Transfer Model: Tryptophan Intake

Module 3: Transfer Models

Why Model Tryptophan?

Tryptophan is an essential amino acid and the second limiting amino acid in maize (after lysine). It serves as a precursor for serotonin and niacin, making it important for both growth and neurological development. By modeling tryptophan intake from maize and non-maize sources separately, we can:

  1. Simulate biofortification scenarios — Predict how quality protein maize (QPM) with higher tryptophan would change total tryptophan intake
  2. Preserve baseline non-maize intake — Keep other dietary sources constant when modeling interventions
  3. Assess protein quality impacts — Tryptophan availability affects both protein utilization and niacin status
NoteWhy Tryptophan Matters

Quality Protein Maize (QPM) varieties contain higher levels of both lysine and tryptophan. Tryptophan is also a precursor for niacin (vitamin B3), so a higher tryptophan intake bears on niacin status as well as on protein quality.

Modeling Approach

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

  • Positive and continuous — People consume some amount of tryptophan 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 tryptophan 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 Tryptophan Intake from Maize

Distribution Selection

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

Table 1: Distribution fit comparison for tryptophan 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 18,321.7055 −36,639.4110 −36,622.5002 0.0341 12.3451 77.8459
Lognormal 16,381.0477 −32,758.0954 −32,741.1845 0.0520 29.5419 217.1557
Exponential 18,240.3163 −36,478.6325 −36,470.1771 0.0491 28.5899 159.9681
Four goodness-of-fit panels comparing observed maize tryptophan intake against a fitted gamma distribution. Top left is a histogram of intake with the theoretical gamma density overlaid as a dashed curve; top right is a quantile-quantile plot of empirical versus theoretical quantiles; bottom left overlays the empirical and theoretical cumulative distribution functions; bottom right is a probability-probability plot. Points lying close to the diagonal reference lines and the density curve tracking the histogram indicate the gamma distribution fits the right-skewed intake data well.
Figure 1: Distribution assessment for tryptophan 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 tryptophan intake from maize.

