The Dyad Ratios Algorithm for Estimating Latent Public Opinion

Abstract

In the study of longitudinal movements in public opinion it is usually the case that data are abundant, but irregular. Both cases (times) and variables are numerous, but it is never the case that all cases are available for any one variable. The dyad ratios algorithm was created to make dimensional analysis possible for this perverse data structure. The central logic of the dyad ratios algorithm is explained. Central focus is on the use of ratios as a starting point, the recursive estimation procedure, validity estimation by iterative procedure and the bootstrapping of standard errors. The ability of the algorithm to estimate a known longitudinal path is tested with artificial data. Then dyad ratios is compared to principal components analysis for a particular real data problem where both are possible. A final section makes a limited comparison between dyad ratios and item response theory.

Macrointerest

“…Simply visualizing the series is useful, but it does not provide any definitive evidence of the commonality between the series. To capture this shared variance and create a measure of macrointerest, we employ the dyad ratio algorithm technique used by Stimson (2018) to measure policy mood and by many other scholars to measure congressional approval, approval of the Supreme Court, trust in politics, and several other time series in the United States and other countries The dyad ratio algorithm (more commonly known as the software Wcalc) takes disparate survey items that generally measure the same concept, and finds the shared over-time variance. The basic idea is that if there are multiple survey items that are each asked at several points in time, the movement over time in each of the items will be a function of both the idiosyncratic variance in each item and the shared variance in the movement of the underlying concept in the aggregate population.…”

“…The Wcalc procedure uses the ratio of the different items at the same points in time, when available, to determine how the items vary similarly. From this, the algorithm extracts the common variance and generates a single series that summarizes a quarterly measure of the electorate's interest in politics (Stimson 1998;Stimson 2015;Stimson 2018).…”

“…Figure 4 presents five of these possible series, but they are not the only measures of political interest available. Following Stimson's (2018) process for developing his measure of public policy mood, we searched the Roper database of survey questions to find any survey that asked the public about its interest in politics. We began by entering a set of keywords into The Roper Center's iPoll, limiting the search to national US polls.…”

The Dynamic American Dream

“…Our approach is to consider the pool of all survey questions that have been asked about components of the American Dream. Using Stimson's (1999Stimson's ( , 2018 dyad ratios algorithm, we develop a single series of the public's belief in the American Dream over time, built on the shared variance that exists between multiple measures across surveys. Just as Stimson (1999) crafts a measure of public policy mood using the shared changes across multiple policy measures, we develop a measure based on the dynamics common to items assessing components of the American Dream, including optimism that the next generation will enjoy a better life and belief in the prospects of achieving a higher standard of living through hard work.…”

“…To create a time-series measure of the public's belief in the American Dream, we rely on Stimson's (1999Stimson's ( , 2018 dyad ratios algorithm. As inputs, we collected survey marginals about people's belief in the American Dream from various published surveys.…”