METHODS AND APPARATUS TO ESTIMATE CENSUS-LEVEL AUDIENCE SIZES AND DURATION DATA ACROSS DIMENSIONS AND/OR DEMOGRAPHICS
Methods and apparatus to estimate census-level audience sizes and duration data across dimensions and/or demographics are disclosed. An example apparatus includes constraint equation control circuitry to select at least one constraint equation corresponding to one or more events, the one or more events corresponding to first audience members and second audience members, the first audience members to include the second audience members, constraint parameter estimation circuitry to solve the at least one constraint equation to determine one or more constraint parameter values, the one or more constraint parameter values corresponding to the one or more events, and output generation circuitry to determine, based on one or more intermediate equations and the one or more constraint parameter values, an event audience size and an event duration corresponding to (a) the first audience members and (b) a combination of the one or more events and one or more demographics.
1 . An apparatus comprising:
constraint equation control circuitry to select at least one constraint equation corresponding to one or more events, the one or more events corresponding to first audience members and second audience members, the first audience members to include the second audience members;
constraint parameter estimation circuitry to solve the at least one constraint equation to determine one or more constraint parameter values, the one or more constraint parameter values corresponding to the one or more events; and
output generation circuitry to determine, based on one or more intermediate equations and the one or more constraint parameter values, an event audience size and an event duration corresponding to (a) the first audience members and (b) a combination of the one or more events and one or more demographics.
2 . The apparatus of claim 1 , wherein the event audience size is a first event audience size, the event duration is a first event duration, the output generation circuitry to determine the first event audience size based on aggregate duration values, second event audience sizes, and second event durations, the aggregate duration values corresponding to the first audience members, and the second event audience sizes and the second event durations corresponding to the second audience members and to the combination of the one or more events and the one or more demographics.
3 . The apparatus of claim 2 , wherein the constraint parameter estimation circuitry is to determine the one or more constraint parameter values based on a range, the range based on a ratio of the second event audience sizes to the second event durations.
4 . The apparatus of claim 2 , further including summary parameter calculation circuitry to calculate summary parameter values based on the second event audience sizes, the second event durations, and universe estimates corresponding to the one or more demographics.
5 . The apparatus of claim 4 , wherein the output generation circuitry is to determine output parameter values by iteratively solving the one or more intermediate equations based on the summary parameter values and the one or more constraint parameter values, the output parameter values including the first event audience size and the first event duration.
6 . The apparatus of claim 1 , further including report generation circuitry to generate a report including the event audience size and the event duration.
7 . The apparatus of claim 1 , wherein the one or more events include at least one of accessing a website, accessing an advertisement, or using a device type.
8 . A system comprising:
memory;
programmable circuitry; and
instructions to cause the programmable circuitry to:
select at least one constraint equation corresponding to one or more events, the one or more events corresponding to first audience members and second audience members, the first audience members to include the second audience members;
solve the at least one constraint equation to determine one or more constraint parameter values, the one or more constraint parameter values corresponding to the one or more events; and
determine, based on one or more intermediate equations and the one or more constraint parameter values, an event audience size and an event duration corresponding to (a) the first audience members and (b) a combination of the one or more events and one or more demographics.
9 . The system of claim 8 , wherein the event audience size is a first event audience size, the event duration is a first event duration, the programmable circuitry to determine the first event audience size based on aggregate duration values, second event audience sizes, and second event durations, the aggregate duration values corresponding to the first audience members, and the second event audience sizes and the second event durations corresponding to the second audience members and to the combination of the one or more events and the one or more demographics.
10 . The system of claim 9 , wherein the programmable circuitry is to determine the one or more constraint parameter values based on a range, the range based on a ratio of the second event audience sizes to the second event durations.
11 . The system of claim 9 , wherein the programmable circuitry is to calculate summary parameter values based on the second event audience sizes, the second event durations, and universe estimates corresponding to the one or more demographics.
12 . The system of claim 11 , wherein the programmable circuitry is to determine output parameter values by iteratively solving the one or more intermediate equations based on the summary parameter values and the one or more constraint parameter values, the output parameter values including the first event audience size and the first event duration.
13 . The system of claim 8 , wherein the programmable circuitry is to generate a report including the event audience size and the event duration.
14 . The system of claim 8 , wherein the one or more events include at least one of accessing a website, accessing an advertisement, or using a device type.
15 . A non-transitory computer readable medium comprising instructions that, when executed, cause programmable circuitry to at least:
select at least one constraint equation corresponding to one or more events, the one or more events corresponding to first audience members and second audience members, the first audience members to include the second audience members;
solve the at least one constraint equation to determine one or more constraint parameter values, the one or more constraint parameter values corresponding to the one or more events; and
determine, based on one or more intermediate equations and the one or more constraint parameter values, an event audience size and an event duration corresponding to (a) the first audience members and (b) a combination of the one or more events and one or more demographics.
16 . The non-transitory computer readable medium of claim 15 , wherein the event audience size is a first event audience size, the event duration is a first event duration, and the instructions are to cause the programmable circuitry to determine the first event audience size based on aggregate duration values, second event audience sizes, and second event durations, the aggregate duration values corresponding to the first audience members, the second event audience sizes and the second event durations corresponding to the second audience members and to the combination of the one or more events and the one or more demographics.
17 . The non-transitory computer readable medium of claim 16 , wherein the instructions are to cause the programmable circuitry to determine the one or more constraint parameter values based on a range, the range based on a ratio of the second event audience sizes to the second event durations.
18 . The non-transitory computer readable medium of claim 16 , wherein the instructions are to cause the programmable circuitry to calculate summary parameter values based on the second event audience sizes, the second event durations, and universe estimates corresponding to the one or more demographics.
19 . The non-transitory computer readable medium of claim 18 , wherein the instructions are to cause the programmable circuitry to determine output parameter values by iteratively solving the one or more intermediate equations based on the summary parameter values and the one or more constraint parameter values, the output parameter values including the first event audience size and the first event duration.
20 . The non-transitory computer readable medium of claim 15 , wherein the instructions are to cause the programmable circuitry to generate a report including the event audience size and the event duration.
21 . The non-transitory computer readable medium of claim 15 , wherein the one or more events include at least one of accessing a website, accessing an advertisement, or using a device type.
22 - 35 . (canceled)