Table 2: Model coefficients for tryptophan intake from maize (full model)
Tryptophan Intake from Maize (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Tryptophan Intake from Maize (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) −2.4148 0.1839 −13.1343 <0.0001
parentescoEsposo(a) o compañero(a) 0.1260 0.0715 1.7608 0.0785
parentescoHermano(a) 0.3462 0.1561 2.2178 0.0267
parentescoHijo(a) 0.2750 0.0656 4.1918 <0.0001
parentescoJefe del hogar 0.1278 0.0681 1.8757 0.0609
parentescoNieto(a) 0.1956 0.0759 2.5777 0.0100
parentescoOtro no pariente 0.1564 0.4779 0.3273 0.7435
parentescoOtro pariente 0.2933 0.1135 2.5848 0.0098
parentescoPadre o madre 0.2551 0.0752 3.3940 0.0007
parentescoSuegro(a) 0.3297 0.1490 2.2128 0.0271
parentescoYerno o nuera 0.1456 0.1209 1.2040 0.2288
sexoMujer −0.0861 0.0163 −5.2800 <0.0001
poly(edad, 2)1 27.9513 3.9502 7.0759 <0.0001
poly(edad, 2)2 −21.0880 1.8820 −11.2050 <0.0001
departamentoEl Progreso 0.1918 0.0991 1.9357 0.0531
departamentoSacatepéquez 0.2714 0.0840 3.2323 0.0013
departamentoChimaltenango 0.4320 0.0802 5.3889 <0.0001
departamentoEscuintla 0.1859 0.0816 2.2794 0.0228
departamentoSanta Rosa 0.4062 0.0967 4.1990 <0.0001
departamentoSololá 0.6542 0.1044 6.2655 <0.0001
departamentoTotonicapán 0.5394 0.0931 5.7961 <0.0001
departamentoQuetzaltenango 0.5826 0.0948 6.1448 <0.0001
departamentoSuchitepéquez 0.4688 0.0774 6.0547 <0.0001
departamentoRetalhuleu 0.4677 0.0947 4.9371 <0.0001
departamentoSan Marcos 0.5321 0.0954 5.5795 <0.0001
departamentoHuehuetenango 0.6318 0.0967 6.5333 <0.0001
departamentoQuiché 0.6010 0.0920 6.5326 <0.0001
departamentoBaja Verapaz 0.5674 0.0945 6.0015 <0.0001
departamentoAlta Verapaz 0.4092 0.1061 3.8558 0.0001
departamentoPetén 0.5135 0.0888 5.7806 <0.0001
departamentoIzabal 0.3525 0.0967 3.6437 0.0003
departamentoZacapa 0.1760 0.1090 1.6139 0.1068
departamentoChiquimula 0.3701 0.1024 3.6144 0.0003
departamentoJalapa 0.5318 0.0924 5.7581 <0.0001
departamentoJutiapa 0.2842 0.0853 3.3332 0.0009
areaRural 0.1131 0.0332 3.4056 0.0007
poly(miembros_hogar, 3)1 9.6047 2.7501 3.4925 0.0005
poly(miembros_hogar, 3)2 2.7877 2.6926 1.0353 0.3007
poly(miembros_hogar, 3)3 −1.7778 3.2326 −0.5500 0.5824
propiedadPropia y pagandola a plazos −0.1296 0.1030 −1.2591 0.2082
propiedadAlquilada −0.0778 0.0585 −1.3299 0.1838
propiedadCedida o prestada 0.0018 0.0489 0.0371 0.9704
propiedadOtro −0.5529 0.2984 −1.8529 0.0641
poly(grado_estudios_hogar, 3)1 −12.0693 4.0300 −2.9949 0.0028
poly(grado_estudios_hogar, 3)2 −2.4558 3.5027 −0.7011 0.4833
poly(grado_estudios_hogar, 3)3 −5.4019 3.0681 −1.7607 0.0785
tipo_viviendaApartamento −0.2049 0.1760 −1.1638 0.2447
tipo_viviendaCuarto en casa de vecindad 0.3725 0.2649 1.4063 0.1599
tipo_viviendaRancho −1.4632 0.1983 −7.3772 <0.0001
tipo_viviendaCasa improvisada 0.1268 0.1741 0.7282 0.4666
material_paredesBlock 0.1076 0.1501 0.7173 0.4733
material_paredesConcreto 0.0306 0.1977 0.1546 0.8771
material_paredesAdobe 0.1982 0.1547 1.2810 0.2004
material_paredesMadera 0.1430 0.1639 0.8724 0.3831
