Adjusting for selection bias in assessing the relationship between sibship size and cognitive performance

type="main" xml:id="rssa12098-abs-0001"> Consistent negative correlations between sibship size and cognitive performance (as measured by intelligence quotient and other mental aptitude tests) have been observed in past empirical studies. However, parental decisions on family size may correlate with variables affecting child cognitive performance. The aim of this study is to demonstrate how selection bias in studies of sibship size effects can be adjusted for. We extend existing knowledge in two aspects: as factors affecting decisions to increase family size may vary across the number and composition of current family size, we propose a sequential probit model (as opposed to binary or ordered models) for the propensity to increase family size; to disentangle selection and causality we propose multilevel multiprocess modelling where a continuous model for performance is estimated jointly with a sequential probit model for family size decisions. This allows us to estimate and adjust for the correlation between unmeasured heterogeneity affecting both family size decisions and child cognitive performance. The issues are illustrated through analyses of scores on Peabody individual achievement tests among children of the US National Longitudinal Survey of Youth 1979. We find substantial between-family heterogeneity in the propensity to increase family size. Ignoring such selection led to overestimation of the negative effects of sibship size on cognitive performance for families with 1–3 children, when known sources of selection were accounted for. However, the multiprocess modelling proposed could efficiently identify and control for such bias due to adverse selection.