Nonresponse Bias in a Dual Frame Sample of Cell and Landline Numbers
J. MICHAEL BRICK is vice president at Westat and a research professor at the Joint Program in Survey Methodology at the University of Maryland. SARAH DIPKO is a survey methodologist at Westat. STANLEY PRESSER is a professor in the Sociology Department and in the Joint Program in Survey Methodology at the University of Maryland. CLYDE TUCKER is a senior methodologist at the Bureau of Labor Statistics. YANGYANG "ANGELA" YUAN is an analytic consultant at Epsilon (she was a survey methodologist at Westat when this research was done).
Address correspondence to J. Michael Brick; e-mail: MikeBrick{at}Westat.com.
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Abstract |
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 TOP Abstract IntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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We conducted a dual frame survey of landline and cell phone numbers in 2004 to evaluate the feasibility of including cell phone numbers in random digit dial telephone surveys in the United States. By sampling cell phone numbers, the coverage bias associated with households that have only cell phones is eliminated. However, we discovered two major sources of nonresponse bias in the dual frame sample. In an attempt to reduce these biases, we applied several different estimation schemes. But a comparison to the 2004 Current Population Survey Cell Phone Supplement showed that none of the estimation schemes substantially reduced the nonresponse bias of the estimates. We suggest other methods that might be used in future surveys that include cell phones and discuss the need for additional data collection and research on this issue.
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Introduction |
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TOPAbstractIntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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As cell phone use in the United States grows, the potential for coverage bias in random digit dial (RDD) telephone surveys will increase if these surveys continue to exclude most cell phone numbers. Nonresponse bias in RDD surveys may also grow if households with landline phones come to rely on cell phones for most of their calls. Thus, sampling cell phones may be necessary to gain access to a growing proportion of households that use cell phones exclusively or extensively.
Tucker, Brick, and Meekins (forthcoming) present estimates from the February 2004 Current Population Survey (CPS) Cell Phone Supplement indicating that over 50 percent of households have one or more cell phones and about 6 percent have only cell phones. Blumberg, Luke, and Cynamon (2006)
report similar estimates for 2004 from the National Health Interview Survey (NHIS), and that survey shows a rapid growth between 2003 and 2004 in cell phone–only households. Both the CPS and NHIS employ area-probability frames, not phone frames. In 2003 Steeh (2004) undertook the first large-scale U.S. telephone survey that sampled from a frame of cell phone numbers. Her research primarily examined the operational aspects and feasibility of interviewing on cell phones and did not delve into issues of statistical estimation.
We designed the Joint Program in Survey Methodology (JPSM) practicum survey in 2004 to evaluate issues associated with both conducting surveys on cell phones and producing population estimates from the data. The study sampled telephone numbers from a frame of cell phone numbers and a frame of landline numbers. The goal of surveying numbers from both landline and cell phone frames is to combine the samples to estimate the characteristics of all households that can be reached by telephone. Data from the "land sample" respondents are used to estimate the characteristics of households that have only landlines. Data from the "cell sample" respondents are used to estimate the characteristics of households that have only cell phones. Estimates of the characteristics of the overlap population—those households with both types of telephones—can be produced from both samples. A dual frame estimator combines the three pieces, using a weighted average of the two sample estimates for the overlap population, to produce estimates for all telephone households.
This article describes the effect of nonresponse on the practicum survey estimates and the usefulness of statistical weighting adjustments in addressing nonresponse bias. After briefly describing the survey in the next section, we identify two important sources of nonresponse bias. We then examine the effect of various estimation strategies designed to reduce the nonresponse bias. We conclude with some thoughts about methods that could be used in future surveys that sample both landline and cell numbers.
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Survey Design and Initial Estimation Plans |
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TOPAbstractIntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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Both the cell and land samples were drawn by Survey Sampling International (SSI) from the May 2004 Telcordia database for all 50 states and the District of Columbia. The cell sample included 8,000 telephone numbers, and the land sample had 4,488 numbers. The survey began with a screener interview that verified the number was residential and the person answering the telephone was at least 18 years old. In the land sample the respondent had to be a household member; there was no within-household sampling. An extended interview was then conducted about phone ownership and usage, attitude toward cell phones, social behaviors, and demographics. Interviews averaged nine minutes in length. Interviewers from Westat conducted the interviews for both samples from July 10, 2004, to September 5, 2004, using a computer-assisted telephone interviewing (CATI) system.