material_paredesLamina metalica −0.0275 0.2620 −0.1048 0.9165
material_paredesBajareque 0.3895 0.1778 2.1907 0.0286
material_paredesLepa, palo o caña 0.1278 0.2382 0.5366 0.5916
material_paredesOtro −0.0688 0.2425 −0.2839 0.7766
material_techoLamina metalica 0.0312 0.0583 0.5342 0.5933
material_techoAsbesto cemento −0.3506 0.1393 −2.5175 0.0119
material_techoTeja 0.1061 0.0874 1.2140 0.2249
material_techoPaja, palma o similar 1.4039 0.1813 7.7422 <0.0001
material_techoOtro −0.0258 0.2525 −0.1020 0.9187
material_pisoLadrillo de cemento −0.0227 0.0673 −0.3371 0.7361
material_pisoLadrillo de barro −0.0176 0.2813 −0.0627 0.9500
material_pisoTorta de cemento 0.0741 0.0470 1.5759 0.1153
material_pisoMadera −0.1402 0.1430 −0.9802 0.3272
material_pisoTierra 0.1011 0.0556 1.8182 0.0693
poly(n_cuartos, 3)1 −5.7847 3.3825 −1.7102 0.0875
poly(n_cuartos, 3)2 −1.8279 2.9593 −0.6177 0.5369
poly(n_cuartos, 3)3 −6.3258 4.1012 −1.5424 0.1232
tipo_sanitarioUso compartido 0.0817 0.0590 1.3858 0.1660
fuente_aguaTubería fuera de la vivienda 0.1154 0.0449 2.5724 0.0102
fuente_aguaChorro publico 0.0458 0.0740 0.6188 0.5361
fuente_aguaPozo perforado 0.0354 0.0398 0.8878 0.3748
fuente_aguaRío, lago, manantial −0.0664 0.0612 −1.0839 0.2786
fuente_aguaCamion cisterna −0.0717 0.1324 −0.5417 0.5881
fuente_aguaAgua de lluvia −0.0095 0.0882 −0.1075 0.9144
fuente_aguaOtro −0.0756 0.0676 −1.1188 0.2634
recoleccion_basuraLa tiran en cualquier lugar −0.1496 0.0645 −2.3207 0.0205
recoleccion_basuraServicio municipal −0.3400 0.0515 −6.6001 <0.0001
recoleccion_basuraServicio privado −0.3972 0.0713 −5.5721 <0.0001
electricidadNo 0.0232 0.0385 0.6022 0.5472
televisorNo −0.0255 0.0341 −0.7472 0.4551
telefonia_celularNo −0.0476 0.0304 −1.5686 0.1170
computadoraNo 0.1447 0.0452 3.1974 0.0014
Scatter chart with observed tryptophan intake from maize in grams per day on the x-axis and the full model's predicted intake on the y-axis. Each semi-transparent point is one individual. Points broadly follow an upward diagonal trend, showing predictions track observed values, though spread around the trend reflects the model's limited precision for individual intake.
Figure 2: Observed vs predicted tryptophan 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 (tryptophan from maize)
Variable Significance Testing. Wald F-test results for tryptophan intake from maize model
Variable Significance Testing
Wald F-test results for tryptophan intake from maize model
variable f_statistic p_value significant
parentesco 5.75 <0.0001 *
sexo 27.88 <0.0001 *
poly(edad, 2) 75.15 <0.0001 *
departamento 5.42 <0.0001 *
area 11.60 0.0007 *
poly(miembros_hogar, 3) 4.32 0.0049 *
propiedad 1.66 0.1557
poly(grado_estudios_hogar, 3) 5.46 0.0010 *
tipo_vivienda 19.39 <0.0001 *
material_paredes 1.84 0.0665
material_techo 15.98 <0.0001 *
material_piso 1.65 0.1450
poly(n_cuartos, 3) 1.67 0.1722
tipo_sanitario 1.92 0.1660
fuente_agua 1.78 0.0867
recoleccion_basura 19.26 <0.0001 *
electricidad 0.36 0.5472
televisor 0.56 0.4551
telefonia_celular 2.46 0.1170
computadora 10.22 0.0014 *
ImportantVariables Retained

