A network Approach to the Development of Attitudes over Time:
Individual’s Attitude Structure and Attitude Change
Tom Hidde Oreel
University of Amsterdam
Abstract
In this longitudinal study, we investigate individual’s attitude structure from a network approach. By modeling the moment-to-moment changes between evaluative reactions in network model, we capture the individual’s attitude structure. Assuming that individual’s attitude networks are a valid methodology to analyze individual’s attitude structure, we hypothesized that the network structure can used to investigate attitude dynamics. First, we hypothesized that degree centrality reveals the underlying process of attitude formation. Second, we hypothesized that network connectivity reveals the underlying process of attitude change. While we did not find any evidence for the hypotheses, results show that individual’s attitude networks can successfully be applied from time series data. By modelling individual’s attitude structure in network model, the individual attitude networks provide a promising tool to investigate attitude dynamics.
Introduction
The ability to change our attitude of the external world is essential to function in a dynamic environment: a person who is friendly at one moment in time might turn untrustworthy at another moment in time. While current literature provides a practical framework to describe the different depths of attitude dynamics (e.g., attitudes become more stable and resistant to change when people are highly motivated and capable to process new stimuli; Petty & Cacioppo, 1986), they give little insight in the process underlying attitude dynamics (e.g., what aspects makes attitudes stable, how these aspects relate to the dynamics; Monroe and Read, 2008). It would be better to have a model directly measuring the underlying process of attitude dynamics. In this longitudinal study, we conceptualize individual’s attitudes as a network of dynamically interacting evaluative reactions. By modeling the moment-to-moment changes between evaluative reactions in network model, we capture the individual’s attitude structure as a network model. We argue that such individual networks provide a realistic representation of the mechanics underlying attitude formation and attitude change. Moreover, we show that the network approach provides a range of novel hypotheses concerning the study of attitude dynamics. This makes the individual attitude networks a promising tool for investigating attitude dynamism.
The attitude is a psychological tendency to respond with a specific pattern evaluative reactions when encountering an attitude object (Eagly & Chaiken, 1993). This pattern of evaluative reactions is typically referred as the attitude’s internal structure (Petty & Krosnick, 1995). The internal structure includes cognitive and affective evaluative reactions (e.g., belief that a person is friendly, or feeling anger towards a person). Furthermore, evaluative reactions are interconnected with each other: activation of a single evaluation opens up a range of other evaluative reactions; Zimbardo & Leippe, 1991). Interestingly, numerous studies documented a strong influence of the attitude’s internal structure and its behavior over time (i.e., attitude change and attitude
formation): First, attitudes with more substantial and complex structures of evaluative responses are found to be more resistant to change (Haugtvedt, Shakarchi, Samuelsen, & Liu 2004; Haugtvedt
& Wegener, 1994; Haugtvedt & Petty, 1992; Wegener, Petty, Smoak, & Fabrigar, 2004). Second, elaboration (i.e., adding evaluative beliefs to the internal structure) is found to create complex attitudes structures, which are more resistant to change (Himmelfarb & Youngblood, 1969; Lewan & Stotland, 1961). While it seems that the attitude’s structure influences the attitude dynamics, much of the research has not explored the underlying process (e.g., what are some attitude structures more resistant to change?). Moroever, analytical tools for investigating the mechanism behind these dynamics have been lacking (Monroe & Read, 2008; van Overwalle & Siebler, 2005).
Traditionally, dual process models, like the elaboration likelihood model (Petty &
Cacioppo, 1981, 1986) and the heuristic-systematic model (Chaiken, 1987; Chaiken, Liberman, & Eagly, 1989), are used to describe the dynamics of attitudes. Generally speaking, dual process models describe attitude dynamics as the result of two routes of information processing: (a) a central route, in which information is carefully processed, and (b) a peripheral route, in which information is quickly processed (Petty & Cacioppo, 1986). The dual process models give a practical framework to describe attitude dynamics (e.g., attitude become more resistant to change when information is processed systematically). However, they do not explain the underlying process (i.e., what makes attitude more stable). They cannot account for the attitude’s internal structure, or how this relates to its dynamics (e.g., what aspects makes attitudes stable, how these aspects relate to the dynamics). For instance, it cannot explain why attitudes with more complex internal structure are more resistant to change, instead, it only describes which of the many principles will be most applicable given a certain situation (e.g., central route when motivated). A model is needed, which gives a realistic representation of the attitude’s internal structure, and how this structure relates to its dynamics.
Attitudes as Networks
Recently, Dalege and colleagues (2016) developed a model, which represents the attitude’s internal structure as a network of causally interacting evaluative reactions. The Causal Attitude
Network model (CAN model) consists of nodes, which are connected by edges. A node resembles an evaluative reaction, an edge resembles an interaction between two evaluative reactions (see Figure 1). Interactions are the result of direct causal relations between evaluative reactions (e.g., Feeling of ‘pleasure’ causes you to think it is ‘good’), and mechanisms that support consistency between related evaluative reactions (i.e., cognitive consistency). Importantly, the network structure of the CAN model naturally captures the interconnected structure between evaluative reactions: if one node gets activated (e.g., belief of danger), it can cause other nodes to activate as well (e.g., the feeling of fear). In doing so, the CAN provides a realistic representation of the attitude’s internal structure (Dalege et al., 2016). As we discuss below, this network representation can also be used to investigate the dynamics of attitudes, providing a possible explanation of the underlying process of attitude dynamics. This makes the network approach a promising tools for studying the dynamics of attitudes.
