Methods and apparatus to determine synthetic respondent level data using constrained Markov chains

A method comprising:

• generating, by executing an instruction with a processor, a first synthetic panel corresponding to a first duration of time and a second synthetic panel corresponding to a second duration of time, the first synthetic panel being based on a (a) seed panel and (b) first duration constraints based on return path data reported by a plurality of media devices, the second synthetic panel being based on (a) the seed panel and (b) second duration constraints based on the return path data reported by the plurality of media devices, the first synthetic panel representative of audiences of media presented by the plurality of media devices during the first duration of time, the second synthetic panel representative of audiences of media presented by the plurality of media devices during the second duration of time;
• generating, by executing an instruction with the processor, synthetic respondent level data corresponding to a third duration of time by linking first synthetic panelists in the first synthetic panel to second synthetic panelist in the second synthetic panel;
• and
• generating an output file based on the synthetic respondent level data.

A tangible computer readable storage medium comprising instructions which, when executed, cause a machine to at least:

• generate, by executing an instruction with a processor, a first synthetic panel corresponding to a first duration of time and a second synthetic panel corresponding to a second duration of time, the first synthetic panel being based on (a) a seed panel and (b) first duration constraints based on return path data reported by a plurality of media devices, the second synthetic panel being based on (A) the seed panel and (b) second duration constraints based on the return path data reported by the plurality of media devices, the first synthetic panel representative of audiences of media presented by the plurality of media devices during the first duration of time, the second synthetic panel representative of audiences of media presented by the plurality of media devices during the second duration of time;
• generate, by executing an instruction with the processor, synthetic respondent level data corresponding to a third duration of time by linking first synthetic panelists in the first synthetic panel to second synthetic panelist in the second synthetic panel;
• and
• generate an output file based on the synthetic respondent level data.