To attenuate you can confounding out of dinner low self-esteem standing which have reduced-earnings position, in addition to limiting the newest analytical take to to help you low-income properties we and provided the common measure of domestic income away from 9 days through preschool due to the fact good covariate throughout analyses. At each and every revolution, parents have been requested so you’re able to report its household’s overall pretax earnings during the the past year, as well as wages, notice, senior years, and so on. We averaged reported pretax household earnings across nine weeks, 2 yrs, and you can preschool, once the long lasting methods of cash are more predictive regarding dinner low self-esteem than simply are procedures out of latest income (e.grams., Gundersen & Gruber, 2001 ).
Lagged intellectual and you will social-emotional actions
In the long run, i included early in the day steps away from child cognitive otherwise societal-mental development to regulate to possess big date-invariant guy-level omitted variables (discussed subsequent lower than). These types of lagged boy outcomes was indeed removed regarding the trend instantly preceding the new measurement off dining low self-esteem; that is, for the designs forecasting preschool cognitive outcomes from 2-season food insecurity, 9-few days cognitive outcomes was basically managed; into the activities forecasting preschool cognitive outcomes out of preschool-12 months food insecurity, 2-season intellectual effects was basically regulated. Lagged methods from societal-psychological working were chosen for patterns forecasting kindergarten societal-emotional consequences.
Analytic 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.