Epidemiologists are often interested in examining the effect on a later-life outcome of an exposure measured repeatedly over the life course. When different hypotheses for this effect are proposed by competing theories, it is important to identify those most supported by observed data as a first step toward estimating causal associations. One method is to compare goodness-of-fit of hypothesized models with a saturated model, but it is unclear how to judge the "best" out of two hypothesized models that both pass criteria for a good fit. We developed a new method using the least absolute shrinkage and selection operator to identify which of a small set of hypothesized models explains most of the observed outcome variation. We analyzed a cohort study with repeated measures of socioeconomic position (exposure) through childhood, early- and mid-adulthood, and body mass index (outcome) measured in mid-adulthood. We confirmed previous findings regarding support or lack of support for the following hypotheses: accumulation (number of times exposed), three critical periods (only exposure in childhood, early- or mid-adulthood), and social mobility (transition from low to high socioeconomic position). Simulations showed that our least absolute shrinkage and selection operator approach identified the most suitable hypothesized model with high probability in moderately sized samples, but with lower probability for hypotheses involving change in exposure or highly correlated exposures. Identifying a single, simple hypothesis that represents the specified knowledge of the life course association allows more precise definition of the causal effect of interest.