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As part of estimating the future prevalence of WEA-capable phones in circulation, researchers used historical data to estimate the rate at which individuals purchase a new mobile phone (i.e., the mobile device turnover rate). Over the next several years, mobile phone manufacturers are expected to increase the number of WEA-capable phone offerings. However, only the most popular phone models receive software updates after they are sold (Hoey, 2012). The majority of existing mobile phones are not updated by CMSPs. Consequently, estimating the mobile device turnover rate is critical to assessing access to a WEA-compatible device.
Two consecutive years (2010–2012) of comScore survey data were used to estimate parameters for a mobile device turnover rate model. Because of the way comScore conducts its surveys (independent annual samples of 30,000 mobile phone owners over the age of 13 drawn from a nationwide sample frame), comparisons between survey years are not straightforward, complicating the estimation of annual mobile device turnover rates.
To overcome this challenge, a conservative approach (i.e., in the sense of underestimating turnover rates) to determining annual mobile device turnover rates was followed. For each mobile phone type in a pair of survey years, the absolute change in the number of people owning the device using the survey population weights was calculated. Next, the number of people with a new mobile device were estimated by summing the absolute changes in the number of people owning each mobile device and dividing the sum by two.
Observe that this is a conservative approach. For instance, suppose that there are two people, A and B, and three mobile devices, 1, 2, and 3. If person A switches from mobile phone 1 to 2 while person B switches from mobile phone 2 to 3, the actual turnover rate is 100, while the estimated turnover rate is 50. Note that the data do not indicate if both persons A and B switched mobile phones, as in this example, or if person A switched from mobile phone 1 to 3 while person B kept mobile phone 2. Hence, this approach will under-predict actual turnover, provided the data are truly representative of the U.S. mobile phone population. Finally, the number of people with a new mobile device is divided by the total population to determine an estimate for the mobile device turnover rate.
Another issue that affects the projection of mobile device turnover rates is the notion of “memory.” That is, given that individual A purchases a new mobile phone in the current year while individual B does not, which individual is more likely to purchase a new mobile phone in the following year? One might argue that individual B is more likely since individual A upgraded in the present year and may not want to incur the cost and/or inconvenience of getting a new mobile phone. However, one could also argue that individual A wants the latest technology while individual B is more utilitarian, and hence individual A would be more likely to upgrade in the next year.
To test each hypothesis, one-year turnover rates were calculated for 2010 to 2011 and for 2011 to 2012, as well as the two-year turnover rate between 2010 and 2012. Next, it was determined how well the two-year turnover rate could be predicted using the estimated one-year turnover rates, assuming that individuals A and B would be equally likely to purchase a new mobile phone. As shown in Table C.1, the predicted two-year turnover rates, displayed by income level, were slightly higher than the turnover rates estimated from the data. One would expect the predicted two-year turnover rates to be higher than the actual turnover rates if the same individuals each get a new mobile phone in each year. Hence, it appears that individual A is slightly more likely to purchase a new mobile phone than individual B.
Table C.1. Predicted and Actual Two-Year Mobile Phone Turn Over Rates
Annual Income Predicted Two-Year Turnover Rate Actual Two-Year Turnover Rate <$25,000 66.6 64.4 $25,000–$50,000 64.8 63.1 $50,000–$75,000 66.7 64.2 $75,000–$100,000 70.3 67.8 >$100,000 70.0 67.6 Weighted Average 67.7 65.4
Source: comScore, 2012 and NDRI analysis.
As another check, the average one-year turnover rate that would result in the two- year turnover observed in the data was inferred, again assuming that individuals A and B would be equally likely to purchase a new mobile phone. Table C.2 compares the average predicted one-year turnover rates with the actual one-year turnover rate estimated from the comScore data. The predicted values are slightly lower than the actual turnover rates,
suggesting once again that individuals who purchased mobile phones in the current year are slightly more likely to purchase a new mobile phone in the following year.
Table C.2. Predicted and Actual One-Year Mobile Device Turnover Rates
Annual Income
Average Predicted One-Year Turnover Rate
Average Actual One-Year Turnover Rate <$25,000 40.4 42.2 $25,000–$50,000 39.3 40.7 $50,000–$75,000 40.2 42.3 $75,000–$100,000 43.2 45.5 >$100,000 43.1 45.3 Weighted Average 41.2 43.2
Source: comScore, 2012 and NDRI analysis.
The above exposition suggests that there are two methods for projecting the time to replace the current stock of mobile phones. One method, which referred to as “method 1” in Figure C.1, is to calculate the average one-year turnover rate from the data. An alternative method, called “method 2,” is to infer the average one-year turnover rate from the two-year turnover rate in the data. For mathematical simplicity, it is assumed that individuals are equally likely to replace their mobile phones in the following year,
regardless of whether they replaced their mobile phone in the current year. The two tables above indicate that this assumption is reasonably consistent with the data. As shown in Figure C.1, the two estimation methods yield a very similar prediction regarding the time to replace the current stock of mobile Phones. The closeness of these projections gives a measure of robustness to the approach.
Figure C.1. Modeled Time to Replace the Current Stock of Mobile Phones
Source: comScore, 2012 and NDRI analysis.
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