INDIVIDUAL VALUE STRUCTURES AND PERSONAL POLITICAL ORIENTATIONS: DETERMINING THE DIRECTION OF INFLUENCE

Transcription

1 INDIVIDUAL VALUE STRUCTURES AND PERSONAL POLITICAL ORIENTATIONS: DETERMINING THE DIRECTION OF INFLUENCE William G. Jacoby Michigan State University April 2013 Prepared for presentation at the 2013 Annual Meetings of the Midwest Political Science Association. Chicago, IL, April 13, 2013.

2 This paper examines the relationship between values, party identification, and liberal-conservative ideology. Of course, this general topic has been revisited a number of times in the political science research literature. But, the approach used here is new in that it focuses on the role of individual value structures, rather than reactions toward single values. The analysis proceeds in three steps. First, I develop a model that succinctly represents people s choices across a set of values. Second, I estimate the model with some unique panel data that enable representation of each person s value choices at two different time points. Third, I estimate a variant of a cross-lagged regression model to explicate the patterns of structural influence between values, partisanship and ideology. The empirical results show that value choices are relatively stable over time, although not as much as partisan attachments or liberal-conservative self-placements. But, value choices do exert stronger effects on the other variables than was previously believed to be the case. BACKGROUND As a theoretical concept, values are usually defined to be a person s abstract, general, ideas about the desirable and undesirable end-states of human life (Rokeach 1973). Values derive theoretical importance from their capacity to provide guidance for the development of beliefs, attitudes, and behaviors. In effect, they function as general evaluative standards that can be invoked in any situation where particular values have substantive relevance (Schwartz 1992). As such, values have long been recognized for their potential importance as determinants of political orientations, such as partisanship, ideology, and issue attitudes (e.g., Kinder 1983; Feldman 1988). Thus, values can structure attitudes in a manner similar to an ideological belief system. But, the latter require comprehension and active use of abstract principles. In contrast, everyone possesses values so the impact of those values is likely to be far more pervasive within the mass public than that of the liberal-conservative continuum (e.g., Feldman 2003; Goren 2004). Despite its theoretical appeal, the preceding account of values has been subjected to some serious challenges. For example, Maio and Olson (1998) argue that many people regard values as truisms, or general beliefs that have very little in the way of cognitive underpinnings (also see Bernard et al. 2003). Accordingly, it is fairly easy to get people to change their expressed value preferences, thereby generating inconsistent choices (Goren, Federico, Kittilson 2006; 2009). More 1

3 generally, priming specific values may increase the degree to which individuals choose those values over others (Seligman and Katz 1996). There is also evidence that value choices are sensitive to external conditions. For example, McCann (1997) shows that feelings about core values vary systematically across the course of a presidential campaign. In a similar vein, several issue framing studies indicate that varied presentations of a political controversy can affect support for different values in ways that lead to opinion change (e.g., Nelson et al. 1997; Grant and Rudolph 2003). With both of these cases, it seems difficult to reconcile the empirical findings with the existence of stable and transsituational value structures. Perhaps most troublesome, the structure of the linkage between values and other orientations has been called into question. The relatively weak correlations between value choices and attitudes has been documented in the psychological literature (Murray, Haddock, Zanna 1996). And more recently, Goren and his colleagues present strong evidence that the causal relationship between value orientations and party identification runs from the latter to the former in other words, precisely the opposite direction from that suggested by theories of pervasive value influence (Goren 2005; Goren, Federico, Kittilson 2009). One conclusion that could be drawn from the preceding work is that values simply are not central psychological constructs with broad effects on human behavior. But, a different response points to a common feature of these studies: All of them measure personal value orientations by taking ratings of individual values. This is potentially problematic because people are rarely affected by single values, in isolation from other values (Sniderman, Fletcher, Russell, Tetlock 1996; Davis and Silver 2004). Instead, rank-ordered value structures are the key to understanding human behavior and the ways that values impinge on other phenomena (e.g., Schwartz and Bilsky 1987; Schwartz 1992; 1996; Verplanken and Holland 2002). The general idea is quite simple: Faced with a decision-making situation, an individual will pursue the course of action that is consistent with the values that he or she believes to be relatively important, while avoiding actions that promote values deemed to be less important. Why might this have affected previous research efforts? Precisely because ideas like freedom, equality, morality, and so on are quite important to just about everybody in modern society. Hence, when asked to rate their importance in experiments or public opinion surveys, there is likely to be 2

