The share of households without a landline phone, but aving at least one cell phone, is steadily growing, and so is evidence of corresponding non-coverage bias in landline surveys. Consequently, surveys increasingly use dual frame sampling, typically with a landline share of 60-80%. The aim of this paper is to find the optimal value of this share (i.e. mixture parameter), while considering survey error and costs.

For this purpose, the target population is divided into five strata, according to possession and availability of landlines and cell phones. Next, by optimizing the product of costs and the mean squared error across strata, we get the analytical solution (a 4th order polynomial). Finally, this approach is illustrated in eight countries with a 2008 Flash Eurobarometer dual frame survey. The questions cover various socioeconomic and political issues: the support of the EU and its currency; attitudes toward economic reforms; and evaluations of household income fluctuations. The optimal mixture parameter is estimated for different variables, countries, sources of population data, and cost options. The solution depends on the landline-cell phone cost ratio. However, it generally lies in a relatively flat optimal area, from 30-70%. Surprisingly, the results are almost invariant to variables, while linear regression (using strata weights and cost ratio) gives excellent prediction of the analytical solution. In countries where the share of the cell-only segment is not very high (less than 25%), it is optimal to have more landline units, and vice versa: where the cell-only segment is larger a predominately cell sample is optimal. However, this connection can be affected by changes in cost ratio, which is the most important factor in determining the optimal design allocation. When the cost of cell interviews is very high in relation to landline phone interviews, taking more landline units is optimal in all countries.