11 predictors show significant relationships with tryptophan intake from maize, spanning demographic, geographic, socioeconomic, housing and asset categories. Variables that do not significantly predict tryptophan 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 tryptophan intake from maize (refined model)
Tryptophan Intake from Maize (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Tryptophan Intake from Maize (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) −2.3506 0.1011 −23.2474 <0.0001
parentescoEsposo(a) o compañero(a) 0.1330 0.0711 1.8706 0.0616
parentescoHermano(a) 0.3382 0.1608 2.1027 0.0357
parentescoHijo(a) 0.2638 0.0652 4.0438 <0.0001
parentescoJefe del hogar 0.1314 0.0679 1.9362 0.0530
parentescoNieto(a) 0.1926 0.0762 2.5259 0.0116
parentescoOtro no pariente 0.2054 0.4785 0.4292 0.6679
parentescoOtro pariente 0.2696 0.1114 2.4207 0.0156
parentescoPadre o madre 0.2317 0.0743 3.1179 0.0019
parentescoSuegro(a) 0.3175 0.1400 2.2685 0.0234
parentescoYerno o nuera 0.1232 0.1256 0.9811 0.3267
sexoMujer −0.0905 0.0164 −5.5234 <0.0001
poly(edad, 2)1 26.1755 3.8839 6.7394 <0.0001
poly(edad, 2)2 −20.2826 1.8689 −10.8527 <0.0001
departamentoEl Progreso 0.2483 0.0993 2.4994 0.0126
departamentoSacatepéquez 0.3009 0.0842 3.5727 0.0004
departamentoChimaltenango 0.4503 0.0790 5.6969 <0.0001
departamentoEscuintla 0.2051 0.0806 2.5442 0.0111
departamentoSanta Rosa 0.4410 0.0950 4.6402 <0.0001
departamentoSololá 0.6946 0.1048 6.6310 <0.0001
departamentoTotonicapán 0.6113 0.0906 6.7501 <0.0001
departamentoQuetzaltenango 0.6189 0.0945 6.5495 <0.0001
departamentoSuchitepéquez 0.5119 0.0771 6.6399 <0.0001
departamentoRetalhuleu 0.5047 0.0946 5.3354 <0.0001
departamentoSan Marcos 0.5863 0.0958 6.1192 <0.0001
departamentoHuehuetenango 0.7004 0.0925 7.5702 <0.0001
departamentoQuiché 0.6705 0.0893 7.5123 <0.0001
departamentoBaja Verapaz 0.6161 0.0902 6.8298 <0.0001
departamentoAlta Verapaz 0.4673 0.0955 4.8936 <0.0001
departamentoPetén 0.5451 0.0845 6.4494 <0.0001
departamentoIzabal 0.3773 0.0939 4.0165 <0.0001
departamentoZacapa 0.2775 0.1101 2.5199 0.0118
departamentoChiquimula 0.4742 0.1041 4.5536 <0.0001
departamentoJalapa 0.5897 0.0903 6.5307 <0.0001
departamentoJutiapa 0.3159 0.0835 3.7829 0.0002
areaRural 0.1208 0.0334 3.6221 0.0003
poly(miembros_hogar, 3)1 9.5200 2.6662 3.5707 0.0004
poly(miembros_hogar, 3)2 2.5616 2.7932 0.9171 0.3593
poly(miembros_hogar, 3)3 −2.2393 3.4338 −0.6521 0.5144
poly(grado_estudios_hogar, 3)1 −13.0614 4.1015 −3.1845 0.0015
poly(grado_estudios_hogar, 3)2 −3.0484 3.4561 −0.8820 0.3779
poly(grado_estudios_hogar, 3)3 −6.1539 3.1317 −1.9651 0.0496
tipo_viviendaApartamento −0.2174 0.1778 −1.2227 0.2217
tipo_viviendaCuarto en casa de vecindad 0.4915 0.2866 1.7150 0.0866
tipo_viviendaRancho −1.4933 0.1185 −12.5982 <0.0001
tipo_viviendaCasa improvisada 0.0414 0.0730 0.5671 0.5707
material_techoLamina metalica 0.1097 0.0588 1.8653 0.0624
material_techoAsbesto cemento −0.3403 0.1447 −2.3518 0.0188
material_techoTeja 0.2280 0.0868 2.6262 0.0087
material_techoPaja, palma o similar 1.5802 0.1013 15.5991 <0.0001
material_techoOtro 0.0815 0.2686 0.3034 0.7616
recoleccion_basuraLa tiran en cualquier lugar −0.1476 0.0647 −2.2830 0.0226
recoleccion_basuraServicio municipal −0.3794 0.0498 −7.6157 <0.0001
recoleccion_basuraServicio privado −0.4293 0.0698 −6.1494 <0.0001
computadoraNo 0.1594 0.0460 3.4666 0.0005
Scatter chart with observed tryptophan intake from maize in grams per day on the x-axis and the refined model's predicted intake on the y-axis. Each semi-transparent point is one individual. The points follow the same upward diagonal pattern as the full model, indicating that reducing to significant predictors preserves predictive accuracy while simplifying the model.
Figure 3: Observed vs predicted tryptophan intake from maize (refined model)