Figure 1: Hypothetical attitude network. Nodes represent evaluative reactions and edges represent causal relations between the evaluative reactions. Evaluative beliefs are represented with blue nodes, evaluative feelings are represented with green node
Attitudes as Complex Dynamical Systems
A great advantage of the attitude network, it that it enables us to represent the attitude as a complex dynamical system of interacting evaluative reactions (Barabási, 2011). A complex dynamical system is a system of interacting components, with no central control, in which interactions between its components give rise to the collective behavior of the system (Mitchell,
2006). Examples of complex dynamical systems are the human brain (system of interacting neurons), groups of people (systems of interacting humans) and ecosystems (systems of
interacting organisms). Importantly, the behavior of complex systems (i.e., system dynamics) cannot be explained in terms of the behavior of the individual components (Scheffer et al., 2009). To investigate the system dynamics, the focus lies on the interactions between components, and how these interactions relate to the behavior (Mitchell, 2006). Network models naturally captures these interactions, thus revealing the underlying mechanics that causes the system dynamics (Mitchell, 2006). If attitude can also be characterized as a complex dynamical system, network models may reveal the underlying mechanics of which causes attitude dynamic.
It has been hypothesized before that attitudes can be characterized as a complex dynamical system (Flay 1978; Latané & Nowak 1994; Tesser & Achee 1994, Zeeman 1976). It was argued that catastrophe theory, a theory used to describe the general behavior of complex systems, could explain and predict the dynamics of attitudes change. According to the catastrophe theory, attitudes are unstable if involvement is high, and positive and negative evaluations are equal. In such unstable attitudes, small changes of information (i.e., persuasive efforts) can ‘flip’ the attitude into a contrasting state (e.g., from extremely positive to extremely negative). Empirical studies supported this hypothesis, as it was found that cusp catastrophe models (models based on catastrophe theory) could predict the likelihood of having extreme attitudes (van der Maas, Kolstein, & van der Pligt, 2003). The cusp catastrophe model (see Figure 2, top image) predict the attitude state (i.e., surface area) using two variables, a normal variable (i.e., information; x-axis) and a splitting variable (i.e., involvement, y-axis). It was found that gradual increase of involvement increases the likelihood of heaving extreme attitudes (see Figure 2, bottom images). These findings supports the idea that attitudes behave as complex dynamical systems. However the cusp catastrophe model does not explain the mechanisms underlying these dynamics (i.e., involvement is not explained with inherent property of the attitude itself). Better
results are expected when the attitude is directly measured in a network model (van der Maas, Kolstein, & van der Pligt, 2003).
Figure 2: The cusp catastrophe model of attitude change. The top image represents the cusp catastrophe model, the folded surface represents the attitude state under different levels of involvement and information. The bottom images represent the dynamics of attitude change when involvement is high and low. The blue line represents the dynamics of attitude change when involvement is low, here we see a linear relation between information and attitude state. The red line represents the dynamics of attitude change when involvement is high, here we see an abrupt transition in attitude state for certain levels of information.
For many complex systems, the network connectivity (i.e., how densely connected are the components in the system) plays an important role on their systems dynamics (Cramer et al., 2013). More specifically, the abrupt transitions of the cusp catastrophe model can be explained with network connectivity (Cramer et al., 2016; Scheffer 2012). In Figure 3 we plotted the relationship between network connectivity and the systems response to stress (i.e., changing
conditions). The networks consists of interconnected nodes that can switch between two
contrasting states (e.g., positive/negative). The likelihood that a node will switch to a contrasting state is influenced by the states of neighboring nodes (e.g., if many neighboring nodes are positive, the node will probably become positive too). Stress causes nodes to ‘switch’ to a
different state: the higher the stress, the more nodes will ‘switch’ to a different state. Interestingly, high and low network connectivity behave differently on increasing levels of stress: In low
connected systems, we see a linear change to increasing levels of stress. This is because the nodes are relative isolated (low influence of neighboring nodes) and thus the nodes will change
independently of each other, causing a step-by-step change of the system (van Nes & Scheffer, 2005). In highly connected systems, we see a non-linear and abrupt change to increasing levels of stress. When stress is relatively low, change in few nodes is rectified by neighboring nodes (Dunne, Williams & Martinez, 2002; van Nes & Scheffer, 2005). However, as stress increases, there will be a point, at which change cannot be rectified by neighboring nodes anymore, at this ‘tipping point’, even a small increase in stress will cause a domino effect propelling the system into a different state. Interestingly, similar dynamics are seen in the cusp catastrophe model of attitude change (See Figure 1 & 2). This suggests that network connectivity is the driving force behind the dynamics of the cusp catastrophe model. If so, attitude networks may provide a more direct explanation of the abrupt transitions of the cusp catastrophe model (i.e., involvement is explained with inherent property of the attitude itself).
Figure 3: The dynamics of network connectivity to changing conditions. High connected system (left) adjust non-linearly and abruptly to increasing levels of stress; first, low stress gets “compensated” by other nodes, until at a critical level of stress is surpassed and the system collapses. Low connected systems (right) adjust gradually and predictable to increasing levels of stress; the nodes change in isolation to increasing levels of stress.