The numbers in the cell sample were randomly assigned to be reimbursed either $5 or $10. Numbers that were text message capable were randomly assigned to receive a text message or to receive no message. Approximately 25 percent of the cell sample was assigned to each of the four conditions. No experiments were done in the land sample, but an advance letter was sent to all land sample numbers for which addresses could be located.
A total of 1,592 screener interviews were completed (943 from the cell sample and 649 from the land sample). Overall, 1,358 extended interviews were completed, with 787 from the cell sample and 571 from the land sample. Up to 22 calls were allowed to obtain the completed interviews. If the household initially refused the screener interview, refusal conversion was attempted until the household completed the interview or refused a second time. The same procedure was used for the extended interview. (As discussed later, a random subsample of the cell sample screener refusals was not fielded.)
Response rates for the two samples were computed using American Association for Public Opinion Research (AAPOR 2004) definitions. The weighted screener RR3 rate was 26.5 percent for the cell sample and 38.6 percent for the land sample. The weighted RR2 extended interview response rate was 83.5 percent for the cell sample and 88.0 percent for the land sample. The combined response rate (screener RR3 multiplied by extended interview RR2) was 22.1 percent for the cell sample and 34.0 percent for the land sample.
More details on the data collection procedures are given in Brick et al. (forthcoming).
INITIAL WEIGHTING ADJUSTMENTS
This section describes the procedures used to create nonresponse-adjusted weights for each sample. As noted earlier, the survey is a sample of households with no sampling of household members. The weights are therefore household weights. Dual frame weighting to combine the two samples is discussed below. The base weights are the ratio of the number of telephone numbers in the frame to the number sampled. In the cell sample the number of completed interviews was close to the targeted number of interviews prior to refusal conversion, so conversions were only attempted for a random sample of about 75 percent of the initial screener refusals. The cell sample weights were adjusted to account for this subsampling (Brick et al. forthcoming). The weights for both samples were then adjusted for telephone numbers with unknown residential status. These weights were used to compute the response rates.
Next, a weighting classes approach was used to adjust for nonresponse. The weighting classes were initially based on region for both the cell and the land samples. However, after discovering that the cell sample estimate of the percentage of households with only cell phones was higher than expected (as discussed in the next section), the weighting classes for the cell sample were revised to reflect the number of call attempts required for first contact (one, two, three, four, five, and six or more calls). This procedure is similar to that recommended by Politz and Simmons (1949) to reduce nonresponse bias due to not being able to reach sampled units, which accounted for slightly less than half of all the nonresponse in the cell sample.
The weights were further adjusted to account for households that had multiple chances of being sampled because they had more than one telephone number. This adjustment was done separately for the cell and land samples by dividing the weight by the number of eligible telephone numbers in the household. In the land sample the divisor (the number of landlines) was three if there were three or more lines (less than 3 percent had more than three landline numbers). In the cell sample the divisor could be as large as four because about 3 percent of cell sample households had four or more cell numbers. Massey and Botman (1988) suggest capping the divisor at two, but we used higher caps because of the growth in the percentage of households with multiple lines.
We refer to these weights as the "nonresponse-adjusted" weights. In the next section the potential for nonresponse bias in each sample is investigated using estimates based on these nonresponse-adjusted weights.
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Indications of Nonresponse Bias |
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TOPAbstractIntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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Comparing the JPSM nonresponse-adjusted estimates of household telephone status (land-only, cell-only, and both) with the 2004 CPS Cell Phone Supplement revealed large disparities that we believe are due to nonresponse bias.1 As shown in the left side of figure 1, the land sample estimated that 71.0 percent of landline households had cell phones, compared with the CPS estimate of only 52.4 percent (Tucker, Brick, and Meekins forthcoming). Thus, households with cell phones are greatly overrepresented in the land sample.
