Methods and apparatus to determine probabilistic media viewing metrics
Methods and apparatus to determine probabilistic media viewing metrics are disclosed herein. An example apparatus for determining a viewing metric for media to be viewed by a plurality of panelists includes a probability identifier to identify a probability for respective ones of the panelists with respect to the panelists viewing the media. The probability identifier is to identify the probability based on viewing data for the respective ones of the panelists. The example apparatus includes a calculator to calculate the viewing metric for the media based on the probabilities for the respective ones of the panelists and a sampling weight assigned to the respective ones of the panelists.
1. An apparatus for determining a viewing metric for media to be viewed by a plurality of panelists, the apparatus comprising:
a probability identifier to identify a probability for respective ones of the panelists with respect to the panelists viewing the media, the probability identifier to identify the probability based on viewing data for the respective ones of the panelists, the viewing data including incomplete viewing data for one or more of the panelists relative to the media; and
a calculator to:
calculate a conditional probability for the respective ones of the panelists based on the probability for the respective ones of the panelists, the conditional probability based on a condition of the respective ones of the panelists viewing respective media presentative devices during a first time period associated with a presentation of the media;
calculate a share weight for the respective ones of the panelists based on a sampling weight assigned to the respective ones of the panelists and a probability of the respective ones of the panelists not viewing the respective media presentation devices during the first time period; and
approximate a share indicative of viewership of the media using a conditional distribution based on the conditional probability and the share weight calculated for the respective ones of the panelists.
2. The apparatus of claim 1 , wherein the media is first media, the probability is a first probability for the respective ones of the panelists, the share is a first share, and the probability identifier is to identify a second probability for the respective ones of the panelists with respect to the panelists viewing second media, the calculator to:
calculate a second share for the second media; and
determine a covariance between the first media and the second media based on the first share and the second share.
3. The apparatus of claim 1 , wherein the calculator is to calculate a rating for the media.
4. The apparatus of claim 1 , further including a subgroup analyzer, the subgroup analyzer to identify the respective probabilities for a subgroup including one or more of the panelists with respect to the panelists of the subgroup viewing the media based on one or more demographics of the respective panelists.
5. The apparatus of claim 4 , wherein the subgroup analyzer is to determine a probability of the subgroup viewing the media based on the probabilities identified for the subgroup.
6. The apparatus of claim 4 , wherein the subgroup analyzer is to determine a portion of the panelists viewing the media who are associated with the subgroup based on the probabilities identified for the subgroup and the probabilities identified for all of the panelists.
7. The apparatus of claim 1 , wherein the sampling weight is based on demographic data for the panelists.
8. The apparatus of claim 1 , wherein the media is first media and the calculator is to calculate the conditional probability by calculating a first conditional probability that the respective ones of the panelists are viewing the first media and a second conditional probability that the respective ones of the panelists are viewing a second media during the first time period.
9. A method for determining a viewing metric for media to be viewed by a plurality of panelists, the method comprising:
identifying, by executing an instruction with a processor, a probability for respective ones of the panelists with respect to the panelists viewing the media, the identifying based on viewing data for the respective ones of the panelists, the viewing data including incomplete viewing data for one or more of the panelists relative to the media;
calculating, by executing an instruction with the processor, a conditional probability for the respective ones of the panelists based on the probability for the respective ones of the panelists, the conditional probability based on a condition of the respective ones of the panelists viewing respective media presentative devices during a first time period associated with a presentation of the media;
calculating, by executing an instruction with the processor, a share weight for the respective ones of the panelists based on a sampling weight assigned to the respective ones of the panelists and a probability of the respective ones of the panelists not viewing the respective media presentation devices during the first time period; and
approximating, by executing an instruction with the processor, a share indicative of viewership of the media using a conditional distribution based on the conditional probability and the share weight calculated for the respective ones of the panelists.
10. The method of claim 9 , wherein the media is first media, the probability is a first probability for the respective ones of the panelists, the share is a first share, and further including:
identifying a second probability for the respective ones of the panelists with respect to the panelists viewing second media;
calculating a second share for the second media; and
determining a covariance between the first media and the second media based on the first share and the second share.
11. The method of claim 9 , further including calculating a rating for the media.
12. The method of claim 9 , further including identifying the respective probabilities for a subgroup including one or more of the panelists with respect to the panelists of the subgroup viewing the media based on one or more demographics of the respective panelists.
13. The method of claim 12 , further including determining a probability of the subgroup viewing the media based on the probabilities identified for the subgroup.
14. The method of claim 12 , further including determining a portion of the panelists viewing the media who are associated with the subgroup based on the probabilities identified for the subgroup and the probabilities identified for all of the panelists.
15. A non-transitory computer-readable medium comprising instructions that, when executed, cause a processor to at least: identify a probability for respective ones of panelists with respect to the panelists viewing a media, the processor to identify the probability based on viewing data for the respective ones of the panelists, the viewing data including incomplete viewing data for one or more of the panelists relative to the media; calculate a conditional probability for the respective ones of the panelists based on the probability for the respective ones of the panelists, the conditional probability based on a condition of the respective ones of the panelists viewing respective media presentative devices during a first time period associated with a presentation of the media; calculate a share weight for the respective ones of the panelists, based on a sampling weight assigned to the respective ones of the panelists and a probability of the respective ones of the panelists not viewing the respective media presentation devices during the first time period; and approximate a share indicative of viewership of the media using a conditional distribution based on the conditional probability and the share weight calculated for the respective ones of the panelists.
16. The non-transitory computer-readable medium of claim 15 , wherein the media is first media, the probability is a first probability for the respective ones of the panelists, the share is a first share, and the instructions further cause the processor to: identify a second probability for the respective ones of the panelists with respect to the panelists viewing second media; calculate a second share for the second media; and determine a covariance between the first media and the second media based on the first share and the second share.
17. The non-transitory computer-readable medium of claim 15 , where the in further cause the processor to identify the respective probabilities for a subgroup including one or more of the panelists with respect to the panelists of the subgroup viewing the media based on one or more demographics of the respective panelists.
18. The non-transitory computer-readable medium of claim 17 , wherein the instructions Further cause the processor to determine a probability of the subgroup viewing the media based on the probabilities identified for the subgroup.
19. The non-transitory computer-readable medium of claim 17 , wherein the instructions further cause the processor to determine a portion of the panelists viewing the media who are associated with the subgroup based on the probabilities identified for the subgroup and the probabilities identified for all of the panelists.