4 very little variation across the different values. It is only when an external context like a political controversy juxtaposes two values against each other, and the person is forced to choose a position based upon which one is personally more important, that the real effect of value choices becomes discernible. I contend that it is important to shift the focus to individual value structures rather than individuals reactions toward values taken singly. But, doing so raises measurement issues. Ever since Rokeach s pioneering work (1973), value structures usually have been elicited by having experimental subjects or survey respondents rank-order a set of values according to their subjective importance. The question is, how can data on these individual rank-orders be represented in a comprehensible manner, with scores that can be used easily within an empirical statistical model? In fact, the challenge of analyzing rank-ordered value choices has been cited as an important reason for using value ratings rather than the rankings (Alwin and Krosnick 1985). The next section takes up this challenge and develops a model of rank-ordered value choices that is readily amenable to empirical analysis. A MODEL OF INDIVIDUAL VALUE STRUCTURES Assume that we have n individuals rank-order k values according to their importance. The resultant information is contained in the n by k matrix, X. Each cell in this matrix, say x ij, contains the score that is assigned to value j for individual i. The score, itself, represents the number of values that i considers to be less important than value j, so the scores can range from zero through k 1 within each row of X. Note that the scores provide strictly ordinal information about each individual s choices, and the scores are inter-personally incomparable. With k values, there are k! possible orderings. The task at hand is to represent the different orderings that occur in the data in a comprehensible and substantively useful manner. Ideally, we would like to represent each individual by a single score, θ i, that summarizes that person s full ranking of the k values. These scores are collected into the variable, Θ, and movement across the range of this variable should be directly interpretable in terms of variability in value structures. A Geometric Representation of Value Choices In order to represent the individual rank-orders of the values contained in the data matrix, X, I will take a geometric approach: The values and the individuals will be shown as k points and n 3

5 vectors within a common space. The dimensionality of this space (indicated by the value, m) is an empirical question. However, if the model is to be useful, m should be a very small number (no larger than three, at most) so the space can be shown as a single picture. Within the space, the points and vectors are arranged so that, to the greatest extent possible, each vector points toward the values that the individual believes are most important, and away from those that he or she considers to be least important. To be more precise, each person s vector will be oriented such that his or her importance ratings for the values are monotonically related to the order in which the value points project onto his or her vector. Figure 1 shows a very simple example of such a model, based upon hypothetical information about two individuals (labeled 1 and 2 ) feelings about three values (labeled A, B, and C ). The 2 by 3 data matrix, X, is shown in the top half of the figure. From that information, we can see that individual 1 says value A is most important, value C is second-most important, and value B is least important. In contrast, individual 2 rates B, A, and C, from most- to leastimportant. The bottom half of the figure shows a two-dimensional geometric space that is consistent with the information in X; the space contains three points representing values A, B, and C along with two vectors for individuals 1 and 2. The dotted line segments running from the value points to the two vectors show the perpendicular projections. Notice that, starting from the terminal point of each vector (i.e., the end with the arrowhead), the order of the projections corresponds to the cell entries in X. On individual 1 s vector, the projection for value A comes first, followed by C and then B. On individual 2 s vector, the projection for value B is closest to the tip, followed by those for values A and C, respectively. Of course, any real model will contain far more than two vectors and probably more than three points. In fact, a much larger dataset than this simple example is necessary in order to fix the positions of the vectors and points relative to each other. But, the basic principle for locating these geometric elements remains the same: The vector orientations relative to the point locations should be consistent with the individuals rankings of the values. As we will see, this kind of model has several features that facilitate analysis of value preferences. But for present purposes, we will focus attention on the angle of each individual s vector, relative to some origin. The exact placement of the origin is arbitrary; for the model in Figure 1, assume it falls at the 3:00 position. Then, let θ i be the angle of individual i s vector, in the counter- 4

6 clockwise direction relative to the origin. Imagine moving a vector from the origin to it s mirror image (i.e., the 9:00 position). As the value of θ increases, from zero to 180 degrees (or π radians), the projections from the value points onto the vector will change systematically. With a vector pointed at 3:00, the order of the value projections would be B, followed by A, then C. Moving counter-clockwise, to an orientation with the vector pointing toward the upper-right (say, the 1:00 position), A could project first, followed by B and C, respectively. Moving a bit farther in the counter-clockwise direction, say to the position of Individual 1 s vector in Figure 1, the projections again switch order, to A, followed by C, then B. And finally, a vector pointing directly to the left (at 9:00) would have the value projections ordered C, A, and B that is, exactly the opposite ordering from the first vector that was pointed in the 3:00 direction. Of course, the vector movement could continue, producing still more orderings. For example, a vector pointed downward (toward 6:00) would be associated with an ordering in which B comes first, C, second, and A third. Hence, the variable containing angles for the n individuals vectors, Θ, can function as a representation of each person s overall preference order. Thus, we can use it as precisely the measure of individual value structures that we are seeking. Model Estimation The geometric structure laid out in the previous section is sometimes called the MDPREF model, an acronym for multidimensional preference scaling (e.g., Carroll 1972; Weller and Romney 1990). The analytic task is to use the information in X to estimate φ, the k by m matrix of coordinates for the value points and Γ, the n by m matrix of coordinates for the individual vectors terminal points; each vector will emanate from the origin of the space. The individual vectors are linear functions of the value points, and the model produces the following relationship: X = Γ φ (1) In equation (1), the X on the left-hand side is a matrix of predicted importance ranking values that is generated from the estimated model parameters. That is, the entries in any row of X, say x i, give the projections from the k value points onto i s vector within the m-space. Of course, Γ and φ are constructed in a way that makes X as similar as possible to the original data matrix, X. Let us assume for the moment that X contains interval-level data. In that case, Carroll (1972) 5