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Topic salience (Groves, Presser, and Dipko 2004
) could account for this. Both the advance letter sent to the land sample cases with addresses and the screener interview introduction said the study was "about new technologies such as cell phones." Thus, persons interested in cell phones were probably more disposed to cooperate.
However, since some research has suggested that telephone nonresponse may be higher for low socioeconomic status (SES) households (Goyder 1987), and those households are less likely to have dual phone service, we reexamined the difference in the estimate between the CPS and the land sample controlling for home ownership, education, income, and Hispanic origin. Even within categories of each of these groups, the land sample consistently overestimates the percentage of households with cell phones. For example, the difference between the land sample estimate and the CPS estimate is 17.7 percentage points for households that owned their home and 21.4 percentage points for those that rented. Thus, the difference does not appear to be due to SES.
If topic salience were responsible for the effect, then we would expect households without cell phones to be more likely to require refusal conversion than those with cell phones, in line with the prediction from leverage-saliency theory (Groves, Singer, Corning 2000) that less effort will be required to obtain the participation of those who are more interested in the topic (in this case, presumably those with cell phones). This is precisely what we observe. The percentage of completed interviews in the land sample that required refusal conversion is 23.9 percent in households with only landlines compared with 18.7 percent in households with both cell and landlines.2 For the cell sample the difference by type of service in the percentage obtained by refusal conversion is not statistically significant (9.4 percent of those with both types of service and 10.4 percent in cell-only households), as would be expected because all the households in the cell sample had cell phones.
To assess whether the refusal conversion effect in the land sample was spurious (due only to SES), we used logistic regression to model refusal conversion using the following predictors: type of service (land-only or dual), home ownership, education, income, and age categories. The F-test for type of service is statistically significant (p = .02), and the odds ratio for this variable is 0.48, indicating that even after controlling for these SES variables, households with only landlines were much more likely to require refusal conversion. Thus, the refusal conversion difference is not due to response differences associated with SES; the only other variable with a significant effect on refusal is age.
The other result displayed in figure 1—that the cell sample nonresponse-adjusted estimate of the percentage of cell phone households with landlines is 11 percentage points lower than the CPS estimate—might stem from topic salience bias as well. But it may also be due to respondent inaccessibility, another source of nonresponse bias, to which we now turn.
Tucker, Brick, and Meekins (forthcoming) report that 31 percent of households that have both land and cell phones receive very few or none of their calls on their cell phones. The CPS item is: "Of all the phone calls that members of your household receive, about how many are received on a cell phone? Would you say . . . All or almost all calls/More than half/Less than half/or Very few or none?" When households that rarely receive calls on their cell phone are sampled in the cell sample, they may be less likely to answer the phone (possibly because it is not turned on) and therefore respond to the survey. Because of this possibility, the number of call attempts was used for nonresponse adjustment in the cell sample, as mentioned above. If the persons who rarely answer their cell phones cannot be reached, the result would be an overestimate of cell-only households in the cell sample.
The CPS also estimates that 8.9 percent of households with both types of telephone service receive all or almost all their calls on cell phones. If these households are less accessible on their landlines, this could lead to overestimating the percentage of households with only landlines from the land sample by roughly 4 to 5 percentage points. As noted above, we observed the opposite: the land sample underestimates the percentage of households with only landlines. This suggests that topic salience, not inaccessibility, is the more important contributor to nonresponse bias in the land sample.
An item similar to the CPS usage item was asked in the practicum survey for households that had both landlines and cell phones: "Now how about receiving calls—on your cell phone, do you receive . . . Many more calls/Somewhat more calls/Somewhat fewer calls/or Many fewer calls on your cell phone, as compared to your regular home phone? (if volunteered: About the same)." After combining categories ("all or almost all calls" plus "more than half" in the CPS and "many more calls" plus "somewhat more calls" in the practicum survey), the CPS estimate of "frequent" cell users is 33.3 percent versus 44.5 percent (SE = 2.3 percent) in the cell sample and 25.9 percent (SE = 2.2 percent) in the land sample. Thus, compared with the CPS, the cell sample respondents are more likely to be frequent cell users, and the land sample respondents less likely.
