How might data be collected for this target response?Log of days when data was collected (non-compliance can be derived from this). Calculate baseline % and work from there.
Identify several interventions that might help improve response rates. Place them in order with the least-restrictive at the top so that the interventions may be introduced systematically, adding more restrictive / less favorable interventions after the outcomes of less restrictive options have been measured.

Set weekly goals for staff for data collection and provide positive feedback for improvement. Consider offering small award such a gift card, bring in coffee, etc. for set days of compliance with data collection: 10 days, then 15, then 20...