DETERMINING RATINGS DATA FROM POPULATION SAMPLE DATA HAVING UNRELIABLE DEMOGRAPHIC CLASSIFICATIONS
Example methods disclosed herein to determine ratings data for media exposure include accessing sets of classification probabilities for respective individuals in a sample population exposed to media. In some examples, a first one of the sets of classification probabilities represents likelihoods that a first one of the individuals belongs to respective ones of a set of possible demographic classification. Disclosed example methods also include estimating, based on the sets of classification probabilities, parameters characterizing population attributes associated with the set of possible demographic classifications. Disclosed example methods further include determining the ratings data based on the estimated parameters.
1 . A method to determine ratings data for media exposure, the method comprising:
accessing, with a processor, sets of classification probabilities for respective individuals in a sample population exposed to media, a first one of the sets of classification probabilities representing likelihoods that a first one of the individuals belongs to respective ones of a set of possible demographic classifications; and
estimating, with the processor and based on the sets of classification probabilities, parameters characterizing population attributes associated with the set of possible demographic classifications; and
determining, with the processor, the ratings data based on the estimated parameters.
2 . A method as defined in claim 1 , wherein the first one of the sets of classification probabilities includes a first probability that the first one of the individuals belongs to a first one of the set of possible demographic classifications and a second probability that the first one of the individuals belongs to a second one of the set of possible demographic classifications.
3 . A method as defined in claim 1 , wherein the parameters include:
average values for the population attributes associated with respective ones of the set of possible demographic classifications;
variance values for the population attributes associated with the respective ones of the set of possible demographic classifications; and
covariance values for the population attributes associated with respective pairs of the set of possible demographic classifications.
4 . A method as defined in claim 3 , wherein estimating the parameters includes:
summing first quantities based on first classification probabilities, from the sets of classification probabilities, representing likelihoods that the respective individuals belong to a first one of the set of possible demographic classifications to estimate a first average value for a first population attribute associated with the first one of the set of possible demographic classifications;
summing second quantities based on the first classification probabilities to estimate a first variance value for the first population attribute associated with the first one of the set of possible demographic classifications; and
summing third quantities based on the first classification probabilities and second classification probabilities, from the sets of classification probabilities, representing likelihoods that the respective individuals belong to a second one of the set of possible demographic classifications to estimate a first covariance value for a first pair of population attributes associated with the first and second ones of the set of possible demographic classifications.
5 . A method as defined in claim 3 , wherein estimating the parameters includes forming a covariance matrix based on the variance values and the covariance values, and determining the ratings data includes using the average values and the covariance matrix to evaluate an expression based on a multivariate normal distribution to determine the ratings data.
6 . A method as defined in claim 1 , wherein the population attributes associated with the set of possible demographic classification include at least one of numbers of individuals associated with respective ones of the set of possible demographic classifications or numbers of media impressions associated with the respective ones of the set of possible demographic classifications.
7 . A method as defined in claim 6 , wherein determining the ratings data includes at least one of:
determining, based on the estimated parameters, a probability that a number of individuals associated with a first one of the set of possible demographic classifications is at least one of less than or greater than a value;
determining, based on the estimated parameters, a confidence interval for a number of media impressions associated with the first one of the set of possible demographic classifications; or
determining, based on the estimated parameters, a probability that the number of media impressions associated with the first one of the set of possible demographic classifications is at least one of less than or greater than a combined number of media impressions associated with a combination of at least a second one and a third one of the set of possible demographic classifications.
8 . A method as defined in claim 6 , wherein determining the ratings data includes:
determining, based on the estimated parameters, at least one of average numbers of individuals associated with the respective ones of the set of possible demographic classifications or average numbers of media impressions associated with the respective ones of the set of possible demographic classifications to include in the ratings data; and
determining, based on the estimated parameters, statistical values characterizing accuracy of the least one of the determined average numbers of individuals associated with the respective ones of the set of possible demographic classifications or the determined average numbers of media impressions associated with the respective ones of the set of possible demographic classifications to include in the ratings data; and
the method further includes transmitting the ratings data electronically from the processor to a provider of the media.
9 . A tangible computer readable storage medium comprising computer readable instructions which, when executed, cause a processor to at least:
access sets of classification probabilities for respective individuals in a sample population exposed to media, a first one of the sets of classification probabilities representing likelihoods that a first one of the individuals belongs to respective ones of a set of possible demographic classifications; and
estimate, based on the sets of classification probabilities, parameters characterizing population attributes associated with the set of possible demographic classifications; and
determine ratings data based on the estimated parameters.
10 . A storage medium as defined in claim 9 , wherein the parameters include:
average values for the population attributes associated with respective ones of the set of possible demographic classifications;
variance values for the population attributes associated with the respective ones of the set of possible demographic classifications; and
covariance values for the population attributes associated with respective pairs of the set of possible demographic classifications.