Model Diagnostics

We verify the model meets statistical assumptions:

Four diagnostic panels for the maize tryptophan gamma model. Top left plots residuals against fitted values with a dashed reference line that should be flat; top right plots the square root of standardized residuals against fitted values to check constant variance; bottom left plots standardized residuals against leverage with dashed Cook's distance contours to flag influential points; bottom right shows variance inflation factors for each predictor with points and error bars against shaded low, moderate and high bands, on the degrees-of-freedom adjusted scale. Reference lines are flat and points sit inside the Cook's contours.
Figure 4: Diagnostic plots for tryptophan 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 Tryptophan Intake from Non-Maize Sources

NoteTryptophan in Non-Maize Foods

Non-maize sources (especially animal products and legumes) are typically tryptophan-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 tryptophan 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 13,165.7536 −26,327.5071 −26,310.5963 0.0286 10.4987 72.4026
Lognormal 8,575.1713 −17,146.3426 −17,129.4318 0.0854 100.4366 636.3691
Exponential 10,526.9236 −21,051.8472 −21,043.3918 0.1290 222.2075 1,217.8812
Four goodness-of-fit panels comparing observed non-maize tryptophan intake against a fitted gamma distribution. Top left is a histogram of intake with the theoretical gamma density overlaid as a dashed curve; top right is a quantile-quantile plot of empirical versus theoretical quantiles; bottom left overlays the empirical and theoretical cumulative distribution functions; bottom right is a probability-probability plot. Points close to the diagonal reference lines and the density curve following the histogram confirm the gamma distribution fits the right-skewed non-maize intake data well.
Figure 5: Distribution assessment for tryptophan intake from non-maize sources
ImportantDistribution Selection

