Figures and Tables for Chapter 4

12 14 16 18 20 22 24 Grouped Procedure Mo de l Si ze

Figure 4.1: Model size under heteroskedasticity across grouped selection methods: Het.1.

iCAP GLASSO 12 14 16 18 20 22 24 Grouped Procedure Mo de l Si ze

Figure 4.2: Model size under heteroskedasticity across grouped selection methods: Het.2.

The figures show box-plots of model sizes over 100 simulations and n = 500 of 2 regression experiments with forms of heteroskedasticity, Het.1 : σ2_{= (3 + 0.2X}

4X5)2 and Het.2 : σ2= 1 + 0.1X42+ 0.2X52. The

iCAP GLASSO OLS 0 50 100 150 200 250 300 Grouped Procedure Mo de l Erro r

Figure 4.3: Model error across grouped and other selection methods, n = 100.

iCAP GLASSO OLS

0.0 0.5 1.0 1.5 2.0 2.5 3.0 Grouped Procedure Mo de l Erro r

Figure 4.4: Model error across grouped and other selection methods, n = 5000.

The figures show box-plots of model errors over 100 simulations for n = 100 and n = 5000 of a regression experiment with heteroskedasticity of the form Het.2 : σ2_{= 1 + 0.1X}2

4+ 0.2X 2 5 .

Table 4.1: Summary statistics for categorical covariates in Ghana 2008 DHS.

Variable Levels n %

Birth order Among first five 1662 82.0

Among next five 364 18.0

Wealth Poorest 674 33.3

Poorer 453 22.4

Middle 329 16.2

Richer 335 16.5

Richest 235 11.6

Water source Bottled Water 95 4.7

Piped Water 630 31.1

River, Dam, Lake etc. 327 16.1

Well/Tubewell 974 48.1

Toilet Flush toilet 129 6.4

Ventillated improved toilet latrine 655 32.3

No Facility/Composting/Bucket/Pan 731 36.1 Other 511 25.2 Fuel Charcoal/Wood/Straw 1887 93.1 Electricity/Biogas 133 6.6 Kerosene 6 0.3 Gender Female 1007 49.7 Male 1019 50.3 Residence Rural 1371 67.7 Urban 655 32.3 Electricity No 1190 58.7 Yes 836 41.3 TV No 1395 68.8 Yes 631 31.1 Fridge No 1656 81.7 Yes 370 18.3 Bicycle No 1177 58.1 Yes 849 41.9 Motorcycle No 1860 91.8 Yes 166 8.2 Car No 1941 95.8 Yes 85 4.2

Table 4.2: Summary statistics for continuous covariates in Ghana 2008 DHS.

Variable n Min Mean Median Max

Child age (months) 2026 0.0 28.9 28.0 59.0

Mother Educ. (years) 2026 0.0 4.5 4.0 16.0

Mother age (years) 2026 16.0 30.5 30.0 49.0

Mother BMI 2026 12.2 23.2 22.3 56.9

Father Educ. (years) 2026 0.0 6.5 9.0 19.0

Table 4.3: Child health by important risk factors.

Wealth Quintiles Maternal BMI

Child size Large Small n Large Small n

Poorest 0.512 0.189 674 BMI < 20 0.486 0.160 405 Poorer 0.559 0.130 453 BMI ∈ [20,25) 0.563 0.146 1090 Middle 0.558 0.116 329 BMI ∈ [25,30) 0.541 0.138 382

Richer 0.544 0.128 335 BMI > 30 0.622 0.126 135 Richest 0.615 0.123 235

Maternal Education Cooking Fuel

Child size Large Small n Large Small n

No Education 0.529 0.164 797 Wood/Straw 0.536 0.156 1352 Educated 0.561 0.134 1215 Other 0.569 0.125 660

Largerefers to proportion of children who are larger than average and very large in their size at birth. Small refers to children who are smaller than average and very small at birth. Wood/Straw are examples of biofuels.

Table 4.4: Performance of selection procedures: 2008 DHS.

i CAP OLS LASSO GLASSO

Prediction error 22.13 27.80 26.78 25.47 (1.92) (2.99) (2.55) (2.34)

Standard error in parenthesis. The prediction error is for an independent test set chosen from the 2008 DHS sample of children younger than 5 years.

Table 4.5: Quantile regression model: categorical variables.

τ = 0.1 τ = 0.5 τ = 0.75 Female -0.384∗∗∗ -0.543∗∗∗ -0.484∗∗∗ (0.048) (0.061) (0.058) Birth order (early) 0.000 0.127∗∗ 0.178∗∗∗

(0.047) (0.060) (0.057) Poorer 0.000 -0.033 0.011 (0.045) (0.059) (0.057) Middle 0.000 0.089 0.037 (0.047) (0.056) (0.056) Richer 0.000 0.000 0.011 (0.041) (0.054) (0.051) Richest 0.152∗∗∗ 0.442∗∗∗ 0.689∗∗∗ (0.041) (0.052) (0.052) Fuel: LPG 0.000 0.014 0.006 (0.045) (0.056) (0.054) Fuel: Natural Gas -0.005 0.000 -0.054

(0.040) (0.068) (0.061) Fuel: Kerosene 0.159∗∗∗ 0.000 0.000 (0.031) (0.054) (0.055) Fuel: Charcoal 0.000 0.000 0.000 (0.039) (0.050) (0.047) Fuel: Wood -0.116∗∗∗ -0.235∗∗∗ -0.033 (0.036) (0.047) (0.043) Aux. Midwife 0.248∗∗∗ 0.108∗∗∗ 0.000 (0.043) (0.057) (0.054) DPT/Hep./Flu Vaccine 0.223∗∗∗ 0.141∗∗ 0.131∗∗∗ (0.045) (0.059) (0.059) TV 0.199∗∗∗ 0.000 0.000 (0.040) (0.054) (0.053) Fridge 0.141∗∗∗ 0.027 0.000 (0.041) (0.056) (0.054)

Dependent variable: child height (in cm). Standard deviation in parenthesis. Significant at∗_10%,∗∗_5%,∗∗∗ _{1%. Aux. Midwife is}

an indicator for the mother having had access to midwife prenatal care.

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