11 . A storage medium as defined in claim 10 , wherein to estimate the parameters, the computer readable instructions, when executed, further cause the processor to:
sum first quantities based on first classification probabilities, from the sets of classification probabilities, representing likelihoods that the respective individuals belong to a first one of the set of possible demographic classifications to estimate a first average value for a first population attribute associated with the first one of the set of possible demographic classifications;
sum second quantities based on the first classification probabilities to estimate a first variance value for the first population attribute associated with the first one of the set of possible demographic classifications; and
sum third quantities based on the first classification probabilities and second classification probabilities, from the sets of classification probabilities, representing likelihoods that the respective individuals belong to a second one of the set of possible demographic classifications to estimate a first covariance value for a first pair of population attributes associated with the first and second ones of the set of possible demographic classifications.
12 . A storage medium as defined in claim 9 , wherein the population attributes associated with the set of possible demographic classification include at least one of numbers of individuals associated with respective ones of the set of possible demographic classifications or numbers of media impressions associated with the respective ones of the set of possible demographic classifications.
13 . A storage medium as defined in claim 12 , wherein to determine the ratings data, the computer readable instructions, when executed, further cause the processor to at least one of:
determine, based on the estimated parameters, a probability that a number of individuals associated with a first one of the set of possible demographic classifications is at least one of less than or greater than a value;
determine, based on the estimated parameters, a confidence interval for a number of media impressions associated with the first one of the set of possible demographic classifications; or
determine, based on the estimated parameters, a probability that the number of media impressions associated with the first one of the set of possible demographic classifications is at least one of less than or greater than a combined number of media impressions associated with a combination of at least a second one and a third one of the set of possible demographic classifications.
14 . A storage medium as defined in claim 9 , wherein to determine the ratings data, the computer readable instructions, when executed, further cause the processor to
determine, based on the estimated parameters, at least one of average numbers of individuals associated with the respective ones of the set of possible demographic classifications or average numbers of media impressions associated with the respective ones of the set of possible demographic classifications to include in the ratings data; and
determine, based on the estimated parameters, statistical values characterizing accuracy of the least one of the determined average numbers of individuals associated with the respective ones of the set of possible demographic classifications or the determined average numbers of media impressions associated with the respective ones of the set of possible demographic classifications to include in the ratings data; and
the computer readable instructions, when executed, further cause the processor to transmit the ratings data electronically from the processor to a provider of the media.
15 . An apparatus to determine ratings data for media exposure, the apparatus comprising:
a classification probability retriever to access sets of classification probabilities for respective individuals in a sample population exposed to media, a first one of the sets of classification probabilities representing likelihoods that a first one of the individuals belongs to respective ones of a set of possible demographic classifications; and
a population attribute parameter estimator to estimate, based on the sets of classification probabilities, parameters characterizing population attributes associated with the set of possible demographic classifications; and
a ratings data determiner to determine the ratings data based on the estimated parameters.
16 . An apparatus as defined in claim 15 , wherein the parameters include:
average values for the population attributes associated with respective ones of the set of possible demographic classifications;
variance values for the population attributes associated with the respective ones of the set of possible demographic classifications; and
covariance values for the population attributes associated with respective pairs of the set of possible demographic classifications.
17 . An apparatus as defined in claim 16 , wherein the population attribute parameter estimator is further to:
sum first quantities based on first classification probabilities, from the sets of classification probabilities, representing likelihoods that the respective individuals belong to a first one of the set of possible demographic classifications to estimate a first average value for a first population attribute associated with the first one of the set of possible demographic classifications;
sum second quantities based on the first classification probabilities to estimate a first variance value for the first population attribute associated with the first one of the set of possible demographic classifications; and
sum third quantities based on the first classification probabilities and second classification probabilities, from the sets of classification probabilities, representing likelihoods that the respective individuals belong to a second one of the set of possible demographic classifications to estimate a first covariance value for a first pair of population attributes associated with the first and second ones of the set of possible demographic classifications.
18 . An apparatus as defined in claim 15 , wherein the population attributes associated with the set of possible demographic classification include at least one of numbers of individuals associated with respective ones of the set of possible demographic classifications or numbers of media impressions associated with the respective ones of the set of possible demographic classifications.
19 . An apparatus as defined in claim 18 , wherein the ratings data determiner is further to at least one of:
determine, based on the estimated parameters, a probability that a number of individuals associated with a first one of the set of possible demographic classifications is at least one of less than or greater than a value;
determine, based on the estimated parameters, a confidence interval for a number of media impressions associated with the first one of the set of possible demographic classifications; or
determine, based on the estimated parameters, a probability that the number of media impressions associated with the first one of the set of possible demographic classifications is at least one of less than or greater than a combined number of media impressions associated with a combination of at least a second one and a third one of the set of possible demographic classifications.
20 . An apparatus as defined in claim 15 , wherein the ratings data determiner is further to:
determine, based on the estimated parameters, at least one of average numbers of individuals associated with the respective ones of the set of possible demographic classifications or average numbers of media impressions associated with the respective ones of the set of possible demographic classifications to include in the ratings data; and
determine, based on the estimated parameters, statistical values characterizing accuracy of the least one of the determined average numbers of individuals associated with the respective ones of the set of possible demographic classifications or the determined average numbers of media impressions associated with the respective ones of the set of possible demographic classifications to include in the ratings data; and
the further includes a ratings data reporter to transmit the ratings data electronically from the processor to a provider of the media.