With panel data important issues can be resolved that can not beaddressed with cross--sectional data. A major drawback is that paneldata suffer from more severe missing data problems. Adding a sampleconsisting of new units randomly drawn from the original populationas replacements for units who have dropped out of the panel, aso--called refreshment sample, can be helpful in mitigating theeffects of attrition, both by allowing for estimation of richermodels and by making estimation of conventional models moreprecise. In this paper we develop a family of models thatincorporate refreshment samples, and we demonstrate in an applicationto a Dutch data set on travel behaviour that such models can lead tosubstantially different results than models that assume that themissing data process is ignorable or conventional econometric modelsfor panel data with attrition.