Individual Attitude Networks
Previous studies investigating attitude networks focused on the analysis of cross-sectional data. Such cross-sectional networks give the average associations between evaluative reactions for a group of people at one moment in time. Cross-sectional networks are limited for investigating attitude dynamics. First, cross-sectional networks lack ability to capture moment-to-moment changes among evaluative reactions (i.e., cannot capture the behavior of attitudes over time). Second, cross-sectional networks cannot account for individual differences. This is problematic because, (a) individuals differ in attitude structure (Huskinson & Haddock, 2004), and (b) attitude structure has an impact on attitude dynamics (Haugtvedt, Shakarchi, Samuelsen, & Liu 2004; Haugtvedt & Wegener, 1994; Haugtvedt & Petty, 1992; Wegener, Petty, Smoak, & Fabrigar, 2004). As such, it is essential to estimate a network model that captures the individual’s moment-to-moment changes of attitudes.
To better capture the individual’s attitude structure, the focus lies on single-subject time-series analysis (Brandt & Williams, 2007; Bringmann, 2016; Molenaar, 1985; Walls & Schafer, 2006). By measuring a set of variables at multiple moments in time, it is possible to estimate how variables interact over a period in time (i.e., contemporaneous associations). By estimating such
contemporaneous associations through a vector autoregressive (VAR) model, it becomes possible to represent the contemporaneous associations a network model (Wild et al., 2010). In such contemporaneous network models, the nodes represent the variables and the edges represent
contemporaneous associations between those variables, highlighting potential causal relationships (Van Borkulo et al., 2014). The network structure reveals the individual’s dynamical dependencies structure (i.e., how variables interact over time). Similarly, contemporaneous network models may be applied on individual’s moment-to-moment changes in attitudes. Such network models would be able to capture the individual’s attitude structure (i.e., how evaluative reactions interact over time), but also allow for investigating of attitudes as a complex dynamical system of interacting evaluative reactions (Wild et al., 2010). This makes contemporaneous network models a
promising tool for investigating individual’s attitude structure and attitude dynamics. Assuming that contemporaneous network models are a valid methodology to analyze individual’s attitude structure, we expect explain the following process in attitude dynamics.
Attitude Formation
The process of attitude formation explains how attitudes take shape and why specific attitudes came to exist. The topic of attitude formation plays an important role in attitude dynamics (e.g., elaboration leads to attitudes which are more resistant to change). However there much debate about the processes underlying attitude formation (Monroe & Read, 2008; van Overwalle & Siebler, 2005). The network approach may provide a possible explanation of the process underlying attitude formation. By analyzing the network structure (i.e., how nodes are connected with each other) it is possible to reconstruct how the network evolved over time (i.e., different ways of adding nodes/edges leads to different classes of network structures; e.g., Barbasi & Albert, 1999; Newman 2001).
Previous research found that the attitude networks resembles a small-world structure (Delage et al., 2016). Nodes of similar evaluative reactions (e.g., ‘friendly’, ‘honest’) are highly interconnected in so called ‘clusters’ and these clusters are only connected by a few edges. From network theory, the formation of such clustered small-world structures is commonly explained by preferential attachment (e.g., Barbasi & Albert, 1999; Newman 2001). Preferential attachment
explains the formation of ‘clusters’ by means of a tendency that new nodes are more likely to connect to highly connected nodes than to sparsely connected nodes (see Figure 4). When looking at attitude networks, preferential attachment implies that newly formed evaluative reactions are more likely to connect with highly connected evaluative reactions (i.e., evaluations which have predictive in before) then with sparsely connected evaluative reactions (i.e., evaluations which have rarely been predictive before). If the same mechanism underlies the process of attitude formation, there should be a relationship between the moment when evaluative reactions are formed, and their influence on the global attitude (i.e., centrality); the earlier formed, the
greater the centrality. Interestingly, the primacy effect suggests a similar mechanism is happening in attitude formation. According to the primacy effect, early presented information will have the strongest effect on people’s attitudes (Lingle & Ostrom, 1981; Sherman, Zehner, Johnson, & Hirt, 1983). This suggests that early formed nodes will have a more central role in the attitude networks then later formed nodes. This shows that new evaluations have a tendency to ‘bind’ to those evaluations which already been predictive before (i.e., earlier evaluations are likely to be predictive before). Given the small-world structure of attitude networks and the primacy effect in attitude formation, we hypothesize that attitude formation reflects the process of preferential attachment. Expecting a negative relation between the moment when evaluations are formed and the centrality (i.e., importance) in the attitude network: the earlier an evaluation is formed, the more central the node in the network.
Figure 4: Illustration of preferential attachment in attitude networks. New evaluations (nodes) are more likely to connect with evaluations, which already have many connections with other evaluations. Therefore, the attitude networks will become more clustered around a few central evaluations.
Attitude Change
Attitude vary in the degree to which they change over time (Erber, Hodges, & Wilson, 1995). The concepts of attitude strength (e.g., Krosnick & Petty, 1995) and attitude involvement (e.g., van der Maas, Kolstein, & van der Pligt, 2003) are commonly used to describe the variability in attitude change. Interestingly, both concepts describe dynamics which are typical for the dynamics of high and low connected networks (see Figure 3).
Strong attitudes are found to be resistant to change and stable to daily fluctuations (e.g., Krosnick & Petty, 1995). In network models, these dynamics are explained with high network connectivity (see Figure 3). Highly connected networks are resistant to change and stable to minor fluctuations. On the other hand, weak attitudes are found to be susceptible to change and fluctuate to daily experiences (e.g., Krosnick & Petty, 1995). In network models, these dynamics are explained by low network connectivity (see Figure 3). In low connected networks, nodes change independently of each other, making them susceptible to change and fluctuate to random changes (van Nes & Scheffer, 2005).