In summary, the nonresponse-adjusted estimates from the practicum suggest that both topic salience and household inaccessibility result in substantial nonresponse biases in estimating households by type of telephone service. Topic salience is more important than inaccessibility in the land sample, whereas the reverse appears to be true in the cell sample.3
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Estimation Strategies |
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TOPAbstractIntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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Dual frame estimation methods produce overall estimates by combining data from households in the overlap: those that could be sampled from both the cell and the land frames. Using the standard dual frame notation of Hartley (1962)
, let A be the landline frame and B be the cell frame. The set of households with landlines only is a = A 
Bc (where c denotes the complement), those with cell phones only are b = Ac B, and those that have both types of lines are ab = A B. Population totals in these sets are denotedYa, Yb, andYab, respectively.
The estimator using the nonresponse-adjusted weights for households with landlines only is ya, and for households with cell phones only is yb. A composite estimator is ycomp = ya + yb + y
, where the overlap population is estimated by 
with 0 < < 1, and 
and 
are the nonresponse-adjusted estimators of households with both cell and landlines from frame A and frame B, respectively. We refer to these weights, with = 0.5, as the "simple composite" weights.4
The dual frame estimator assumes that all sampled units respond. An unbiased composite estimate relies on unbiased estimates of all the components, including the weighted average of two unbiased estimates of the overlap population, namely 
. Under these assumptions the dual frame estimator has no bias from either noncoverage or nonresponse.
However, the nonresponse biases in the estimated percentages of households by type of telephone service are substantial for the components. For example, the simple composite weights estimate that 72.3 percent (SE = 1.7 percent) of telephone households have cell phones, compared with the CPS estimate of 55.4 percent. The simple composite estimate of the percentage of telephone households with only cell phones is 14.2 percent (SE = 1.2 percent), compared with the CPS estimate of 6.4 percent. Thus, the simple composite estimates are highly biased for estimating the percentage of households by telephone service, and this leads us to consider estimation strategies that might reduce nonresponse bias.
Various alternatives are possible, but we restrict our attention to three that attempt to reduce nonresponse bias by raking the estimates to control totals from an independent source. While research in dual frame theory using auxiliary data has generally focused on variance estimation rather than bias reduction, Skinner (1991) and Skinner and Rao (1996) show that raking may be beneficial in reducing nonresponse biases. The first scheme rakes the simple composite weights to demographic control totals. The demographic totals are the CPS estimates of the number of households with landlines by (1) Hispanic origin of the reference person; (2) the number of adults and their marital status (one adult, two married adults, two unmarried adults, and more than two adults); and (3) whether the home was owned or rented. We refer to the weights from this raking as the "raked composite" weights.
The second scheme rakes the weights from the two samples separately and then combines them. The land sample nonresponse-adjusted weights are raked to the CPS number of households with landlines by the demographic variables. The cell sample nonresponse-adjusted weights are raked to the CPS number of households with cell phones by the same demographic variables. These raked weights are then combined with = 0.5. While this procedure uses data on telephone status from the CPS in raking, it does not force the practicum estimates to equal the CPS estimates of service types. We refer to these weights as the "separate composite" weights.
The third scheme uses the CPS estimates of household telephone status as control totals. The simple composite weights are raked to four dimensions: the three demographic variables and the number of households by telephone service (cell-only, both cell and land, and land-only). This forces the practicum estimates of telephone status to be identical to the CPS estimates. We refer to these weights as the "service composite" weights.
A final estimator considered is a standard RDD frame estimator that completely ignores the observations from the cell sample. In this estimator the land sample is raked to the demographic variables, and the cell sample is deleted. This is equivalent to the standard RDD approach that samples only landlines, and thus we refer to these as the "RDD weights." The RDD weights are clearly not appropriate for estimating telephone service, but, like the service composite weights, they provide a useful comparison point for the estimation of other characteristics.
Table 1 shows the estimated percentage of households by telephone status for the three alternative weighting schemes and the RDD approach. As noted above, the CPS estimates are identical to those from the service composite. The raked composite estimates are very similar to the simple composite estimates. The separate composite estimates reduce the bias in the cell-only category but increase the bias for the "cell and landline" category.