7 shows that the model can be estimated very easily, using a singular value decomposition. Begin by standardizing the entries within each row to zero mean and unit variance, producing X std. While not absolutely necessary, this preliminary step is useful because it places the origin of the space at the centroid of the points and vector terminii. Next, factor X std using the Eckart-Young decomposition: X std = UDV (2) On the right-hand side of equation (2), U is the n by q matrix of left singular vectors, D is the q-order diagonal matrix of singular values (arranged from largest to smallest), and V is the k by q matrix of right singular vectors. Note that q is the rank of X std, which typically will be k 1 (assuming that k < n, as will generally be the case), since the scores add to a constant within each row. The next step is to determine m, the dimensionality of the model space. This is specified by the analyst, but the general objective is to choose m so that it is as small as possible, while still producing a model that provides a sufficiently good fit to the empirical data. Some guidance can be obtained from the fact that the squared singular values give the sums of squares in X std that are explained by each pair of singular vectors. A goodness-of-fit measure for the model in m dimensions can be defined as follows: R 2 = tr(d 2 m)/tr(d 2 ) (3) Where tr is the matrix trace, or sum of the diagonal elements, and D 2 m is the diagonal matrix containing the squares of the first m singular values. As with a linear regression model, R 2 is interpreted as the proportion of variance in X std that is explained by the m-dimensional model. Alternatively, it is the squared correlation between the entries in X std and the entries in the X that is produced by the points and vectors in m-space. After determining the appropriate value of m, it is a simple matter to obtain φ and Γ. Simply 6

8 take the first m singular vectors and singular values and use them to define the following: φ = V m (4) Γ = U m D m (5) These values for φ and Γ comprise the best solution in the least-squares sense, because they generate the largest R 2 that is possible for an m-dimensional representation of the data. As already mentioned, the preceding estimation procedure assumes that X contains intervallevel data. This implies that, for i = 1, 2,..., n, the projections from the k value points onto i s vector, or x i, are linearly related to the entries in the corresponding row of the data matrix, x i. But, the entries within each row of X only give the rank-order of each individual s importance judgments about the values. It seems very unlikely either that the differences in importance across successive ranks are always constant, or that these differences are identical from one individual to the next. Therefore, it is more appropriate to specify a model in which the projections from the value points onto the individual vectors are idiosyncratic and row-specific monotonic functions of the importance ratings. In order to address this issue, a strategy called alternating least squares, optimal scaling or ALSOS (Young 1981; Jacoby 1999), is used to perform a nonmetric version of the singular value decomposition. ALSOS does not carry out the analysis on the original data matrix. Instead, the ALSOS routine uses a transformation of X, designated X, that contains optimally-scaled versions of the original data values. This means that the entries within any row of X, say x i, are a monotonic transformation of the entries in corresponding row of X, or x i. The specific monotonic transformation is allowed to vary across the n rows of x i. The monotonic transformations are chosen so that they maximize the model s R 2 in a given dimensionality, m. The only real difference from the interval-level situation is that this R 2 is now the squared correlation between the entries in X and the entries in X (rather than X). Briefly, the steps in an ALSOS version of multidimensional preference scaling are as follows: 1. At the outset, specify m, the dimensionality of the space, initialize R 2 to zero, and initialize X by setting it equal to the original X matrix. 2. Carry out the singular value decomposition, as described earlier, on the current version of X 7