High involvement is found to result in more extreme attitude change (van der Maas, Kolstein, & van der Pligt, 2003; see Figure 2). In network models, these dynamics are explained by high network connectivity. In highly connected networks, the system will have so called ‘tipping point’, at which the system can flip to an alternative state. Because of this, highly
connected networks typically switch between alternative stable states (van Nes & Scheffer, 2005; Scheffer, 2012). Furthermore, low involvement is found to result in moderate attitude change. In network models, similar dynamics are explained by low network connectivity. In low connected networks change independently of each other, causing a more gradual change across time (See Figure 3).
Given these similarity, we hypothesize that attitude change can be characterized by network connectivity: expecting that attitudes will change more in an all-or-none fashion (i.e., either no change or extreme change) when connectivity increases.
Overview present study
The goal of this study is to examine individual’s attitude dynamics from a dynamical network perspective. First, we present the longitudinal study to measure individual’s moment-to-moment changes in attitude. Second, we derive individual attitude networks from individual’s moment-to-moment changes in attitude. Third, we will analyze each network on centrality and attitude formation. Here, we expect to find a negative relation between the moment when
evaluations are formed and the centrality in the attitude network. Fourth, we will analyze each network on network connectivity and attitude change. Here, we expect to find a positive relation between network connectivity and the likelihood that attitude will change according to the all-or-none attitude fashion (i.e., either no change or extreme change).
Method Participants
A total of 49 undergraduate students from the University of Amsterdam (51% female) participated in this longitudinal study. All participants were recruited from the university testing laboratory and received study points as a reward. The study was conducted on a computer at the laboratory of the University of Amsterdam.
Design and procedure
Over the course of two days, participants watched the complete documentary-series Making a Murderer (Abad-Santos and Lopez, 2016). At fixed times, the series was paused and participants were asked to fill out questionnaires concerning their attitude towards the main character of the series. At six times, participants were asked to rate which evaluative reactions were suitable to evaluate the main character. At 69 times, participants were asked to rate their attitude towards the main character. Only evaluative reactions rated as suitable were used to measure participant’s attitude. After completing the series, a follow-up was conducted. In the follow-up, participants were presented with counter-attitudinal information about the main character. After this information, participants were asked to rate their attitude towards the main character again. The complete study took approximately 12 hours, divided over two sessions of six hours.
Manipulations.
Series. To manipulate moment-to-moment changes in attitude, participants watched the
complete documentary-series Making a Murderer (Abad-Santos and Lopez, 2016). The series describes the true crime story of Steven Avery (i.e., the main character), a man who was found guilty of murder and rape of a young woman. At the beginning of the series, all the evidence
points the guilt of the main character, but as the series unfolds, it seems possible that he is wrongfully convicted for murder (i.e., he might be framed by the police). During the series, viewers may hold different attitudes towards the main character; at one moment you might belief that he is a murderer, while at another moment you might belief he is innocent. This makes it suitable for manipulating moment-to-moment changes in attitude. The series was presented on a PowerPoint presentation, each slide presenting a consecutive fragment of the series.
Follow-up. To manipulate additional attitude change, participants were presented with
counter-attitudinal information at the end of the series. Counter-attitudinal information was aimed at changing participant’s attitude towards the main character. The counter-attitudinal information consisted of positive (i.e., evidence showing he is innocent) or negative (i.e., evidence showing he is guilty) information about the main character. Depending on participant’s belief that the main character was guilty/innocent, they would receive different information: (a) if
participants believed that the main character was innocent, they would receive negative
information; (b) if participants believed the main character was guilty, they positive information. The counter-attitudinal information was presented on qualtrics.
Measurements
Attitude dynamics were measured with three questionnaires: (a) A questionnaire measuring participant’s attitude towards the main character. (b) A questionnaire measuring participant’s attitude formation of the main character. (c) A questionnaire measuring participant’s belief of guilt of the main character. All items are translations from the original Dutch items and presented in qualtrics.
Attitude. For measuring the attitude towards the main character, participants rated a
subset of 16 items measuring their evaluative beliefs and evaluative feelings towards the main character. Items measuring evaluative beliefs consisted of 10 semantic contrast pair items (e.g., ‘I find the main character... ‘Naïve-Clever’, ‘Friendly-Unfriendly’, ‘Honest-Dishonest’ and
‘Intelligent-Stupid’, ‘Kind-Aggressive’, ‘Elegant-Blunt’, ‘Attractive-Ugly’,
‘Modest-Presumptuous’). Items were rated by placing a marker on a line between the contrast pairs. Items were scaled by measuring the distance from the left border of the line to the placed marker, ranging from (0) ‘naïve’ to (200) ‘wise’. Items measuring evaluative feelings consisted of six items (e.g., ‘To which degree, did you experienced the following feelings toward the main character ... ‘Anger’, ‘Disgust’, ‘Sympathy’ , ‘Pity’, ‘Hope’, ‘Distrust’). Items were rated by placing a marker on a line, ranging from (0) ‘not at all’ to (100) ‘to a very high degree’. Items were scaled by measuring the distance from the left border of the line to the placed marker, ranging from (0) ‘not at all’ to (100) ‘to a very high degree’.
Global attitude measure. To get a global attitude measure, a composite of the mean for
items measuring evaluative beliefs and evaluative feelings was used.
Attitude extremity. Attitude extremity was measured in two ways: (a) by taking the absolute
distance of the global attitude measure from the center of the scale (100), (b) by taking the standardized distance (z-score) between the global attitude measure during the follow-up, and the mean global attitude during the series.
