Supplemental table 1: Sample size of children before and after weighting

/ Unweighted / Weighted
Child age (months) / N / % / N / %
6-11 / 874 / 40.7 / 906 / 40.4
12-17 / 631 / 29.4 / 644 / 28.7
18-23 / 644 / 30.0 / 694 / 30.9
Total / 2149 / 100.0 / 2244 / 100.0

Supplemental table 3: Standardized regression weights and validation parameters for the structural equation model

Equation / Estimates
(un-standardized) / Estimates (standardized) / T-value / Standard Error
Structure
Hemoglobin concentration
Meal frequency / 0.04 / 0.07 / 3.28*** / 0.012
Recent ARI or diarrhea / -0.05 / -0.02 / -0.73 / 0.065
Iron-rich food / 0.3 / 0.10 / 4.45*** / 0.067
Vaccine / -0.12 / -0.03 / -1.46 / 0.081
Growth monitoring / 0.1 / 0.03 / 1.27 / 0.078
Altitude / 0.38 / 0.17 / 7.33*** / 0.052
Male sex / -0.15 / -0.05 / -2.4** / 0.06
Recent ARI and diarrhea
Hand washing / -0.07 / -0.07 / -3.32*** / 0.021
Latrine / 0 / -0.00 / -0.07 / 0.023
Iron-rich food
Diet diversity / 0.14 / 0.55 / 30.25*** / 0.005
Altitude / -0.07 / -0.10 / -5.46*** / 0.013
Dietary diversity
Breastfeeding / -0.39 / -0.10 / -4.38*** / 0.088
Altitude / -0.73 / -0.25 / -12.93*** / 0.056
Maternal Education / 0.32 / 0.12 / 6.31*** / 0.050
Left-behind / -0.38 / -0.07 / -3.56*** / 0.107
Child age / 0.1 / 0.28 / 12.63*** / 0.008
Meal frequency
Breastfeeding / -3.63 / -0.67 / -34.72*** / 0.105
Child age / -0.06 / -0.12 / -6.10*** / 0.010
Area in poverty / -0.22 / -0.09 / -5.70*** / 0.038
Breastfeeding
Sibling / 0.06 / 0.06 / 3.09** / 0.018
Left-behind / -0.4 / -0.28 / -15.66*** / 0.025
Child age / -0.04 / -0.46 / -25.70*** / 0.002
Hand washing
Altitude / -0.24 / -0.32 / -15.65*** / 0.015
Vaccine
Altitude / -0.08 / -0.13 / -6.27*** / 0.012
Maternal education / 0.06 / 0.11 / 5.55*** / 0.011
Child age / 0.02 / 0.30 / 14.74*** / 0.001
Latrine
Altitude / -0.28 / -0.40 / -20.06*** / 0.014
Ethnicity / 0.08 / 0.09 / 4.44*** / 0.019
Weight monitoring
Altitude / -0.2 / -0.32 / -15.53*** / 0.013
Ethnicity / 0.11 / 0.13 / 6.31*** / 0.018
Covariate
Hand washing & Latrine / 0.02 / 0.07 / 3.76*** / 0.004
Diet diversity & Frequency / 0.67 / 0.13 / 8.70*** / 0.077
Latrine & Diet diversity / 0.12 / 0.14 / 7.62*** / 0.015
Altitude & Area in poverty / 0.2 / 0.26 / 12.72*** / 0.016
Sibling & Education / -0.09 / -0.25 / -11.74*** / 0.007
Education & Area in poverty / -0.22 / -0.26 / -12.54*** / 0.017
Education & Ethnicity / 0.06 / 0.19 / 9.09*** / 0.007
Area in poverty & Ethnicity / -0.13 / -0.24 / -11.56*** / 0.012

*p<0.05, **p<0.01, ***p<0.001

Degrees of Freedom = 115

Validation parameters

Minimum Fit Function Chi-Square = 566.23 (P = 0.0)

Normal Theory Weighted Least Squares Chi-Square = 567.07 (P = 0.0)

Estimated Non-centrality Parameter (NCP) = 452.07

90 Percent Confidence Interval for NCP = (381.54 ; 530.14)

Minimum Fit Function Value = 0.26

Population Discrepancy Function Value (F0) = 0.21

90 Percent Confidence Interval for F0 = (0.18 ; 0.25)

Root Mean Square Error of Approximation (RMSEA) = 0.043

90 Percent Confidence Interval for RMSEA = (0.039 ; 0.046)

P-Value for Test of Close Fit (RMSEA < 0.05) = 1.00

Expected Cross-Validation Index (ECVI) = 0.32

90 Percent Confidence Interval for ECVI = (0.28 ; 0.35)

ECVI for Saturated Model = 0.16

ECVI for Independence Model = 3.32

Chi-Square for Independence Model with 153 Degrees of Freedom = 7062.24

Independence AIC = 7098.24

Model AIC = 679.07

Saturated AIC = 342.00

Independence CAIC = 7218.35

Model CAIC = 1052.75

Saturated CAIC = 1483.04

Normed Fit Index (NFI) = 0.92

Non-Normed Fit Index (NNFI) = 0.91

Parsimony Normed Fit Index (PNFI) = 0.69

Comparative Fit Index (CFI) = 0.93

Incremental Fit Index (IFI) = 0.93

Relative Fit Index (RFI) = 0.89

Critical N (CN) = 581.27

Root Mean Square Residual (RMR) = 0.075

Standardized RMR = 0.038

Goodness of Fit Index (GFI) = 0.97

Adjusted Goodness of Fit Index (AGFI) = 0.96

Parsimony Goodness of Fit Index (PGFI) = 0.65

Supplemental table 4:Classification of variables into categories for the structural equation model

Sex
Male / 1
Female / 0
Ethnicity
Han / 1
Minority / 0
Having elder sibling
Yes / 1
No / 0
Left-behind Child
Yes / 1
No / 0
Maternal age
<25 / 1
26-30 / 2
>31 / 3
Maternal education
Illiterate / 1
Primary school / 2
Junior high school / 3
Senior high school and above / 4
Level of poverty in place of residence
Poor / 1
Very poor / 2
Poverty-stricken / 3
Altitude in place of residence
<1000 / 1
≥1000-<3000 / 2
>3000 / 3
Still breastfeeding
Yes / 1
No / 0
Consumption of iron-rich or iron-fortified foods
Yes / 1
No / 0
Acute respiratory or diarrhea illness in the past two weeks
Yes / 1
No / 0
Washing child's hands before meal
Never / 1
Sometimes / 2
Often / 3
Sanitary latrine in household
Yes / 1
No / 0
Growth monitoring chart maintained
Yes / 1
No / 0
Vaccine uptake in first six months of life
According to China schedule / 1
Not according to schedule / 0