Variables to be investigated as predictors of LAZ were selected a priori and were known or hypothesized to influence LAZ based on our earlier findings of resource-poor rural infants, as well as theoretical evidence from the literature. LAZ was treated as a continuous variable rather than dichotomized to minimize the loss of information, maximize the statistical power, preserve the variation in the outcome, and avoid residual confounding.

LAZ is the primary outcome and was measured at 6, 9 and 12 months of age. There were three groups of predictors: demographic predictors (which included maternal predictors and handwashing practices measured at 6, 9 and 12 months of age); nutrient intake predictors (at 6 and 9 months of age); and biomarker predictors of micronutrients and systemic inflammation (at 6 and 9 months of age). Each of these groups of predictors was assessed against LAZ at 9 and 12 months separately before generating a complete model with all relevant predictors. This was to allow the comparison of ‘unadjusted’ and ‘adjusted’ estimates of association.

To estimate relationships between predictors and LAZ, dynamic panel data models were fitted using maximum likelihood estimation within structural equation models, using the xtdpdml command in Stata 16.1 (StataCorp, Texas) [32]. This method was selected for its ability to use longitudinal data with lagged predictors while accounting for unobserved confounders and it has been shown to be more efficient than other methods [32]. Full information maximum likelihood was used for missing data and robust standard errors were calculated. For comparison of effect sizes, all continuous predictors were standardized to be in units of standard deviations. For completeness and because standardized variables in SEM may affect the standard errors [33], unstandardized estimates were also calculated and presented. However, it is the standardized coefficients that are used to answer the primary research question and limited dependence on p-values is used for interpretation [34]. All models were adjusted for LAZ at the previous age. Goodness-of-fit was assessed by RMSEA (ideally less than 0.06); CFI and TLI (both ideally greater than 0.95) [35] and lagged predictors were free to vary with time. Regression coefficients, 95% confidence intervals, and p-values were calculated.

In the assessment of demographic predictors of LAZ (at 6, 9 and 12 months), the time-invariant predictors of wealth score, maternal height and education, improved drinking source, improved sanitation, and sex of infant were assessed from baseline measures. Handwashing practices were included as a time-varying predictor. As the relationships between demographic predictors and LAZ were not substantially different at each age, estimates were constrained across time. This means that associations represent the average association between the predictor and LAZ at each age.

The relationships between nutrient intake and LAZ were assessed using lagged predictors and estimates at each age were reported separately. To understand how the different measures of nutrient intake were related to LAZ, three different models were run: (1) energy intake and nutrient quality score as predictors; (2) energy intake and protein intake as predictors; and (3) energy, calcium, iron, zinc, retinol, and riboflavin intake as predictors. The regression coefficients for nutrient quality score were compared with those when protein intake was included in the model instead of nutrient quality (as nutrient quality and protein intake are correlated so only one should be included) and the strongest predictor of these was taken to be used in the full model with all predictors.

The relationships between biomarkers (serum ferritin, zinc, RBP, selenium, CRP, and AGP) and LAZ were assessed using lagged predictors and estimates at each age were reported separately. AGP was transformed into categorical variable using > 1 g/L cut-off, as it was not normally distributed even after log-transformation.

The full model of all predictors (demographics, nutrient intake, and biomarkers) was generated with time-invariant demographic predictors, and all other variables lagged and allowed to vary freely with time. Estimates for 6 months predicting 9 months were reported, and 9 months predicting 12 months.

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