9 and obtain current estimates of X and R If the current R 2 is larger than the previous value, then continue. If R 2 has not changed from the previous iteration (i.e., its value has converged) then terminate the procedure and go to step For i = 1, 2,..., n, use Kruskal s monotonic regression (1964) to find a new estimate of x i, containing values that are maximally correlated with the entries in the current x i, but weakly monotonic to the entries in the original x i. 5. Return to step 2 and carry out another iteration of the estimation procedure on the new version of X that was obtained in step When R 2 converges, construct the φ and Γ matrices from the singular vectors and values, and use the final R 2 as the goodness-of-fit. Thus, the nonmetric approach simply estimates the MDPREF model on a transformed (i.e., optimally-scaled) version of the data matrix. In practice, the procedure works very well. It usually converges quickly and it optimizes the appropriate monotonic, rather than linear, correspondence between the model elements and the original data values. The ALSOS model still represents the original data, since the various x i are linear functions of the x i, while the latter are monotonic functions of the x i. And, since the monotonic function can vary from one row of X to the next, the procedure explicitly recognizes that the entries in the original data matrix, X, are not comparable across the rows. Hence the model provides the best-fitting (in the least-squares sense) m-dimensional representation of the n individuals rank-ordered importance ratings of the k values. The n rows of the Γ matrix contain the coordinates for the terminal points of the individuals vectors (the vectors all emanate from the origin of the space). The vectors are normalized to unit length for convenience in presentation. After doing so, the normed coordinates can be regarded as direction cosines. These, in turn, can be used to obtain the angles of the vectors, relative to a reference direction, very easily. Of course, these angles are the θ i s that summarize each person s value choices. DATA The data for the analysis are taken from the 2006 Cooperative Congressional Election Study (CCES). The CCES is an internet survey; the component used here involves a nationally representative sample of 1000 American adults. 1 The survey is actually a panel study, with the first 8

10 wave of responses obtained in October 2006, and the second wave during the two weeks after the November 2006 midterm elections. Survey Items and Variables The 2006 CCES is a uniquely appropriate data source for present purposes because it contains items eliciting individual value choices, party identification, and ideology on both of panel study s two waves. Thus, we have replicated measures for these three concepts. Value choices are measured differently on each wave, although both approaches yield individual respondents rank-orders for the values. In the pre-election wave, the method of triads (Gulliksen and Tucker 1961) is used to provide replicated paired comparisons among five politically relevant values: Freedom; equality; economic security; social order; and morality. This relatively small set of values clearly does not represent the full range of terminal values in Rokeach s theory of values. Nor does it reflect the fully articulated system of universal values proposed more recently by Schwartz. Nevertheless, these five values are firmly rooted in American political culture, and they have direct relevance to current political controversies. Therefore, it seems likely that they will be meaningful to the survey respondents and be related to their other political orientations. The exact question wordings from the CCES instrument are shown in the Appendix. Briefly, the survey respondents are first shown a screen containing short definitions for each of the five values. Then, they are shown a series of ten screens containing all possible subsets of three values (i.e., triads ) from the full set of five. The ordering of the triads and the ordering of the three values within each triad is randomized across the respondents. For each triad, the respondents are instructed to select the value they believe to be the most important of the three, and the value they believe to be least important. These selections imply pairwise comparisons across the three values. So, for example, assume that a triad contains values i, j, and k. A respondent says i is most important and k is least important. This implies three pairwise choices: i is more important than j; i is more important than k; and, j is more important than k. Across the full set of ten triads, each pair of values occur together within a triad three times. So, the triads provide three replications of each pairwise value comparison. For each of the ten distinct pairs of values, the value that is chosen two or three times over the other is the dominant 9

11 choice for that pair. For each value, we calculate the number of times it is the dominant choice over any of the other four values. These scores comprise each person s rank-ordering of the values according to their perceived importance. If an individual s choices are transitive, then the five value scores for that person will consist of all five integers from four (indicating the most important value, with dominant choices over the other four values) to zero (for the value that is never the dominant choice over any other value). If a person has intransitive dominant choices, then there will be tied value scores; the ranking will be incomplete. The measurement strategy for value choices employed in the second panel wave is much simpler: The CCES respondents were simply asked to rank a set of seven values five of which were the same values included in the first-wave triads according to their importance. 2 Again, the exact question wording is shown in the Appendix. But, the general approach presented respondents with the full set of values (along with their brief definitions) and asked them to select the one they thought was most important. Then, the next screen presented the remaining (i.e., non-chosen) values and asked respondents to choose the most important from this set. This is continued down through the full set of values. In this manner, we obtain a full rank-ordering of the values for each respondent that completed the items. Once again, we assign each value a score which gives the number of values that were considered less important. Note that we only use the relative orderings of the five values from the pre-election wave; thus, the post-election value scores also range from a maximum of four to a minimum of zero. Turning to the other two variables that will be used in the analysis, the 2006 CCES included the standard sequence of ANES-style party identification questions on both waves of the survey. Ideology was measured using an innovative strategy. Survey respondents were shown a screen with the following text: One way that people talk about politics in the United States is in terms of liberal, conservative, and moderate. We would like to know how you view the parties and candidates using these terms. The scale below represents the ideological spectrum from very liberal to very conservative. At the bottom of the screen, they were shown a horizontal line with the left and right endpoints labeled Very liberal and Very conservative, respectively. Respondents were then asked, Where would you place yourself on this line? and they used their computer mouse to select a location. The mouse clicks were digitized on a zero to one-hundred scale. This item also was included on both panel waves. 10

