I've been thinking about mixed-mode surveys a great deal over the last few months. And I notice that research publications tend to use a lot of shorthand to describe the approach -- e.g. "Mail-Telephone." Of course, they describe it in more detail, but the shorthand definition focuses on the modes. Since the shorthand describes the sequence, we end up comparing different sequences. But there are other important design features at play that make these comparisons tenuous.
Of course, these other design parameters include the dosage of each mode in the sequence. Different dosages may result in different proportions of the interviews be conducted in each mode. For example, in the mail-telephone design, more mailings can increase the proportion of interviews in the mail mode. A recent article by Klausch, Schouten, and Hox includes a parameter for the mixture of modes \(\pi\).
I'm concerned that we may do lots of experimentation to design a mixed mode survey that is consistent with the current single-mode approach in terms of the estimates, but then let the mixing parameter vary after the switch is made. Of course, this is another reason to try to disentangle measurement error and nonresponse error in these surveys. Then the changes in the errors due to changes in the mixing parameter can still be controlled or, at least, understood.