Attitude formation. For measuring attitude formation, participants rated 16 multiple choice
items measuring which evaluative reactions can be used to describe the main character (‘Which of the following evaluative dimensions, you think, are relevant to describe the main character?... ‘Naïve-Clever’, ‘Friendly-Unfriendly’, ‘Honest-Dishonest’, ‘Intelligent-Stupid’, ‘Kind-Aggressive’, ‘Elegant-Blunt’, ‘Attractive-Ugly’, ‘Modest-Presumptuous’, ‘Anger’, ‘Disgust’, ‘Sympathy’ , ‘Pity’, ‘Hope’, ‘Distrust’ ). Items were rated on a 3-point scale (‘Yes’ (1), ‘I don’t know’ (2) and ‘No’ (3)). Items were scaled by taking the time when rated with ‘Yes’, ranging from (1) ‘first measurement’ to (6) ‘sixth measurement’.
Belief of Guilt. For measuring respondent’s belief of guilt, respondents rated one item
measuring the belief that the main character was guilty of the murder (‘to which degree do you think the main character is guilty of the murder?’). Items were rated by placing a marker on a line, ranging from (0) ‘Guilty’ to (200) ‘Innocent’. The item was rated by measuring the distance from the left border of the line to the placed marker, ranging from (0) ‘Guilty’ to (200) ‘Innocent’. Assuming a belief of guilt when scoring lower then 100, assuming a belief of innocence when scoring higher than 100.
Network Estimation
Attitude networks were estimated by analyzing the partial contemporaneous associations between evaluative items over time. Contemporaneous association are estimated by linear
regressing variables at time t, with variables at the same time t. If two evaluative items are likely to activate at the same time, they will have high contemporaneous associations. If two evaluative items are unlikely to activate at the same time, they will have low contemporaneous associations. To model these contemporaneous associations in a network structure, we estimated a graphical VAR model on each individual’s longitudinal data. By setting regression coefficients and entries in the concentration matrix to zero, it enables for a structural VAR model of the contemporaneous associations between variables (Wild et al., 2010). In doing so, the contemporaneous associations can be visualized in a network. In a graphical VAR model, the nodes represent the variables (i.e., beliefs and feelings), and the edges represent the partial contemporaneous associations between those variables. The direction of the contemporaneous association is represented with the color of the edge; a positive association is visualized as a green edge; a negative association is visualized as a red edge. The strength of the contemporaneous association is represented with the edge saturation; the weaker the contemporaneous association, the more saturated the edge color. When two variables are independent of each other, no edge is drawn between the two variables (Epskamp, Cramer, Waldrop, Schmittmann, & Borsboom, 2012). To correct for spurious
relationships, the network models were estimated through LASSO estimation in combination with the Extended Bayesian information criterion (EBIC; Rothman, Levina & Zhu, 2010). The LASSO method estimates a range of possible networks; ranging from densely connected
(spurious) networks, to sparsely connected (conservative) networks. From this range of possible networks, the EBIC selects the best fitting network. In doing so, the LASSO method selects the best fitting network model. Furthermore, the VAR models assumes stationary of the data (i.e., mean and variance do not change over time). Since our data was not stationary, we transformed the data by taking the difference scores between consecutive measures (Box, Jenkins & Reinsel, 1994).
Analysis
First, we tested for the hypothesis of preferential attachment, analyzing attitude formation and node centrality. Second, we tested for the hypothesis that attitude change is characterized by network connectivity, analyzing attitude extremity and network connectivity.
Analysis 1: attitude formation and node centrality. We hypothesized that attitude
formation reflects the process of preferential attachment: expecting to find a negative association between the node centrality (i.e., importance) and attitude formation (i.e., the moment when evaluative reactions are formed). Node centrality was analyzed by taking the degree centralities for every network. We then compared each node’s degree centrality with its attitude formation.
Centrality analysis. For each network, we estimated the node’s degree centrality. Degree
centrality is a function of the number of neighbors a given node has and of the weights of the edges between the given node and its neighbors (Freeman, 1978). Thus, degree centrality refers to how strongly a given node is directly connected to all other nodes in the network.
Centrality and attitude formation. For the analysis of preferential attachment, we tested
attitude formation (i.e., time when rated as relevant). Expecting a negative correlation between degree centrality and attitude formation.
Analysis 2: attitude change and network connectivity. We hypothesize that attitude
change is characterized by network connectivity: expecting to find more all-or-none attitude change (i.e., either no change or extreme change) when connectivity increases. All-or-none attitude change in attitude was measured by taking the attitude extremity. Network connectivity
was measured by taking the Average Shortest Path Length (ASPL; West, 1996).
Connectivity analysis. For each network, we measured the network connectivity by
calculating the ASPL. ASPL is defined as the average number of steps along the shortest paths for all possible pairs of nodes. Dijkstra’s algorithm was used to calculate the shortest paths for all possible pairs of nodes, the algorithm minimizes the inverse of the distance between two given nodes using the weight of the edges (Dijkstra, 1959). A low ASPL indicates high network
connectivity. A high ASPL indicates low network connectivity. In the case of unconnected nodes, the infinite path lengths were replaced by the maximum path length of the network.
Connectivity and attitude extremity. For the analysis that attitude change is
characterized by network connectivity, we tested the Spearman’s rank correlation
coefficient between each network’s connectivity and the network’s corresponding attitude extremity at the follow-up: expecting a negative correlation between ASPL and attitude extremity.
Software
All analyses were conducted in R (CRAN, 2013). R-package graphicalVAR was used to estimate the individual attitude networks (Epskamp, 2015). R-package qgraph was used to analyze the individual attitude networks (Epskamp, 2012).