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

Full Model

Table 6: Model coefficients for tryptophan intake from non-maize sources (full model)
Tryptophan Intake from Non-Maize Sources (Full Model) - Model Coefficients. Survey-weighted gamma regression with log link
Tryptophan Intake from Non-Maize Sources (Full Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) −1.2410 0.1116 −11.1238 <0.0001
parentescoEsposo(a) o compañero(a) −0.1501 0.0645 −2.3255 0.0202
parentescoHermano(a) −0.0247 0.1185 −0.2088 0.8346
parentescoHijo(a) −0.0222 0.0652 −0.3407 0.7334
parentescoJefe del hogar −0.1131 0.0640 −1.7670 0.0775
parentescoNieto(a) −0.0194 0.0729 −0.2666 0.7898
parentescoOtro no pariente −0.4204 0.3306 −1.2713 0.2038
parentescoOtro pariente −0.0872 0.0730 −1.1953 0.2322
parentescoPadre o madre −0.0411 0.0726 −0.5660 0.5715
parentescoSuegro(a) 0.0178 0.0803 0.2212 0.8250
parentescoYerno o nuera 0.1269 0.0826 1.5363 0.1247
sexoMujer −0.1171 0.0094 −12.5094 <0.0001
poly(edad, 2)1 29.3062 2.5281 11.5920 <0.0001
poly(edad, 2)2 −29.4799 1.1339 −25.9977 <0.0001
departamentoEl Progreso 0.0141 0.0439 0.3207 0.7485
departamentoSacatepéquez 0.0280 0.0424 0.6620 0.5081
departamentoChimaltenango −0.0344 0.0472 −0.7298 0.4657
departamentoEscuintla 0.0740 0.0459 1.6111 0.1074
departamentoSanta Rosa 0.0316 0.0484 0.6527 0.5141
departamentoSololá −0.0999 0.0662 −1.5100 0.1313
departamentoTotonicapán −0.1028 0.0595 −1.7262 0.0845
departamentoQuetzaltenango −0.1195 0.0468 −2.5551 0.0107
departamentoSuchitepéquez −0.0847 0.0449 −1.8855 0.0596
departamentoRetalhuleu −0.0055 0.0547 −0.1015 0.9192
departamentoSan Marcos 0.0480 0.0624 0.7689 0.4421
departamentoHuehuetenango 0.0588 0.0506 1.1608 0.2459
departamentoQuiché −0.1020 0.0568 −1.7959 0.0727
departamentoBaja Verapaz −0.1496 0.0592 −2.5279 0.0116
departamentoAlta Verapaz −0.2281 0.0670 −3.4060 0.0007
departamentoPetén −0.1393 0.0543 −2.5643 0.0104
departamentoIzabal −0.0632 0.0549 −1.1515 0.2497
departamentoZacapa −0.0530 0.0505 −1.0512 0.2933
departamentoChiquimula −0.1373 0.0623 −2.2052 0.0276
departamentoJalapa −0.0774 0.0550 −1.4091 0.1590
departamentoJutiapa 0.0081 0.0519 0.1562 0.8759
areaRural −0.0522 0.0230 −2.2737 0.0231
poly(miembros_hogar, 3)1 −28.5337 2.0530 −13.8986 <0.0001
poly(miembros_hogar, 3)2 −1.1816 2.2469 −0.5259 0.5991
poly(miembros_hogar, 3)3 5.3703 2.3049 2.3300 0.0200
propiedadPropia y pagandola a plazos 0.0668 0.0527 1.2669 0.2054
propiedadAlquilada 0.0130 0.0318 0.4070 0.6841
propiedadCedida o prestada 0.0345 0.0261 1.3230 0.1861
propiedadOtro −0.1312 0.1378 −0.9522 0.3412
poly(grado_estudios_hogar, 3)1 6.7588 1.7984 3.7582 0.0002
poly(grado_estudios_hogar, 3)2 −3.4259 1.3963 −2.4536 0.0143
poly(grado_estudios_hogar, 3)3 0.5784 1.3417 0.4311 0.6664
tipo_viviendaApartamento −0.0905 0.2073 −0.4367 0.6624
tipo_viviendaCuarto en casa de vecindad −0.0720 0.0888 −0.8104 0.4179
tipo_viviendaRancho 0.2786 0.2035 1.3690 0.1712
tipo_viviendaCasa improvisada 0.0794 0.2071 0.3834 0.7015
material_paredesBlock 0.1632 0.0779 2.0936 0.0365
material_paredesConcreto 0.2362 0.0906 2.6077 0.0092
material_paredesAdobe 0.0728 0.0816 0.8913 0.3729
material_paredesMadera 0.1011 0.0855 1.1829 0.2371
material_paredesLamina metalica 0.1506 0.2233 0.6741 0.5003
material_paredesBajareque −0.0457 0.1034 −0.4422 0.6584
material_paredesLepa, palo o caña −0.1148 0.2084 −0.5508 0.5819
material_paredesOtro 0.1225 0.1480 0.8281 0.4078
material_techoLamina metalica 0.0791 0.0277 2.8549 0.0044
material_techoAsbesto cemento −0.0043 0.1040 −0.0415 0.9669
material_techoTeja 0.1467 0.0538 2.7286 0.0064
material_techoPaja, palma o similar −0.0326 0.1833 −0.1779 0.8588
material_techoOtro 0.0505 0.1633 0.3090 0.7573
material_pisoLadrillo de cemento 0.0145 0.0392 0.3696 0.7117
material_pisoLadrillo de barro 0.0742 0.1199 0.6188 0.5362
material_pisoTorta de cemento −0.0319 0.0246 −1.2979 0.1946
material_pisoMadera −0.0421 0.1256 −0.3350 0.7377
material_pisoTierra −0.0956 0.0359 −2.6635 0.0078
poly(n_cuartos, 3)1 7.4978 2.2151 3.3849 0.0007
poly(n_cuartos, 3)2 −0.1562 1.9965 −0.0782 0.9377
poly(n_cuartos, 3)3 1.1460 1.8504 0.6193 0.5358
tipo_sanitarioUso compartido −0.0407 0.0312 −1.3041 0.1924
fuente_aguaTubería fuera de la vivienda −0.0208 0.0349 −0.5944 0.5524
fuente_aguaChorro publico 0.0048 0.0705 0.0675 0.9462
fuente_aguaPozo perforado 0.0180 0.0321 0.5588 0.5764
fuente_aguaRío, lago, manantial −0.1579 0.0608 −2.5983 0.0095
fuente_aguaCamion cisterna 0.1409 0.0701 2.0093 0.0447
fuente_aguaAgua de lluvia 0.0205 0.0778 0.2632 0.7925
fuente_aguaOtro −0.0514 0.0555 −0.9253 0.3550
recoleccion_basuraLa tiran en cualquier lugar −0.0502 0.0484 −1.0384 0.2993
recoleccion_basuraServicio municipal 0.0117 0.0249 0.4714 0.6374
recoleccion_basuraServicio privado 0.0455 0.0318 1.4323 0.1523
electricidadNo −0.0410 0.0353 −1.1622 0.2453
televisorNo −0.0495 0.0189 −2.6204 0.0089
telefonia_celularNo −0.0267 0.0220 −1.2121 0.2257
computadoraNo −0.0736 0.0244 −3.0202 0.0026
Scatter chart with observed tryptophan intake from non-maize sources in grams per day on the x-axis and the full model's predicted intake on the y-axis. Each semi-transparent point is one individual. Points follow an upward diagonal trend showing predictions track observed values, with scatter around the trend reflecting individual-level prediction uncertainty.
Figure 6: Observed vs predicted tryptophan intake from non-maize sources (full model)