12 Preliminary Results Let us begin by presenting some descriptive information about value choices. Figures 2 and 3 show histograms of the first- and second-wave choice scores for each of the five values; in effect, these scores indicate where the values fall within individual value structures. There are a few patterns that can be seen, all of which are relatively weak. For example, the modal position for freedom is at the top of individual value hierarchies, although nontrivial proportions of respondents place this value much lower, especially in the post-election wave. Morality shows a bimodal distribution of scores, with modal numbers placing this value both at the top and at the bottom of their hierarchies; the latter do outnumber the former, especially in the post-election wave. The remaining three values, social order, economic security, and equality, occur most frequently in the middle ranges of individual value hierarchies, relatively rarely being chosen as most- or least-important. Overall, the predominant conclusion to be drawn from Figures 2 and 3 is that there is great heterogeneity across individual value choices. Each value appears frequently at every possible position within the rank-orders. We have value rankings for each CCES respondent at two time points. This information can be used to assess the stability of individual value structures by calculating the Spearman rank correlation for each person s rankings across the two waves of the panel. The histogram for the respondent-specific correlations is shown in Figure 4. The most prominent feature of the distribution is its very pronounced negative skew. Precisely as we would expect from traditional theories of human values, the vast majority of the CCES respondents show strong positive correlations between their value structures measured at the two time points. The median Spearman correlation is (the mean value, 0.530, is pulled downward by the long left tail of the distribution), and 29% of the respondents have coefficients of or higher, including 9% with perfect correlations of 1.000). At the same time, we cannot ignore the fact that the lower tail of the distribution in Figure 4 really does extend a long way beyond the zero point. In fact, 80 people (or about 12% of the sample) have negative correlations between their replicated sets of value choices. The minimum value, exhibited by six people, is -.900; for these individuals, the two estimates of value structure are almost mirror images! The temporal variability in value structures will be the focus of the main analysis, below. But, it is useful to consider one possible explanation at this early point: It could be that stability in 11

13 value choices is affected by levels of sophistication. Unfortunately, the 2006 CCES does not contain detailed measures of political interest, knowledge, or engagement in the interview process. But, it does include a variable tapping levels of education. The correlation between respondent education and the value of an individual s Spearman coefficient is only The very small size of this coefficient suggests that it is not sophistication differences that are generating the distribution of stability levels in value choices. Turning briefly to the other two variables used in the analysis, both party identification and ideology show their typical very high levels of temporal stability. The correlation between the firstwave and second-wave measurements of party identification is The scatterplot in Figure 5 (note that the points are jittered to reduce overplotting) shows that the vast majority of the CCES respondents placed themselves into the same partisan category on both panel waves. Most of those that changed at all just moved one or two categories along the seven-point scale. Only a very tiny handful of people (six, to be precise) moved any farther than this. The over-time correlation for liberal-conservative self-placement is also very high, at and Figure 6 confirms the strong linear pattern connected these replicated measures of ideology. This temporal stability is particularly impressive, given the relatively continuous nature of the variable. Recall that the CCES respondents indicated their ideologies by selecting positions along a line segment, with no labels at intermediate positions to provide them with cues. Nevertheless, their second-wave scores tend to be very close to their first-wave scores; there are very few people who move from one side of the liberal-conservative continuum to the other. THE VECTOR MODEL OF VALUE STRUCTURES The CCES data provide repeated measures of each respondent s rank-ordered preferences for the five values. In order to analyze temporal stability and change in these choices, we will estimate the geometric model described earlier, using two vectors to represent each survey respondent. One vector will represent the person s value structure in the pre-election wave of the CCES survey, and the other will represent the structure in the post-election wave. If an individual has the same value structure at both time points then his or her two vectors should point in the same direction; if a person reports different rank-orders in the two panel waves, then his or her vectors will point in different directions. The angular separation between an individual s two vectors can be interpreted 12