Results
The results-section will be organized as follows: In the first part, we present an overview of the data (e.g., how does the attitude behave in time). In the second part, we present the result of the preferential attachment hypothesis. In the third part, we present the results of the attitude change hypothesis.
Data
Six of the 49 participants (12%) were excluded from the dataset because they did not complete the study as intended. This resulted in a final dataset of 43 respondents. For 6
respondents, 18 items failed to capture any dynamics across time (i.e., consecutively scoring the same value for more than 25% of the measures). These items were removed from the dataset.
Attitude. The average trend in evaluative beliefs and feelings is plotted in Figure 5. We
can see that evaluations of similar valence show similar trends (e.g., if positive evaluations increase, other positive evaluations increase), and evaluations of different valence show opposite trends (e.g., if positive evaluations increase, negative evaluations decrease). During the series (i.e., before counter-attitudinal information), participants hold a positive attitude towards the main character (𝑀 = 116.19; 𝑆𝐷 = 42.62). At the follow-up (i.e., after counter-attitudinal information), participants hold a more negative attitude towards the main character (𝑀 = 91.08; 𝑆𝐷 = 42.62). This indicates that counter-attitudinal information changed participant’s attitude towards the main character.
Attitude extremity. Figure 5 shows the frequency distribution of participant’s attitude
extremity at the follow-up. Looking at absolute attitude extremity (left distribution), we find a global attitude measure with the center of scale at the follow-up (M = 45.32; SD = 17.05). Looking at standardized attitude extremity (right distribution), taking the z-score of attitude at the follow-up (M = 1.68; SD = .79).
Attitude formation. Table 2 and Figure 6 gives the descriptive statistics of the time when
evaluations were rated as relevant. Most evaluations were rated relevant at the beginning of the series. Also, evaluative beliefs were more regularly selected as relevant then evaluative feelings.
Variable Mean score (series) Mean score (follow up) Absolute difference Evaluative beliefs: Witty 95.04 93.93 1.11 Friendly 134.27 90.07 44.20 Honest 139.10 84.27 55.63 Intelligent 67.51 65.41 2.10 Gentle 129.01 77.41 51.67 Compassionate 115.42 80.88 34.54 Elegant 60.31 41.43 18.87 Attractive 53.92 37.65 16.27 Strong 137.26 133.27 3.99 Evaluative feelings: Anger 60.32 79.18 18.86 Disgust 66.32 103.00 36.68 Sympathy 128.80 91.70 37.11 Pity 136.76 104.50 32.25 Distrust 87.04 131.40 44.36 Global attitude 116.19 91.08 34.26 Belief guilt 173.12 92.63 80.49
Table 1: The averages in evaluative beliefs and feelings, before (series) and after (follow-up) the counter-attitudinal information (follow-up). Absolute differences gives the differences between the series and the follow-up.
Figure 5: The trend in means of the variables through time. The top figure represents the average trends of the evaluative beliefs. The bottom image represents the average trends of the evaluative feelings. The follow-up measurements are in the shaded grey area.
Figure 6: Frequency histograms of the moments that items are rated as relevant. The blue colored histograms are the beliefs, the red colored histograms are the feelings.
Variable Frequency Moment Median Total (of 43) 1 2 3 4 5 6 Witty 6 22 3 3 0 0 2 35 Friendly 34 4 3 1 0 0 1 42 Honest 22 12 1 2 1 0 1 38 Intelligent 10 12 11 0 0 0 2 35 Gentle 28 8 3 1 0 0 1 40 Compassionate 11 6 7 6 2 3 3 35 Elegant 12 13 2 2 1 0 2 30 Attractive 15 2 2 2 3 0 1 24 Strong 21 5 7 4 1 0 1 38 Anger 0 6 1 2 3 6 4.5 18 Disgust 1 14 0 0 1 5 2 21 Sympathy 33 3 1 0 0 0 1 37 Pity 30 2 4 0 0 0 1 36 Distrust 9 11 3 2 2 1 2 28 Total (cumm%) 233 (51%) 120 (77%) 48 (88%) 25 (94%) 14 (97%) 14 (100%) - 454
Table 2: Table of the descriptive of the moments evaluative items were rated as relevant. Analysis 1: Attitude Formation and Degree Centrality.
Centrality. The descriptive statistics of the degree centrality are given in Table 3 and
plotted in Figure 7. On average, evaluative feelings have a higher degree centrality (Mdn = .54) than evaluative beliefs (Mdn = .15) W = 11720, p < .001, 95% CI [.35, .22]. This indicates that
evaluative feelings play a more central role in respondent’s attitudes than evaluative beliefs. Comparing evaluative beliefs, we find that ‘honest’ has the highest degree centrality (Mdn = .35) compared with average evaluative beliefs W = 8151, p < .001, 95% CI [.08, .28]. This indicates that evaluative belief honest plays a central role in most individual’s attitudes towards the main character. This high degree centrality of belief ‘honest’ is in line with the topic of the series. Whether you belief that the main chracter is honest/lying eventually decides whether you think that the main character is a murderer or not. As such, it is no surprise that this belief plays such a central role on people’s attitude
Example. To illustrate degree centrality, we plotted a network with high degree centrality for
evaluative belief ‘friendliness’ (Degree centrality = 1.04, left network Figure 8), and a network with low degree centrality for evaluative belief ‘friendliness’ (Degree centrality = 0.01, right network Figure 8). For the network with high degree centrality, evaluative belief friendly is a strong indicator of other evaluative reactions in the attitude network; node “friendly” has many connections with
other nodes. This indicates that this individual’s attitude is strongly influenced by whether he/she judges the main character as friendly. Persuading on the belief of friendliness would likely change his/her attitude towards the main character. For the network with low degree centrality, we can see that evaluative belief friendly is a poor indicator of other evaluative reactions in the attitude network (i.e., node “friendly” has few connections with other nodes). This indicates that this individual’s attitude is weakly influenced by whether he/she judges the main character as friendly. Persuading on the belief of friendliness would unlikely change his/her attitude towards the main character.
