Corrections are calculated for use in controlling a lithographic apparatus. Using a metrology apparatus a performance parameter is measured at sampling locations across one or more substrates to which a lithographic process has previously been applied. A process model is fitted to the measured performance parameter, and an up-sampled estimate is provided for process-induced effects across the substrate. Corrections are calculated for use in controlling the lithographic apparatus, using an actuation model and based at least in part on the fitted process model. For locations where measurement data is available, this is added to the estimate to replace the process model values. Thus, calculation of actuation corrections is based on a modified estimate which is a combination of values estimated by the process model and partly on real measurement data.