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The behavior of time allocation to two types of discretionary activities is formulated as a doubly-censored Tobit model. The model is capable of incorporating cases where the entire amount of time available for discretionary activity is allocated to one type of activity and the other type of activity is not engaged at all. The model is applied to examine individuals' allocation of time to in-home and out-of-home discretionary activities on working days and non-working days, using a weekly time-use data set from the Netherlands. Workers' daily activity patterns vary significantly between working days and non-working days, while it can be expected that patterns of time allocation are correlated between working days and non-working days. A set of error components is introduced into the model to represent this correlation, adopting a mass point approach which requires no assumption about the distribution of the error …