Centrality and attitude formation. We found no negative correlation between time
relevant and degree centrality, r(43) = 0.02, p = 0.49. None of the 43 networks showed significant correlations between time relevance and degree centrality. Against our expectations, there was no relationship between the moment a node was formed into the network, and the centrality in the network. This indicates there is no evidence for the process of preferential attachment in individual attitude networks.
Variable Unconnected Mean Quantiles
(25%-50%-75%) Extremes Min (<0) -Max
Q1 Q2 Q3 Beliefs Witty 15 0.12 0.00 0.00 0.25 >.01 - 1.00 Friendly 8 0.33 0.03 0.19 0.60 >.01 - 1.04 Honest 1 0.46 0.15 0.34 0.79 0.02 - 1.20 Intelligent 6 0.20 0.01 0.10 0.22 >.01 - 1.06 Gentle 3 0.34 0.06 0.27 0.56 >.01 - 1.20 Compassionate 5 0.26 0.03 0.13 0.40 >.01 - 1.20 Elegant 6 0.22 0.03 0.12 0.34 .02 - 0.92 Attractive 11 0.20 0.00 0.03 0.36 .03 - 0.91 Strong 13 0.19 0.00 0.08 0.32 .02 - 1.09 Feelings Anger 0 0.70 0.50 0.67 0.92 .19 - 1.31 Disgust 0 0.66 0.51 0.66 0.79 .08 - 1.28 Sympathy 1 0.51 0.28 0.55 0.70 .02 - 1.19 Pity 4 0.46 0.11 0.49 0.72 .02 - 1.09 Distrust 1 0.44 0.22 0.37 0.66 >.01 - 1.14
Figure 7: The degree distributions of the contemporaneous networks. The blue bars indicate the evaluative beliefs. The red bars indicate the evaluative feelings.
Figure 8: Visualization of individual attitude networks with high and low degree centrality on friendliness. The left network (id26) represents the attitude network with high degree centrality on friendliness. Right (id21): network with low degree centrality on friendliness. Evaluative reaction of friendliness node is represented with ‘Frien’ in the networks.
Analysis 2: Attitude Change and Network Connectivity.
Network connectivity of individual attitude networks indicates how strongly the evaluative reactions are interconnected. To illustrate, we plotted a network with high network
connectivity (𝐴𝑆𝑃𝐿𝐼𝐷9 = 12.00, right network Figure 9) and a network with low network connectivity
(𝐴𝑆𝑃𝐿𝐼𝐷14 = 342.09, left network Figure 9). For the high connected network, we see that evaluative
reactions are highly interconnected with each other (e.g., many connections between nodes). Change in a single evaluative reaction would likely effect the whole attitude of this individual. For the low connected network, we see that evaluative reactions are weakly interconnected with each other (e.g., less connections between nodes). Change in a single evaluative reaction would not affect the whole attitude of this individual. We compared the two individuals on their global attitude across time (see Figure 10). It seems that the two individuals differ in stability; the highly connected network shows more stable global attitude across time than the low connected network. The role of network connectivity on attitude dynamics (e.g., attitude change) will be discussed in more detail below.
Attitude extremity and network connectivity. In Figure 11, we plotted the association
between network connectivity and attitude extremity at the follow-up. Against our expectations, we did not find any relationship between network connectivity and attitude extremity. This indicates that network connectivity of the individual attitude networks did not influence individual’s attitude change.
Figure 9: Visualization of individual attitude networks with high and low network connectivity. The left network represents an individual network with high network connectivity (ASPLid9= 12.00). The right network represents an individual network with low network connectivity (ASPLid14 = 342.09).
Figure 10: The global attitude score across time for individual with high and low network connectivity. The left figure represents trend for the individual with a high connected network. The right figure represents trend for the individual with a low connected network.
Figure 11: The relationship between network connectivity and attitude change. The red scatterplot is the absolute attitude extremity. The blue scatterplot is the standardized attitude extremity.
Discussion
This study is the first, to our knowledge, that derived individual attitude networks from individual’s time series data. By modelling individual’s moment-to-moment fluctuations of evaluative reactions in a network model, the network structure reveals the individual’s attitude structure. This makes the individual attitude networks a promising tool for investigating individual differences in attitude structure. Furthermore, the network approach enables us to form testable predictions of attitude dynamics using properties of the attitude itself (i.e., attitude structure). This makes individual attitude networks a promising tool for investigating individual attitude dynamics. In line with this reasoning we hypothesized that individual’s attitude structure, characterized by the network structure, reveals theprocess underlying attitude formation and attitude change. Although networks varied strongly among individuals, we found no associations between individual’s network structure and the process of attitude formation and attitude change, thus rejecting our hypothesis.
Detailed discussion of the results.
Analysis 1: attitude formation and centrality. The hypothesis that attitude formation
reflects the process of preferential attachment was not confirmed. There was no association between attitude formation and network centrality (i.e., no correlation between the moment when evaluations were formed and degree centrality).
