In a lithographic process in which a series of substrates are processed in different contexts, object data (such as performance data representing overlay measured on a set of substrates that have been processed previously) is received. Context data represents one or more parameters of the lithographic process that vary between substrates within the set. By principal component analysis or other statistical analysis of the performance data, the set of substrates are partitioned into two or more subsets. The first partitioning of the substrates and the context data are used to identify one or more relevant context parameters, being parameters of the lithographic process that are observed to correlate most strongly with the first partitioning. The lithographic apparatus is controlled for new substrates by reference to the identified relevant context parameters. Embodiments with feedback control and feedforward control are described.