I have a household travel survey where information about travel characteristics were obtained from a sample of households. The respondents were given a diary and a GPS device to log their trips for a single day. However, for some respondents additional travel days were collected from the GPS device. Because the additional days of available data are closely correlated with respondents' diary day data, it is not correct to treat these data simply as independent data points. On the other hand, it would be wasteful and unnecessary to completely discard the additional data. So my question is the following:
How do I treat the additional data?
How do I weight this additional data?
Any pointers to the literature is appreciated.