Multivariate Regression Analysis for the Item Count Technique

Abstract

The item count technique is a survey methodology that is designed to elicit respondents' truthful answers to sensitive questions such as racial prejudice and drug use. The method is also known as the list experiment or the unmatched count technique and is an alternative to the commonly used randomized response method. In this article, I propose new nonlinear least squares and maximum likelihood estimators for efficient multivariate regression analysis with the item count technique. The two-step estimation procedure and the Expectation Maximization algorithm are developed to facilitate the computation. Enabling multivariate regression analysis is essential because researchers are typically interested in knowing how the probability of answering the sensitive question affirmatively varies as a function of respondents' characteristics. As an empirical illustration, the proposed methodology is applied to the 1991 National Race and Politics survey where the investigators used the item count technique to measure the degree of racial hatred in the United States. Small-scale simulation studies suggest that the maximum likelihood estimator can be substantially more efficient than alternative estimators. Statistical efficiency is an important concern for the item count technique because indirect questioning means loss of information. The open-source software is made available to implement the proposed methodology.

Using the Predicted Responses from List Experiments as Explanatory Variables in Regression Models

“…We begin by briefly reviewing the multivariate regression analysis of list experiments proposed by Imai (2011) and Blair and Imai (2012). We then propose two new estimators.…”

“…The very feature of list experiments to provide a degree of anonymity to respondents makes it impossible to estimate standard regression models in a straightforward fashion. Although multivariate regression models have been developed to identify respondent characteristics that are associated with certain answers to sensitive questions (Imai 2011;Blair and Imai 2012), simply taking the predicted probabilities from these models and using them as an explanatory variable in the outcome regression, as shown later, fail to recover the true coefficient and result in the underestimation of standard error. To the best of our knowledge, no method exists to appropriately use the responses from list experiments as explanatory variables in regression models to predict other outcomes, such as (in this case) turnout or opinions about the candidates.…”

“…The validity of the estimate from the list experiment relies upon the assumption that respondents do not lie about the sensitive item and that adding the sensitive item does not change responses to the control item list (Imai 2011;Blair and Imai 2012). Although these assumptions are not directly testable, Blair and Imai (2012) propose a statistical test that can be used to detect certain violations.…”

“…First, multivariate regression models have been developed to help researchers identify the respondent characteristics that are associated with certain answers to sensitive questions (Corstange 2009;Imai 2011;Blair and Imai 2012). Second, statistical methods have been developed for testing whether the key assumptions of list experiments are violated and for reducing the potential biases that arise from violation of such assumptions (Blair and Imai 2012).…”

“…To overcome these problems, we propose the maximum likelihood (ML) estimator that is statistically efficient and is applicable to a wide range of models (Section 3.4). Both of our estimators build upon the general likelihood framework proposed by Imai (2011) and Blair and Imai (2012). The proposed methods are implemented in the opensource software list: Statistical Methods for the Item Count Technique and List Experiments, which offers a comprehensive set of statistical methods for analyzing list experiments (Blair, Imai, and Park 2014).…”