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The last row of the table shows the approximate design effect due to weighting, computed as one plus the squared coefficient of variation of the weights. Both the simple composite and raked composite weights have a design effect of about 1.5, due largely to the differential weighting from combining (the mean weight for the land-only respondents is 3.1 times the mean weight of those with both types of service; the mean weight for the cell-only respondents is 1.6 times the mean of those with both types of service). The approximate design effect for the RDD weights is smaller than for any of the others because these weights do not have the combining factor. The design effect for the service composite weights is 2.3, due to the substantial perturbations needed to obtain the CPS distribution by telephone status. For the service composite, the mean weight for the land-only households is 5.9 times the mean weight for households with dual service, and the mean for cell-only households is 0.8 times the mean weight for those with dual service. While the overall design effect is not excessive, the increased variation can make other estimates, including those not related to telephone service, less reliable.
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Estimates Using the Different Weights |
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TOPAbstractIntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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The biases in the estimates of the percentage of households by type of telephone service are very large, but they may not be relevant to the goals of most sample surveys. In this section we consider the potential for bias in other estimates.
We computed estimates using all the weighting schemes for nine other items from the practicum survey: five on opinions about cell phones and four about political participation, reading newspaper editorials, and difficulty in meeting living expenses. These nine items produced 23 estimates, one for each response category except the last one. For example, reading newspaper editorials has four categories—"most days," "some days," "rarely," and "never"—so estimates were computed for the first three (the fourth estimate can be derived from the other three).
The variation across the schemes indicates that weighting matters for some of the estimates (data not shown). For example, with the service weights the percentage strongly agreeing that cell phones should be prohibited when driving a car is about 5 percentage points higher than the comparable simple and raked weight estimates. The variation in estimates is less pronounced for the four items about topics other than cell phones, but even some of those estimates vary. When the estimates are compared using t-tests, over 30 percent of the 230 comparisons are statistically significant, including some small differences.5 The largest differences are about 5 to 8 percentage points and are between the service composite scheme and schemes other than RDD (the differences between the service composite and RDD estimates are small). The differences between the simple, raked, and separate estimates are generally small (less than a percentage point) and usually not statistically significant.
While many estimates vary across the weighting schemes, it is unclear which, if any, is superior. To evaluate the schemes, we compared practicum estimates (other than phone status) with estimates from the CPS supplement, and the most comparable estimates are shown in table 2. The CPS estimates are obtained under different survey conditions, which may affect the comparisons; thus, it is not possible to disentangle nonresponse errors from other biases such as measurement error. For example, in the practicum age and race refer to the adult who responded to the survey, while in the CPS the characteristics are those of the reference person.
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Some of the estimates, such as those by census region, show little or no significant variation from the CPS estimates. Others, such as household income, show greater variation. The separate composite weight estimates perform the poorest, with substantial biases for most of the statistics produced. The service composite weights that include controls for demographics and type of service have biases comparable to those from the other composite estimates. In fact, we could not identify any systematic differences among the estimates from the simple, raked, and service composite schemes. The addition of type of telephone service as an auxiliary variable in raking does not reduce the biases for these estimates.
The RDD estimates are the only ones subject to coverage bias because they do not include cell-only households in the sample. Nevertheless, the estimates for the RDD scheme have biases that are not larger than those from the schemes that utilize the cell sample data. Most of the other estimates from the RDD scheme have relatively small biases.
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Discussion |
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TOPAbstractIntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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The evidence from the practicum survey suggests that both topic salience and household inaccessibility contributed to nonresponse bias. The nonresponse bias due to topic salience can be avoided in other surveys by eliminating references to technology and cell phones in the survey introduction. The nonresponse bias due to inaccessibility is more problematic.
In both the 2004 practicum and the earlier study by Steeh (2004), the cell phone samples resulted in many more cell-only households than expected. It appears that cell-only households are more likely to respond to cell phone surveys than households that have both types of service. This is at least partly due to households with cell phones that rarely answer their cell phones. RDD samples drawn from landline numbers may also suffer from inaccessibility bias due to frequent cell phone users who rarely answer their landlines. However, the data from the 2004 practicum suggest this latter problem is currently not severe.