Variable Selection

Table 7: Wald test results for predictor significance (tryptophan from non-maize)
Variable Significance Testing. Wald F-test results for tryptophan intake from non-maize model
Variable Significance Testing
Wald F-test results for tryptophan intake from non-maize model
variable f_statistic p_value significant
parentesco 9.58 <0.0001 *
sexo 156.48 <0.0001 *
poly(edad, 2) 355.27 <0.0001 *
departamento 3.42 <0.0001 *
area 5.17 0.0231 *
poly(miembros_hogar, 3) 87.53 <0.0001 *
propiedad 1.00 0.4047
poly(grado_estudios_hogar, 3) 5.36 0.0011 *
tipo_vivienda 0.82 0.5142
material_paredes 2.90 0.0033 *
material_techo 2.40 0.0351 *
material_piso 1.89 0.0927
poly(n_cuartos, 3) 4.08 0.0068 *
tipo_sanitario 1.70 0.1924
fuente_agua 1.80 0.0828
recoleccion_basura 1.26 0.2865
electricidad 1.35 0.2453
televisor 6.87 0.0089 *
telefonia_celular 1.47 0.2257
computadora 9.12 0.0026 *
ImportantVariables Retained

12 predictors significantly predict tryptophan 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 tryptophan intake from non-maize sources (refined model)
Tryptophan Intake from Non-Maize Sources (Refined Model) - Model Coefficients. Survey-weighted gamma regression with log link
Tryptophan Intake from Non-Maize Sources (Refined Model) - Model Coefficients
Survey-weighted gamma regression with log link
Term Estimate Std. Error t-statistic p-value
(Intercept) −1.1920 0.1092 −10.9197 <0.0001
parentescoEsposo(a) o compañero(a) −0.1540 0.0645 −2.3856 0.0172
parentescoHermano(a) −0.0149 0.1178 −0.1264 0.8994
parentescoHijo(a) −0.0230 0.0653 −0.3518 0.7250
parentescoJefe del hogar −0.1175 0.0639 −1.8396 0.0660
parentescoNieto(a) −0.0184 0.0734 −0.2508 0.8020
parentescoOtro no pariente −0.4008 0.3352 −1.1954 0.2321
parentescoOtro pariente −0.0923 0.0739 −1.2487 0.2120
parentescoPadre o madre −0.0349 0.0728 −0.4792 0.6319
parentescoSuegro(a) 0.0128 0.0802 0.1591 0.8736
parentescoYerno o nuera 0.1171 0.0839 1.3959 0.1630
sexoMujer −0.1162 0.0094 −12.3732 <0.0001
poly(edad, 2)1 29.8339 2.5051 11.9095 <0.0001
poly(edad, 2)2 −29.5575 1.1574 −25.5369 <0.0001
departamentoEl Progreso 0.0008 0.0435 0.0185 0.9853
departamentoSacatepéquez 0.0082 0.0415 0.1984 0.8427
departamentoChimaltenango −0.0564 0.0455 −1.2391 0.2155
departamentoEscuintla 0.0582 0.0431 1.3524 0.1765
departamentoSanta Rosa −0.0010 0.0468 −0.0213 0.9830
departamentoSololá −0.1283 0.0634 −2.0247 0.0431
departamentoTotonicapán −0.1423 0.0573 −2.4824 0.0132
departamentoQuetzaltenango −0.1512 0.0435 −3.4757 0.0005
departamentoSuchitepéquez −0.1029 0.0416 −2.4738 0.0135
departamentoRetalhuleu −0.0324 0.0495 −0.6549 0.5126
departamentoSan Marcos 0.0064 0.0615 0.1041 0.9171
departamentoHuehuetenango 0.0197 0.0481 0.4095 0.6823
departamentoQuiché −0.1425 0.0533 −2.6727 0.0076
departamentoBaja Verapaz −0.1805 0.0599 −3.0159 0.0026
departamentoAlta Verapaz −0.2909 0.0616 −4.7212 <0.0001
departamentoPetén −0.1696 0.0524 −3.2393 0.0012
departamentoIzabal −0.0829 0.0541 −1.5313 0.1259
departamentoZacapa −0.0881 0.0493 −1.7856 0.0744
departamentoChiquimula −0.1688 0.0620 −2.7235 0.0065
departamentoJalapa −0.1278 0.0540 −2.3662 0.0181
departamentoJutiapa −0.0121 0.0518 −0.2347 0.8145
areaRural −0.0714 0.0219 −3.2527 0.0012
poly(miembros_hogar, 3)1 −29.1906 2.0098 −14.5240 <0.0001
poly(miembros_hogar, 3)2 −1.5096 2.2328 −0.6761 0.4991
