because directly asking about income was gauged to be both a sensitive question and potentially difficult to report in the context of irregular income streams.

# **Statistical Analysis**

All analyses were conducted in Stata Version 17.0. Survey probability weights were applied. For all regression analyses, we used Stata’s ‘svy’ prefix to account for the complex survey design, employing linearized standard errors. Analyses were conducted separately by child age group, as child development outcomes were measured differently for the two age groups (i.e., CREDI for children ages 0-35 months and MELQO-MODEL for children ages 36-72 months). Additionally, examining these age groups separately has a conceptual justification, in that prior qualitative evidence from rural communities in Pakistan has found that children’s experiences of individual, family and household, community, social and cultural factors can vary as the child ages and becomes increasingly mobile and independent (Jeong et al., 2018). This includes how mothers and fathers differently engage with their children (Jeong et al., 2018). Disaggregating by child age allowed us to more precisely explore the relationship between child gender and key risk and protective factors across the early childhood period.

Risk and protective factors were selected a priori informed by literature indicating associations of variables of interest with child development outcomes in Pakistan and globally (Hentschel et al., 2023; Rathore et al., 2023; Rahman et al., 2003; Tomlinson et al., 2023). Province, child age, caregiver gender and monthly expenditure on mobile phone (a proxy for income) were also identified a priori as covariates given existing evidence in the Pakistan context (Hentschel et al., 2023). We additionally controlled for sociodemographic variables including maternal and paternal education, rural residence, and household size. Descriptive statistics and bivariate associations of child development outcomes, risk and protective factors, and demographics with child gender were first summarized within each age group in the non-imputed data. Bivariate relationships were explored using Pearson chi squared tests for categorical and dichotomous variables and unadjusted Ordinary Least Squares (OLS) linear regression for continuous variables. We adjusted for multiple hypothesis testing by computing sharpened false discovery rate (FDR) q-values for each of the bivariate associations (Benjamini et al., 2006; Anderson, 2008).

To answer research question 2, we conducted an initial exploratory analysis running separate multivariate OLS linear regression models for each risk or protective factor (henceforth factor) to examine whether child gender is a moderator in the association between the factor and child development outcomes in the imputed datasets. Prior to imputation, z-scores were computed for variables for school readiness, psychosocial stimulation, and parental distress using surveyweighted means and standard deviations to support interpretation of coefficients. A separate regression analysis was conducted for each factor. Model 1 contained the risk or protective factor and child gender as discrete predictors and child development as the outcome, adjusted for sociodemographic covariates. Model 2 additionally included the interaction between the factor and child gender. We adjusted for multiple hypothesis testing across interaction terms within each age group by computing sharpened false discovery rate (FDR) q-values (Benjamini et al., 2006; Anderson, 2008).

Lastly, we used multivariate OLS regression to simultaneously test associations of child gender, risk or protective factors and their interactions with child development outcomes in a fully interacted model. For each age group, direct effects of all independent variables on ECD were first 8