14 as a measure of change in value structures. And, because the orientations of the vectors correspond to specific value choices, the change measure should be readily interpretable in terms of the ways that a person s value preferences vary over the time period between the two panel waves. Within the CCES sample, 652 respondents provided complete information about their value choices on both panel waves; the empirical analysis is, therefore, limited to this subset. The input data matrix for the analysis, X contains two rows of information for each respondent, so it is 1304 by 5. The i th row of this matrix, x i, is the five-element vector containing individual i s scores for the values on the first panel wave. The i th row of this matrix, x 652+i, is the five-element vector containing individual i s scores for the values on the second panel wave. For purposes of the estimation procedure, the two vectors for each respondent are regarded as completely separate observations. Preliminary analysis indicated that a two-dimensional model is appropriate for the CCES panel data on value choices. The R 2 for the two-dimensional representation is 0.900, showing that the model accounts for more than nine-tenths of the total variance in the optimally-scaled value importance rankings. The goodness of fit is much lower for a unidimensional solution (R 2 = 0.514) and the improvement in fit for a three-dimensional solution is not great enough to justify the increased complexity (R 2 for three dimensions is , an increase of only or about five percent of the total variance). The great advantage of the two-dimensional model is the ease with which it can be depicted with a graphical display. The model is shown in Figure 7. It contains two distinct sets of components: The points representing the values are shown as labelled s. The terminal points of the individual vectors are shown as open circles (all vectors emanate from the origin of the space); their exact locations have been jittered so that it is easier to discern variations in the density of vectors around the perimeter of the scaled space. Looking first at the configuration of value points, the general rule for interpretation is that the relative distances between the points are related to the similarity with which the respondents rank the corresponding values. That is, two values that tend to fall at adjacent positions within the individual rank-orders should be represented by two points located close to each other within the space. Conversely, two values that tend to fall at opposite ends of the individual rank-orders should have points that are quite distant from each other within the space. In Figure 7, the most salient 13

15 feature is the wide separation between the points representing freedom and morality, suggesting that these two values tend to anchor the opposing extremes of the individual rank-orders. Recall that freedom was often chosen as the most important value, and morality showed a bimodal distribution of choice scores. So, the relative positions of these two points seems quite reasonable, in terms of actual value choices. The other three values are represented by a cluster of points in the lower half of the space. Their distinctiveness in the scaling solution is almost certainly due to the previously-noted fact that these values economic security, equality, and social order tend to fall at intermediate positions within the individual rank-orders. But, within this cluster, there is a separation between the point for social order and the points for the other two values. The social order point is farther to the right, suggesting that its ranking tends to be more similar to that of morality. In contrast, the points for economic security and equality are farther to the left, indicating that their positions within an individual rank-order tend to be more similar to that given to freedom. The vector terminal points in Figure 7 are widely dispersed around the entire radius of the unit circle. 3 It is important to reiterate that it is the projections from the value points onto the vectors that is important, and not the distances from the vector points to the individual values. Again, the order in which the points project onto a vector corresponds to the rank-order of the values for that individual. The sparsest interval in the circular distribution of vectors falls near the bottom, around the 6:00 position. This makes perfect sense, since those represent the individuals who rank economic security, equality, and social order above the other two values; this occurs infrequently within the CCES data. The highest concentration of vectors occurs on the left side of the space, from about the 7:00 position to just past the 10:00 position, with the greatest density occurring around the 9:00 position. These people place freedom highest in their rankings, followed by equality, economic security, social order, and morality. Another tightly-grouped cluster of vectors points upward, around the 12:00 position. This corresponds to value structures in which both freedom and morality are ranked highly, with the other three values placed at less important positions. Finally, there is another, somewhat lighter, concentration of vectors on the right side of the space, extending from about the 1:30 position to about 4:00. These represent value structures in which morality is ranked as most important, followed by some combination of placements for social order, 14

16 economic security, and equality, and freedom in last place. Figure 7 shows the full model, so it includes the vectors for both time points. In order to see how value structures changed over time, the panels of Figure 8 show the separate vector distributions for the two waves of the CCES panel (note that the value point positions are constant, so they are identical in both displays). The figure reveals a potentially interesting pattern in the temporal variability of the distributions. In the first panel wave (Figure 8A), the greatest concentration of vectors occurs in the upper left side of the space. But, in the second wave (Figure 8B), the vectors are much more evenly dispersed around the unit circle. Figure 8 also shows the mean vector for each time point. The mean vector is defined by taking the mean of the coordinates for the individual vectors. Just as with the scalar mean, the mean vector represents the central tendency of the circular distribution of vectors; the point projections onto the line collinear with the mean vector represent the average value structure for that time point. The length of the mean vector is also relevant, because it is inversely related to the dispersion of the vectors. If all of the individual vectors pointed in the same direction, then the mean vector would have a length of one. As the individual vectors spread out around the mean, the length of the mean vector becomes shorter. In the limiting case, there are a variety of situations (e.g., half of the vectors are mirror images of the other half) in which the mean vector length would be zero. Thus, the length of the mean vector (which is usually called the mean resultant length in the statistical literature) can be used to gauge the amount of heterogeneity in the value choices at each of the time points. The mean vector for the first time point is oriented so that the value projections run in order from freedom (most important), through equality, morality, and economic security, down to social order. The mean vector for the second time point has almost the same ordering of the values: freedom, equality, economic security, morality, and social order. But, the big difference across the panel waves is in the mean resultant lengths. The mean vector for the first time point is units long, while that for the second time point is only units. In fact, the latter is so close to zero that the orientation of the second mean vector is almost meaningless (no pun intended!) in substantive terms. Substantively, this result shows that the distribution of value structures polarized sharply from the first time point to the second. 15