poly(miembros_hogar, 3)3 5.3790 2.3418 2.2970 0.0218
poly(grado_estudios_hogar, 3)1 7.8336 1.7964 4.3608 <0.0001
poly(grado_estudios_hogar, 3)2 −3.6211 1.4271 −2.5375 0.0113
poly(grado_estudios_hogar, 3)3 0.5578 1.3355 0.4177 0.6762
material_paredesBlock 0.1514 0.0812 1.8658 0.0623
material_paredesConcreto 0.2234 0.0941 2.3750 0.0177
material_paredesAdobe 0.0246 0.0845 0.2914 0.7708
material_paredesMadera 0.0451 0.0877 0.5146 0.6069
material_paredesLamina metalica 0.1815 0.0878 2.0678 0.0388
material_paredesBajareque −0.0903 0.1068 −0.8454 0.3980
material_paredesLepa, palo o caña −0.1182 0.1844 −0.6410 0.5216
material_paredesOtro 0.0946 0.1283 0.7373 0.4610
material_techoLamina metalica 0.0635 0.0251 2.5270 0.0116
material_techoAsbesto cemento −0.0009 0.1047 −0.0084 0.9933
material_techoTeja 0.1416 0.0530 2.6740 0.0076
material_techoPaja, palma o similar 0.1839 0.0802 2.2935 0.0220
material_techoOtro 0.0149 0.1309 0.1138 0.9094
poly(n_cuartos, 3)1 9.7078 2.0895 4.6460 <0.0001
poly(n_cuartos, 3)2 −0.6158 2.0187 −0.3050 0.7604
poly(n_cuartos, 3)3 1.1408 1.8679 0.6108 0.5415
televisorNo −0.0627 0.0188 −3.3394 0.0009
computadoraNo −0.0818 0.0243 −3.3654 0.0008
Scatter chart with observed tryptophan intake from non-maize sources in grams per day on the x-axis and the refined model's predicted intake on the y-axis. Each semi-transparent point is one individual. The points follow the same upward diagonal pattern as the full model, indicating that keeping only significant predictors retains predictive accuracy in a simpler model.
Figure 7: Observed vs predicted tryptophan intake from non-maize sources (refined model)

Model Diagnostics

Four diagnostic panels for the non-maize tryptophan gamma model. Top left plots residuals against fitted values with a dashed reference line that should be flat; top right plots the square root of standardized residuals against fitted values to check constant variance; bottom left plots standardized residuals against leverage with dashed Cook's distance contours to flag influential points; bottom right shows variance inflation factors for each predictor with points and error bars against shaded low, moderate and high bands, on the degrees-of-freedom adjusted scale. Reference lines are flat and points sit within the Cook's contours.
Figure 8: Diagnostic plots for tryptophan 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 Tryptophan from maize Tryptophan from non-maize
N observations 34,732 34,732
N predictors 54 59
Pseudo-R² (McFadden)1 0.176 0.179
Pseudo-R² (Cragg-Uhler)2 0.281 0.229
AIC 38,042 18,577
Dispersion 1.084 0.411
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)
Tryptophan from maize 11 variables Age, department, education, area
Tryptophan from non-maize 12 variables Age, household size, wall and roof materials, rooms

Key Findings

  1. Retained set close to lysine: The tryptophan models select the same predictors as the lysine models in the maize channel, and differ by a single variable in the non-maize channel

  2. Housing variables in the non-maize model: Wall materials, roof materials and number of rooms are retained for non-maize tryptophan, and only roof materials is retained in the maize model

Application

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

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