# Regression Modeling and Meta-Analysis for Decision Making: A Cost-Benefit Analysis of Incentives in Telephone Surveys

## Article excerpt

Regression models are often used, explicitly or implicitly, for decision making. However, the choices made in setting up the models (e.g., inclusion of predictors based on statistical significance) do not map directly into decision procedures. Bayesian inference works more naturally with decision analysis but presents problems in practice when noninformative prior distributions are used with sparse data. We do not attempt to provide a general solution to this problem, but rather present an application of a decision problem in which inferences from a regression model are used to estimate costs and benefits. Our example is a reanalysis of a recent meta-analysis of incentives for reducing survey nonresponse. We then apply the results of our fitted model to the New York City Social Indicators Survey, a biennial telephone survey with a high nonresponse rate. We consider the balance of estimated costs, cost savings, and response rate for different choices of incentives. The explicit analysis of the decision problem reveals the importance of interactions in the fitted regression model.

KEY WORDS: Decision analysis; Hierarchical linear regression; Meta-analysis; Survey nonresponse.

1. INTRODUCTION

Regression models are often used, explicitly or implicitly, for decision making. However, the choices made in setting up the models (e.g., stepwise variable selection, inclusion of predictors based on statistical significance, and "conservative" standard error estimation) do not map directly into decision procedures. We illustrate these concerns with an application of Bayesian regression modeling for the purpose of determining the level of incentive for a telephone survey.

Common sense and evidence (in the form of randomized experiments within surveys) both suggest that giving incentives to survey participants tends to increase response rates. From a survey designer's point of view, the relevant questions are as follows:

* Do the benefits of incentives outweigh the costs?

* If an incentive is given, how and when should it be offered, whom should it be offered to, what form should it take, and how large should its value be?

The answers to these questions necessarily depend on the goals of the study, costs of interviewing, and rates of non-response, nonavailability, and screening in the survey. Singer (2001) reviewed incentives for household surveys, and Cantor and Cunningham (1999) considered incentives along with other methods for increasing response rates in telephone surveys. The ultimate goal of increasing response rates is to make the sample more representative of the population and to reduce nonresponse bias.

In this article we attempt to provide an approach to quantifying the costs and benefits of incentives, as a means of assisting in the decision of whether and how to apply an incentive in a particular telephone survey. We proceed in two steps. In Section 2 we reanalyze the data from the comprehensive meta-analysis of Singer, Van Hoewyk, Gebler, Raghunathan, and McGonagle (1999) of incentives in face-to-face and telephone surveys and model the effect of incentives on response rates as a function of timing and amount of incentive and descriptors of the survey. In Section 3 we apply the model estimates to the cost structure of the New York City Social Indicators Survey, a biennial study with a nonresponse rate in the 50% range. In Section 4 we consider how these ideas can be applied generally and discuss limitations of our approach.

The general problem of decision analysis using regression inferences is beyond the scope of this article. By working out the details for a particular example, we intend to illustrate the challenges that arise in going from parameter estimates to inferences about costs and benefits that can be used in decision making.

By reanalyzing the data of Singer et al. (1999), we are not criticizing their models for their original inferential purposes; rather, we enter slightly uncharted inferential territory for poorly identified interaction parameters to best answer the decision questions that are important for our application. …