LATENT CLASS ANALYSIS OF SURVEY QUESTIONS THAT INCLUDE DON'T KNOW RESPONSES

This paper develops and describes latent class models which can be used to analyze dichotomous questions that include don't know (DK) responses. The models allow the researcher to account for different origins of the DK response; in particular, to account for DKs originating from nonattitudes, from equivocation, from an item whose cut point lies near a respondent's ideal point on the attitude, and from item misunderstanding. The models are illustrated on data involving the trade-off between environmental and economic concerns obtained by mail survey in the Pittsburgh, Pennsylvania, area. A model which includes a modified Guttman scale structure for substantive attitude holders and a separate DK class fits these data very well. In order to show the usefulness of the models, the respondents are assigned to latent classes according to this model and the characteristics of the latent classes are contrasted on attitudinal, behavioral, and demographic variables. The question of how best to handle don't know (DK) responses continues to be a vexing problem to survey researchers. Nevertheless, research on DKs has improved our understanding of the origins of this type of response. Broadly speaking, DK responses can be attributed to characteristics of respondents and to characteristics of questions. Empirical results suggest that DK responses are more likely for individuals who are older, less educated, nonwhite, in lower income categories, and women (Converse, 1976; Francis and Busch, 1975; Rapoport, 1982). Issue involvement and opinion strength are also related to DK rates (Francis and Busch, 1975; Schuman and Presser, 1981). Questions with more complex instructions, those requiring a longer view into the future, or those on more remote topics also generate a greater LAWRENCE F. FEICK is Associate Professor of Business Administration and Associate Dean in the Joseph M. Katz Graduate School of Business at the University of Pittsburgh. This research was completed with support from a faculty research grant from the Joseph M. Katz Graduate School of Business at the University of Pittsburgh. Public Opinion Quarterly Volume 53:525-547 ? 1989 by the American Association for Public Opinion Research Published by The University of Chicago Press / 0033-362X/89/0053-04/$2.50 This content downloaded from 207.46.13.64 on Sat, 03 Sep 2016 04:49:21 UTC All use subject to http://about.jstor.org/terms 526 Lawrence F. Feick number of DK responses (Converse, 1976). The upshot of these research results is that one common means of dealing with DK responses-treating them as nonresponses-is inappropriate because the DK responses are not random. Simply ignoring nonrandom DK responses will induce sample selection bias and affect sample statistics (for an introduction to sample selection bias, see Berk, 1983). Another popular method for dealing with DK responses is to attempt to discourage them, either by not offering a DK alternative or through probing instructions to interviewers. Schuman and Presser (1981) note that interviewers at the Survey Research Center at the University of Michigan are instructed to probe all DKs to try to obtain substantive responses. In their research comparing questions offered with and without DK options, Schuman and Presser found that although marginals on the two types of questions were similar, relationships among questions differed unpredictably between the two types. This research suggests that for issues in which there are nontrivial numbers of DKs, researchers should offer this response alternative. If researchers should offer DK alternatives and then not ignore them, how should such responses be analyzed? In this paper, we will examine latent class models useful in analyzing sets of items that include DK responses. In developing these models, we will focus on sets of questions with dichotomous response categories that also include a DK category. Data of this type can be seen as a set of k items represented as a 3k table. The problem is to make sense of the response patterns in the data by accounting for origins of the DK response with the models. We will develop scaling models, quasi-independence models, and other latent class models that, in certain respects, can account for a number of different origins of the DK response. After an examination of the origins of DK responses, we briefly review basic latent class methods, develop applicable latent class models for analyzing DK responses, and then illustrate them on public opinion data on the tradeoff between the environment and the economy. Origins of DK Responses Before we can formulate latent class models that account for DK responses, it will be useful to examine the sources of DKs. Previous research suggests that a DK response can occur for a number of reasons. First, a DK can be an error response (a response inconsistent with the attitudinal position) of an attitude holder. That is, a respondent may misunderstand an item because of poor instructions, lack of attention to the item, ambiguous phrasing, distraction, and so on. Coombs and Coombs (1976) described this source of DK response as This content downloaded from 207.46.13.64 on Sat, 03 Sep 2016 04:49:21 UTC All use subject to http://about.jstor.org/terms Latent Class Analysis of Questions with DKs 527 item ambiguity, although misunderstanding can be due to both characteristics of the items and characteristics of the respondents (Converse, 1976).l Second, a DK response can occur because of equivocation on an item. In such cases, a respondent feels ambivalence about the alternative substantive responses. This might occur if an individual's attitudinal position is very close to an item's cut point. This equivocation has been deemed respondent uncertainty by Coombs and Coombs (1976). In essence, the attitude holder equivocates because the item is in his or her "gray" region. Presumably, other attitudinal items (of greater or lesser difficulty) could be asked of these individuals and these would yield a substantive, rather than DK, response. In addition, we would assume that if the question had been asked in a Likert-type format, the respondent would have been likely to have chosen the middle option-neither agree nor disagree. We will call this source of the DK response item-specific equivocation. Equivocation need not be item-specific, however. For example, for some individuals there may not be "black" and "white" regions on a topic. To these individuals, everything is gray, and an appropriate response to all items on the topic is DK. These individuals are ambivalent about the topic, even though they may have considered it at some length. Such individuals have neither attitudes or nonattitudes and seem to be holders of what Faulkenberry and Mason (1978) call ambivalent opinion. We can call this source of DKs topical equivocation to distinguish it from item-specific equivocation.2 Finally, a DK response can be due to a nonattitude. Individuals who have not considered a topic, or who have not formulated a position, can be classified as nonattitude holders. Nonattitudes could be due to a lack of interest in or awareness of a topic (Bogart, 1967), or due to a trait which predisposes individuals to not develop positions (Rapoport, 1982, 1985). The extent to which nonattitudes are a major source of DK responses seems to depend on the topic. Schuman and Presser (1980) and Tourangeau (1984) suggest that individuals without specific opinions on an attitude object will respond to questions based on general feelings about the subject matter. Many respondents who lack a well-developed 1. A DK also can arise as an error response if a respondent who is an attitude holder is unwilling to express an attitude because of inarticulateness, a lack of confidence, and so on (see Rapoport, 1982, 1985). 2. Empirically, however, we can distinguish item-specific equivocation from topical equivocation only if the items vary across the range of positions on the topic. If the items are clustered near a particular scale point, we will not be able to distinguish types of equivocation. This content downloaded from 207.46.13.64 on Sat, 03 Sep 2016 04:49:21 UTC All use subject to http://about.jstor.org/terms 528 Lawrence F. Feick opinion will give a substantive response that seems close to their general feelings. Empirical evidence that documents substantial respondent willingness to provide opinions on nonexistent entities supports this view (e.g., Hawkins and Coney, 1981). In addition, research comparing the responses on closed versus open-ended items indicates that DK rates on open-ended items appear to be underestimates of the incidence of nonexistent attitudes (Lastovicka and Bonfield, 1982). This line of reasoning suggests respondents are more likely to manufacture opinions on topics about which they have some general knowledge even if they do not have an attitude. Topics which are completely foreign should elicit more DKs from nonattitude holders. Individuals who manufacture opinions should be less likely to have consistent opinions and less likely to demonstrate attitude-behavior consistency. Such responses might be particularly unstable over time. In fact, the definition and operationalization of nonattitudes typically is based on longitudinal inconsistency in substantive responses (Brody, 1986; Converse, 1970; Taylor, 1983). Models for Items with DK Responses