0345 0.9725
fuente_aguaOtro −0.1012 0.0563 −1.7985 0.0723
televisorNo −0.0647 0.0199 −3.2509 0.0012
computadoraNo −0.0759 0.0264 −2.8789 0.0041
Scatter chart with observed lysine intake from non-maize sources in grams per day on the x-axis and predicted intake in grams per day on the y-axis, for the refined model using only significant predictors. The positive, dispersed pattern closely matches the full-model plot, showing that dropping non-significant predictors preserves predictive accuracy.
Figure 7: Observed vs predicted lysine intake from non-maize sources (refined model)

Model Diagnostics

Grid of regression diagnostic panels for the gamma model of lysine intake from non-maize sources. The panels show residuals plotted against fitted values with no systematic pattern, residual quantiles that fall approximately along the normal reference line, a leverage plot with no overly influential observations, and degrees-of-freedom adjusted variance inflation factors plotted against shaded low, moderate and high bands.
Figure 8: Diagnostic plots for lysine 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 Lysine from maize Lysine from non-maize
N observations 34,672 34,672
N predictors 54 61
Pseudo-R² (McFadden)1 0.173 0.155
Pseudo-R² (Cragg-Uhler)2 0.277 0.206
AIC 38,078 21,521
Dispersion 1.090 0.456
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)
Lysine from maize 11 variables Age, department, education, area
Lysine from non-maize 12 variables Age, household size, area, wall materials, rooms

Key Findings

  1. Same retained set as digestible protein: The lysine models select the same predictors as the digestible protein models, which follows from lysine being one component of the protein intake being modeled

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

  3. Housing variables in the non-maize model: Wall materials and number of rooms are retained for non-maize lysine and not for maize lysine

Application

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

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