Improving the statistical performance of tracking studies based on repeated cross-sections with primary dynamic factor analysis

摘要

Tracking studies are prevalent in marketing research and virtually all the other social sciences. These studies are predominantly implemented via repeated independent, non-overlapping samples, which are much less costly than recruiting and maintaining a longitudinal panel that track the same sample over time. In the existing literature, data from repeated cross-sectional samples are analyzed either independently for each time period, or longitudinally by focusing on the dynamics of the aggregate measures (e.g., sample averages). In this study, we propose a multivariate state-space model that can be applied directly to the individual-level data from each of the independent samples, simultaneously taking advantage of three patterns embedded in the data: a) inter-temporal dependence within the population means of each variable, b) temporal co-movements across the population means of different variables and c) cross-sectional co-variation across individual responses within each sample. We illustrate our proposed model with two applications, demonstrating the benefits of making full use of all the available data. In the first illustration, we have access to all the individual-level purchase data from one large population of grocery shoppers over a span of 36 months. This provides us a testing ground for benchmarking our proposed model against existing approaches in a Monte Carlo experiment, where we show that our model outperforms all the alternatives in inferring population dynamics using data sampled through repeated cross-sections. We find that, as compared with using simple sample averages, our proposed model can improve the accuracy of repeated cross-sectional tracking studies by double digits, without incurring any additional data-gathering costs (or equivalently, reducing the data-gathering costs by double digits while maintaining the desired accuracy level). In the second illustration, we apply the proposed model to repeated cross-sectional surveys that track customer perceptions and satisfaction for an automotive dealer, a situation often encountered by marketing researchers.