To attenuate you can easily confounding out of eating low self-esteem updates that have reduced-earnings condition, in addition to restricting brand new analytic shot so you’re able to lower-income homes i as well as integrated an average way of measuring domestic earnings out-of 9 days courtesy kindergarten because the a covariate in most analyses. At each and every revolution, moms and dads was in fact asked to help you report the household’s overall pretax earnings within the the last seasons, as well as salaries, notice, senior years, and so on. I averaged said pretax household money across the 9 days, two years, and you can preschool, since permanent actions of cash be a little more predictive out of eating low self-esteem than simply was tips away from latest earnings (elizabeth.grams., Gundersen & Gruber, 2001 ).
Lagged intellectual and personal-emotional procedures
Fundamentally, we provided earlier steps of son cognitive otherwise societal-psychological creativity to adjust getting date-invariant child-level excluded details (talked about next less than). These lagged child consequences were drawn regarding the revolution immediately preceding the new measurement away from food low self-esteem; that is, inside the models forecasting preschool cognitive outcomes of dos-12 months restaurants insecurity, 9-few days intellectual consequences was basically regulated; within the models predicting preschool intellectual consequences out-of preschool-year food low self-esteem, 2-12 months cognitive outcomes was in fact regulated. Lagged methods from public-mental working were used in habits anticipating preschool personal-psychological consequences.
Analytical Approach
In Equation 1, the given kindergarten outcome is predicted from household food insecurity at 2 years, the appropriate lagged version of the outcome (Bayley mental or adaptive behavior scores at 9 months), and covariates. ?1 and ?2 represent the difference in the level of the outcome at kindergarten for children in households who experienced low and very low food security, respectively, relative to those who were food secure at 2 years, conditional on the child’s lagged outcome from the wave prior to when food insecurity was assessed. Although this approach controls for the effect of food insecurity on outcomes up to 9 months, it does not capture food insecurity that began at age 1 and extended until 2 years. Likewise, for the model predicting kindergarten outcomes from preschool-year food insecurity in which 2-year outcomes are lagged (Equation 2, below), food insecurity experienced prior to age 2 that might have influenced age 2 outcomes is controlled for, but food insecurity that might have occurred after the 2-year year interview and before preschool is not.
To address the possibility that ?1 and ?2 in Equations 1 and 2 are absorbing effects of food insecurity at subsequent time points, we ran additional models in which we control for food insecurity at all available time points, estimating the independent association of food insecurity at any one time point on kindergarten outcomes, net of other episodes of food insecurity (Equation 3).
Here, ?1 (for instance) is limited to the proportion of the association between low food security at 9 months and kindergarten outcomes that is independent of the association between food insecurity at other time points and the same outcomes. Finally, Equation 4 presents the model estimating associations between intensity of food insecurity across early childhood and kindergarten outcomes. 
In this model, ?1 (for example) represents the average difference in kindergarten outcomes between children who lived in a food-insecure household at any one time point (e.g., 9 months, 2 years, or preschool), relative to children who lived in households experiencing no food insecurity across the early childhood years.
In addition to including lagged outcome measures as additional predictors in the above models, we also included a near-exhaustive set of covariates as described above. This vector of covariates is expressed as ?k in the above equations. Alongside the lagged dependent variable, the inclusion of this rich set of covariates yields the most appropriate analysis given limitations of the available data.