One of my primary interests is how educational quality affects later life cognition, specifically whether there are critical points in which educational quality matters more, such as in elementary school regardless of status in the high school period. My hypothesis is that disparities in educational quality in early childhood would have a substantively different effect on shaping interpersonal relationships, agency, coping skills, and other behaviors that may affect cognitive aging than educational exposures in adolescence, due to differences in development (e.g. a higher influence of outside social factors in adolescence) and classroom structure/teacher interaction. Mishra et al. propose a critical period model using the assumptions that Y111 = Y101 = Y110 = Y100 = Y1** and Y011 = Y001 = Y010 = Y000 = Y0** - in my situation, because educational characteristics are available only in elementary school and high school, the assumption would be that children with exposure to high quality education in early years (Y1*) would have the same benefit in cognitive outcomes, regardless of their later status, and vice versa for those exposed to low quality education (Y0*). The change in the early critical period (Δearly crit. period) would be equal to Y1* - Y0*, which would be represented by β1 in the linear regression model of E(Y) = α + β1S1. One consideration would be the potential inclusion of actual educational attainment as a third subscript, which would lead to the assumption that the effects of early childhood educational quality on later life cognition are the same regardless of actual grade completion, though the validity of this assumption is questionable, and may be more suited as a separate accumulation model for inclusion in a saturated model.
A secondary question that I would be interested in exploring is whether moving between districts of differing quality affects later life cognition. One way that this could be addressed is using the general model of social mobility proposed by Mishra et al., considering changes in downwards mobility as Y10 – Y11 (high to low verses constantly high) and upwards mobility as Y01 – Y00 (low to high verses constantly low). The corresponding regression equation would be E(Y) = α + δ12D12 + γ12U12 = α + β1S1 + β2S2 + θ12S1S2, in which Y is a function of the first school quality exposure and the post-migration quality exposure. Mishra et al. propose an alternative model that assumes all downward changes are equally harmful and all upward changes are equally beneficial, but I do not believe that relevant for this research question. One issue that arises in addressing this research question is how to address children moving school districts at different ages. Conceptually, I would propose basing an analytic approach off the results of the previous question and looking only within one age range (e.g. elementary) if a critical point of exposure was found, and condensing all ages if no critical points of exposure were found.
Because this exposure-outcome combination involves both a late-life outcome and details of an early-life exposure, there are few datasets with adequate residential characteristics. Educational characteristics are publicly available dating back to the early/mid 20th century for the US at the state and county levels, but a cohort of older adults with information on childhood residence is required for linkage. Two potential datasets with residential history are REGARDS and PSID, though PSID may be subject to lower availability of cognitive measures. A major concern in interpreting my proposed model is the dependency between early education and other educational/socioeconomic factors, and how to define assumptions in the presence of such interaction.