17 The evidence presented in Figure 8 speaks to the aggregate amount of change in value structures. But, we are more interested in the changes that occur within individuals over time. In other words, how much does each person s value structure change across the two CCES panel waves? Individual change can be assessed by looking at the angular separation between the two vectors representing a person s value choices at each of the two time points. Again, perfect stability will correspond to identical vector orientations (and, hence, an angle of zero radians). The greater the amount of change, the larger the angular separation, up to a maximum of π radians, which means that the person s rank-order of the values at one time point is the mirror-image of his or her rank-order at the other time point. Figure 9 shows the histogram of angular separations for the individual vectors over time. The angles do vary across the entire range of possible values (i.e., from zero through 3.14 radians), showing that temporal variability ranges from perfect stability in value structures up to mirrorimage rankings of the values. But, the distribution shows a very strong positive skew. As a result, the median angular separation is radians (or degrees), and the mean is pulled to the right, to radians (46.79 degrees). Given the range of possible values (3.14 radians), the inter-quartile range is quite small, at radians. While there are a few people who show marked change in their value choices over time, the bulk of the CCES respondents are characterized by very stable value structures. Of course, this is precisely the same conclusion that we drew from inspection of the individual-level Spearman correlations for the two replications of the rank-ordered values. The difference here is that the geometric model makes it a straightforward task to describe how a person s value structure changes, based upon the differences in the point projections on his or her vector across the two panel waves. One basic question is whether the observed changes in value choices are substantively meaningful or just random fluctuations due to measurement error or lack of model fit. And, if the temporal changes do appear to be non-random, what is their source? In the next section, we will address these questions by examining how changes in value structures correspond to temporal variability in party identification and ideology. 16

18 VALUE STRUCTURES, PARTY IDENTIFICATION, AND IDEOLOGY Values are considered to be critical theoretical constructs precisely because they have the potential to exert a pervasive influence on human behavior. Similarly, party identification and ideology maintain their own theoretical status because they structure subsequent political beliefs, attitudes, and behavior. But, even if we believe that these three concepts are exogenous to most other aspects of public opinion and political behavior, it remains unclear how they relate to each other. As discussed earlier, recent research has emphasized the causal influence from partisanship to values. But if values are, themselves, affected by other orientations, their relevance as transsituational behavioral cues may be compromised. Therefore, it is important to sort out the structural connections between values on the one hand, and party identification and ideology on the other. The bivariate relationship between party identification and value structure can be illustrated very easily, by calculating and plotting the mean vectors for the individuals who place themselves within each of the seven party identification categories, at each of the two time points. Similarly, the ideology variable can be collapsed into five equal-width categories corresponding to extreme liberals, nonextreme liberals, moderates, nonextreme conservatives, and extreme conservatives. Again, mean vectors are calculated and plotted for each of these groups, at each of the time points. The differences in the mean orientations for the various subgroups are reflected in the angles between the mean vectors for those groups. In fact, the cosine of the angle between any pair of vectors is related to the correlation between the average value rankings for the respective groups. Figures 10 and 11 show the results for party identification and ideology, respectively. In each case, the general orientations of the vectors make sense in substantive terms. Those for Democrats and liberals tend to point toward the left side of the space, showing that they tend to rank freedom and equality over social order and morality. The vectors for Republicans and conservatives point in the upper right direction, indicating that morality is placed uppermost in their rank-orders. The second-place value for these groups is either social order or freedom, leaving equality and economic security as least important. In most cases, the vectors for nonleaning independents and ideological moderates fall in between the contrasting partisan and ideological groups. The only exception to the latter pattern is that moderates converge to the liberal side at the second time point (Figure 11B). 17

