Methods and apparatus to estimate population reach from marginal ratings
Methods, apparatus, systems, and articles of manufacture are disclosed to to estimate population reach from marginal ratings. An example apparatus includes an interface to access marginal ratings of the media for a recorded audience, marginal ratings of the media for a population audience, and reach of the media for the recorded audience; a reach determiner to iteratively estimate a reach of the media for the population audience based on the marginal ratings for the recorded audience, the marginal ratings for the population audience, and the reach for the recorded audience; and the interface to output the estimated reach for the population audience.
1. An apparatus to determine a reach of media for a total population audience from marginal ratings, the apparatus comprising:
memory including computer readable instructions; and
a processor to execute the instructions to at least:
access (i) first marginal ratings for a plurality of margins, the first marginal ratings representative of corresponding different portions of a recorded audience of panelists exposed to media at corresponding different periods of time, (ii) second marginal ratings provided by a media provider for the total population audience of the media, and (iii) a first reach of the media for the recorded audience of the panelists exposed to the media across the plurality of margins, the media divided into the different periods of time;
iteratively converge on an output estimate of a reach of the media for the total population audience, wherein for a first process iteration, the processor is to (i) determine a first total population audience reach estimate for the first process iteration, the first total population audience reach estimate based on (a) the first marginal ratings representative of the corresponding different portions of the recorded audience exposed to the media at the corresponding different periods of time, (b) the second marginal ratings for the population audience of the media, (c) the reach for the recorded audience of the panelists exposed to the media across the plurality of the margins, and (d) a link expression based on a first pseudo universe estimate of the total population audience determined based on a first pseudo universe estimate of the recorded audience corresponding to the first process iteration, the link expression to link at least one dependency associated with the second marginal ratings to at least one dependency associated with the first marginal ratings; and (ii) evaluate an error between the first total population audience reach estimate determined from the first process iteration and a prior second total population audience reach estimate determined from a prior second process iteration; and
output the estimate of the reach for the total population audience.
2. The apparatus of claim 1 , wherein the processor is to:
determine a second pseudo universe estimate of the recorded audience; and
execute a subsequent third process iteration when the error between the first total population audience reach estimate and the prior second total population audience reach estimate does not satisfy an error threshold.
3. The apparatus of claim 2 , wherein the processor is to initialize the estimate of the reach for the total population audience reach prior to the first iteration.
4. The apparatus of claim 3 , wherein the processor is to initialize the first pseudo universe estimate of the recorded audience prior to the first iteration.
5. The apparatus of claim 4 , wherein the first pseudo universe estimate of the recorded audience is initialized with a total population size.
6. The apparatus of claim 4 , wherein the processor is to execute the subsequent third process iteration when a second error corresponding to a comparison of the second pseudo universe of the recorded audience and the first pseudo universe of the recorded audience does not satisfy the error threshold.
7. The apparatus of claim 6 , wherein the processor is to determine the estimate of the reach for the total population audience to be at least one of the first total population audience reach estimate or the prior second total population audience reach estimate when the error threshold is satisfied.
8. The apparatus of claim 2 , wherein the reach for the total population audience is a reach across two or more time intervals corresponding to the second marginal ratings for the total population audience.
9. The apparatus of claim 8 , wherein:
the second pseudo universe estimate of the recorded audience is based on an assumed independence among the first marginal ratings for the recorded audience; and
the first pseudo universe estimate of the total population audience is based on an assumed independence among the second marginal ratings for the total population audience.
10. The apparatus of claim 9 , wherein the processor is to execute the first process iteration and the subsequent third iteration to converge on the estimate of the reach for the total population audience corresponding to a deduplicated number of persons exposed to the media across the time intervals.
11. The apparatus of claim 10 , wherein the time intervals are quarter hours.
12. The apparatus of claim 2 , wherein the processor is to execute a fourth process iteration when a second error corresponding to the subsequent third process iteration does not satisfy the error threshold.
13. A method to determine reach of media from marginal ratings, the method comprising:
accessing (i) first marginal ratings for a plurality of margins for a recorded audience of panelists exposed to media, the first marginal ratings representative of corresponding different divisions of the media with respect to time, (ii) second marginal ratings provided by a media provider for a population audience of the media, and (iii) a first reach of the media for the recorded audience of the panelists exposed to the media across the plurality of margins;
iteratively converging on an output estimate of a reach of the media for the population audience, wherein for a first process iteration, wherein the iterative converging includes: (i) determining a first population audience reach estimate for the first process iteration, the first population audience reach estimate based on (a) the first marginal ratings for the recorded audience exposed to the media, (b) the second marginal ratings for the population audience of the media, (c) the reach for the recorded audience of the panelists exposed to the media across the plurality of the margins, and (d) a link expression based on a first pseudo universe estimate of the total population audience determined based on a first pseudo universe estimate of the recorded audience corresponding to the first process iteration, the link expression to link at least one dependency associated with the second marginal ratings to at least one dependency associated with the first marginal ratings; and (ii) evaluating an error between the first population audience reach estimate determined from the first process iteration and a prior second population audience reach estimate determined from a prior second process iteration; and
outputting the estimate of the reach for the population audience.
14. The method of claim 13 , wherein iteratively estimating the reach for the population audience includes:
determining a second pseudo universe estimate of the recorded audience; and
executing a subsequent third process iteration when the error between the first population audience reach estimate and the prior second population audience reach estimate does not satisfy an error threshold.
15. The method of claim 14 , further including initializing the estimate of the reach for the population audience reach prior to the first iteration.
16. The method of claim 15 , further including initializing the first pseudo universe estimate of the recorded audience prior to the first iteration.
17. The method of claim 16 , wherein the first pseudo universe estimate of the recorded audience is initialized with a total population size.
18. The method of claim 16 , further including executing the subsequent third process iteration when a second error corresponding to a comparison of the second pseudo universe of the recorded audience and the first pseudo universe of the recorded audience does not satisfy the error threshold.
19. The method of claim 18 , further including, when the error threshold is satisfied, determining the estimate of the reach for the population audience to be at least one of the first population audience reach estimate or the prior second population audience reach estimate.
20. A non-transitory computer readable storage medium comprising instructions which, when executed, cause a machine to at least:
access (i) first marginal ratings for a plurality of margins for a recorded audience of panelists exposed to media, (ii) second marginal ratings provided by a media provider for a population audience of the media, and (iii) a first reach of the media for the recorded audience of the panelists exposed to the media across the plurality of margins, the margins including a first margin and a second margin, the first margin corresponding to a first duration of time for the media and the second margin corresponding to a second duration of time for the media;
iteratively converge on an output estimate of a reach of the media for the population audience, wherein for a first process iteration, wherein the iterative converging includes (i) determining a first population audience reach estimate for the first process iteration, the first population audience reach estimate based on (a) the first marginal ratings, (b) the second marginal ratings, (c) the reach for the recorded audience of the panelists exposed to the media across the plurality of the margins, and (d) a link expression based on a first pseudo universe estimate of the total population audience determined based on a first pseudo universe estimate of the recorded audience corresponding to the first process iteration, the link expression to link at least one dependency associated with the second marginal ratings to at least one dependency associated with the first marginal ratings; and (ii) evaluating an error between the first population audience reach estimate determined from the first process iteration and a prior second population audience reach estimate determined from a prior second process iteration; and
output the estimate of the reach for the population audience.