Our evaluation of different estimation schemes showed that none of the alternatives resulted in substantial reductions in nonresponse bias. Using control totals of numbers of households by type of service in addition to the demographic controls did not reduce the nonresponse bias. Since sampling cell phones may be necessary as the proportion of persons and households without landlines increases, this is discouraging. However, the nonresponse biases in other dual frame surveys of landlines and cell phones may not be as severe as those in the practicum if nonresponse bias due to mention of the survey topic is avoided.
A different weighting approach would adjust the cell sample for nonresponse due to inaccessibility before combining it with the land sample. For example, respondents with cell phones in the practicum were asked, "When you are at home, how often is your cell phone turned on? Would you say . . . Always/Most of the time/Some of the time/Rarely/or Only when you make a call? (if volunteered: Never)." If items like this were routinely asked in surveys such as the CPS or NHIS, then it would be possible to use the resulting estimates as control totals to adjust cell sample weights. Such an adjustment would reduce the weights for households that answered always and increase the weights for those that answered rarely or never. While no survey currently collects data of this type, we understand the NHIS is considering additions along these lines.
Inaccessibility bias can also be avoided by designing the sample differently. Rather than using a full dual frame estimation approach, the numbers from the cell sample could be screened and interviews conducted only in those households without a landline. This is the method used by Fleeman (2006). The cell-only households are combined with the regular RDD sample to eliminate the coverage bias due to cell-only households. This approach avoids the nonresponse bias due to inaccessibility since households that rarely answer their cell phones are screened out. A drawback to this approach is its inefficiency, as it discards those households with a landline, which constitute a very large part of the cell sample. As a result, only the data from the land sample are used to estimate the characteristics of households with both types of service.
The RDD estimates from the practicum suggest that the coverage bias due to excluding cell-only households was not substantial in 2004. This finding is consistent with analyses from the 2004 CPS and NHIS (Blumberg, Lake, and Cynamon 2006; Tucker, Brick, and Meekins forthcoming). Similarly, Keeter (2006) shows that the bias in 2004 voting preference due to the exclusion of cell-only households is essentially eliminated when age is used in the weighting. Despite this, RDD surveys will probably have to incorporate cell phone samples at some point in the future as the proportion of cell-only households increases. Our results suggest that attempts to use dual frame surveys of landlines and cell phones need to address nonresponse bias, especially the bias due to inaccessibility in the cell sample. Otherwise, the reduction in coverage bias from including cell phones may be more than offset by an increase in nonresponse bias.
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Acknowledgements |
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TOPAbstractIntroductionSurvey Design and Initial...Indications of Nonresponse BiasEstimation StrategiesEstimates Using the Different...DiscussionAcknowledgementsReferences |
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We thank the students of the 2004 JPSM Practicum for their participation in this research, the Bureau of Labor Statistics, the Census Bureau, Westat, and Survey Sampling International (especially Linda Piekarski) for contributions that made the research possible, and Charlotte Steeh for advice and encouragement. The views expressed herein do not necessarily represent those of the Bureau of Labor Statistics or the Department of Labor.
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Footnotes |
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1. The CPS and the NHIS are large government surveys that estimated the distribution of households by telephone status in 2004. Both surveys have relatively high response rates, and their 2004 estimates of telephone households by cell phone status were similar (the CPS estimated 6.4 percent were cell-only, and the NHIS estimated 5.1 percent). We use the 2004 CPS for comparisons because only the CPS has estimates of telephone usage along with type of service.
2. A t-test of the difference in conversion rates has a p-value of less than .01.
3. One of the anonymous referees suggested that measurement error might account for the findings we interpret as nonresponse error, but we do not think this is likely because the differences from the CPS estimates are in opposite directions for the two samples even though the same questionnaire was used for both.
4. Using sample sizes to approximate the optimal value of gives = 0.42. Minor deviations from the optimal value generally have little effect on the efficiency of the estimates.
5. The estimates across schemes are highly positively correlated because the same data are used to produce all but the RDD estimates. A replicate variance estimator was used to appropriately compute the variances of the differences.
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References |
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