19 By far, the most salient feature of both Figures 10 and 11 is the polarization of the partisan and ideological groups that occurs from the first time point to the second. In Figure 10A and Figure 11A, Democrats and Republicans, and liberals and conservatives, show weakly contrasting preference orders. In each panel, there are obtuse angles between the vectors for opposing groups, showing that there are negative correlations between their rank-orders for the values. But, these angles generally are not all that much larger than π/2 radians (or 90 degrees); thus, the absolute values of these correlations are not that large. The situation changes markedly in Figures 10B and 11B. Clearly, the opposing vectors now point in almost exactly the opposite directions from each other. And, of course, this corresponds to mirror-image value rankings. The polarization is not only sharp, but also relatively symmetric. That is, the vectors for Democrats and liberals move from their original positions in a counter-clockwise direction while the vectors for Republicans and conservatives move just about the same amount, but in a clockwise direction. By the post-election wave of the CCES panel it is no exaggeration at all to say that Democrats and Republicans exhibit value structures that are diametrically opposed to each other. The same is true for liberals and conservatives. So, the temporal changes that occur in value structures, party identification, and ideology are systematic and directional in nature. The spreading of the respective fans of vectors that takes place across the two panels of Figures 8 and 9 simply could not occur if changes over time in these three variables were merely random noise. But, we still need to determine what is taking place at the individual level. Are people sorting themselves into partisan categories and ideological proclivities based upon their feelings about these five values (Levendusky 2009? Or, are partisan and ideological groups becoming more extreme over time, perhaps in response to elite cues (Bafumi and Shapiro 2009)? The 2006 CCES data provide a unique opportunity to address the preceding questions by estimating a cross-lagged model of the relationships between value structures, party identification, and ideology (Finkel 1995). The model structure is very simple: Each of the three variables at the first time point specified to influence each of the three variables at the second time point. But, after taking these temporal influences into account, there is no further connection between the variables at the second time point. The relatively short time interval between the two panel waves (no more than about six weeks, and usually less than that) makes the cross-lag specifica- 18

20 tion reasonable. Values, partisanship, and liberal-conservative placements are all considered to be longstanding fundamental predispositions for most people. Therefore, they should possess a great deal of psychological inertia; that is, any changes which do occur should be relatively slow and gradual. There should not be immediate contemporaneous feedback loops running between these variables at any given time point. One of the practical advantages of the cross-lagged specification is that the parameters usually can be estimated easily, using ordinary least squares. Here, however, the circular nature of the value structure variable introduces a complication. There is no problem when the individual vector orientations are used as an independent variable. In that case, we will simply use the signed angular separation between each person s vector and a designated baseline vector (which will be discussed below). But, it is problematic when vector orientations are the dependent variable, because the important information is contained in the angular separation of the vectors, regardless of the baseline angle. In order to deal with this, we can rely upon statistical methods that have been developed for directional data (Mardia 1972). Specifically, the circular regression model developed by Fisher and Lee (1992) and introduced to political scientists by Gill and Hangartner (2010) uses the following generalized linear model: µ i = µ + g 1 (x i β) (6) Where µ i is the position of the i th observation s vector around the unit circle (in radians, moving counter-clockwise from a baseline position), µ is an intercept, x i is the set of independent variable values for observation i, β is the coefficient vector, and g 1 is a link function mapping from the values of the linear predictor (x i β) into the interval from zero to 2π. The parameters of the circular regression model are estimated by maximizing a likelihood function based upon the Von Mises distribution. From a mathematical perspective, the baseline angle is arbitrary. But, in order to facilitate substantive interpretation, it is useful to set the baseline to a meaningful position. Here, we will set the baseline to the angle that falls halfway between the mean vector for self-identified Democrats and liberals and the mean vector for self-identified Republicans and conservatives. This bisecting angle falls at radians ( degrees from the 3:00 position), or at about the 10:30 position. 19

21 The individual vector angles are transformed to represent the signed angle from this baseline. Table 1 presents the maximum likelihood estimates for the three equations in the cross-lagged model (these are just the OLS estimates for party identification and ideology). Each column of the table gives the results for one of the structural equations. For each of the independent variables, the coefficient is presented along with the standard error in parentheses. The numbers below these estimates are the observed probability values for a one-sided test of the hypothesis that the associated population parameter is equal to zero. The results for the second-wave value structures are presented in the leftmost column of Table 1. Here, the only variable with a significant coefficient is an individual s value structure in the first wave of the panel. A one-radian difference in the pre-election wave of the panel study corresponds to an average radian difference in the post-election wave. And, once this is taken into account, first-wave party identification and issue attitudes have no further effect at all. The coefficient estimate for the former is zero out to three decimal places, and the coefficient for the latter is only Neither of these coefficients are statistically different from zero. Thus, individual value structures are characterized by a high level of temporal stability; a person s preference ordering for the values at the first time point does have a strong impact on his or her rank-ordering of the values at the second time point. Beyond this, there appears to be no systematic movement in value choices due to other factors. Even with the strong autoregressive tendency in value choices, it is important to recognize that the equation s fit to the data is rather mediocre. The squared correlation between the predicted vectors from the circular regression and the actual second-wave individual vectors is only So, there is a great deal of variability in value structures that remains to be explained. But, this does not alter the basic finding that the other variables have no serious impact on temporal change in value choices. The situation is very different with party identification and ideology, as shown in the middle and rightmost columns of Table 1, respectively. Both of these equations fit the data very well, with R-squared values of and 0.812, respectively. In each case, the respondent s position at the first time point has, by far, the strongest effect on their position at the second time point. This is fully to be expected, given the well-known stability in both of the dependent variables. But, here, the other independent variables also affect the respective dependent variables. In the equation 20