We found that most evaluations were formed at the first or second measurement (Figure 6). This means that attitude formation happened very rapidly. To illustrate, after the first video fragment, which took about one minute, most participants already believed the main character was ‘friendly’ and ‘gentle’, and felt ‘pity’ towards the main character. This rapid attitude formation was quite unexpected. Based on the first two video fragments, viewers should know little about the main character (e.g., his personality, his role in the series). A possible explanation for this rapid attitude formation is that information in the first video fragments might be highly suggestive. It has been documented that people rapidly form attitudes when early presented information are seen as highly for the future attitude object (Fazio, Lenn, Effrein, 1984).
Interestingly, it was found that evaluative feelings have a higher degree centrality than evaluative beliefs. This indicates that, for most participants, evaluative feelings play a more central role in their attitudes then evaluative beliefs. Interestingly, these findings are in line with empirical findings. Is has been documented that evaluative feelings are more influential to the global
attitude then evaluative beliefs (Farley & Stasson, 2003). Furthermore, it was found evaluative feelings have a bigger impact on attitude behavior then evaluative beliefs (Breckler & Wiggins, 1991; Lavine et al., 1998; Farley & Stasson, 2003). This might suggest that degree centrality might provide an explanation why some evaluations are more influential than others (i.e., compared with a sparsely connected node, activation from a highly connected node causes more activation to the total network). For future research it might be interesting to investigate the association between degree centrality and impact on attitude behavior.
Analysis 2: attitude change and network connectivity. The hypothesis that attitude
change is influenced by network robustness was not confirmed. We found no relationship between network connectivity and the attitude extremity. There was no increased all-or-none fashion in attitude change when connectivity increased. This was unexpected, what was
problematic was that almost all participants changed their attitude in a similar fashion. As such, we have little variance in the data.
When looking at the results in figure 11, there seems to be a pattern worth mentioning. For the networks with high connectivity (ASPL/N < 5), we see a small subgroup of individuals which show extremely big attitude change (Z-scores > 3). It seems that, for higher network connectivity, some individuals ‘jump’ to the extreme, while others remain moderate. However, given the small sample size it is difficult to draw any conclusion from this pattern in the data.
Another interesting finding can be seen in figure 10. From this we can see that, as expected, the highly connected network remains stable across time (resistant to random fluctuations), while the low connected network fluctuates easily across time (susceptible to random fluctuations). This points to the fact that network connectivity influences the stability of attitudes across time. For future research it might be interesting to investigate the association network connectivity and stability across time.
Limitations and recommendations. First, we did not capture the moment-to-moment
formation of evaluations. Most evaluations were already formed after the first and second measurement. This indicates that the measurement of attitude formation were to ‘slow’ to fully capture process of attitude formation. In future research, the time-intervals between the measurements should be shortened.
Second, the study had limitations in manipulating attitude change. Counter-attitudinal information was to strong, that almost all participant’s changed their attitude in a similar fashion (i.e., from very positive to negative). It would be more informative to have higher variance in attitude change (e.g., some participants did not change their attitude, while other change highly in
their attitude). In future studies, it would be better to make the counter-attitudinal information less extreme (present with less information). It could also be possible to make different categories of counter-attitudinal information, ranging from very strong counter-attitudinal information, to very weak counter-attitudinal information. This way, create a greater spread in the data.
Thirdly, this study had limitations concerning comparability of attitude dynamics between individuals. Individuals selected different sets of evaluative reactions in their networks. As such, networks differed in size and content. This differences makes comparing difficult. In future research, it would be better to provide each individual with similar sets of evaluate reactions. Or force them to select a fixed amount of evaluative reactions. This makes comparing way easier.
Conclusion. This study is the first, to our knowledge, that derived individual attitude
networks from individual’s time series data. By modeling the moment-to-moment changes between evaluative reactions in network model, we capture the individual’s attitude structure in a network model. Such networks provide a more realistic representation of the mechanics
underlying attitude dynamics then current models. It not only gives a better representation of attitudes, it also opens up a new range of analyses and research questions to investigate attitude dynamics. This makes the individual attitude networks a promising tool to investigate attitude dynamics and attitude structure.
Literature
Abad-Santos, A. and Lopez, G. (2016). Netflix's Making a Murderer: the case of Steven Avery, explained. [online] Vox. Available at: http://www.vox.com/2016/1/8/10734268/netflix-making-a-murderer-avery [Accessed 3 Apr. 2016].
Barabási, A. L., & Albert, R. (1999). Emergence of scaling in random networks. Science, 286(5439), 509-512.
Box JEP, Jenkins GM, Reinsel GC (1994) Time series analysis: Forecasting and control. Englewood Cliffs, NJ: Prentice Hall.
Brandt, P. T., & Williams, J. T. (2007). Multiple time series models (No. 148). Sage.
Breckler, S. J., & Wiggins, E. C. (1991). Cognitive responses in persuasion: Affective and evaluative determinants. Journal of Experimental Social Psychology, 27(2), 180-200.
Bringmann, L. F., Pe, M. L., Vissers, N., Ceulemans, E., Borsboom, D., Vanpaemel, W., ... & Kuppens, P. (2016). Assessing temporal emotion dynamics using
networks. Assessment, 23(4), 425-435.
Chaiken, S. (1987). The heuristic model of persuasion. In M. P. Zanna, J. M. Olson, & C. P. Herman (Eds.), Social influence: the ontario symposium (Vol. 5, pp. 3-39).
Chaiken, S., & Eagly, A. H. (1989). Heuristic and systematic information processing within and. Unintended thought, 212, 212-252.
Cooke, J., & Zeeman, E. C. (1976). A clock and wavefront model for control of the number of repeated structures during animal morphogenesis. Journal of theoretical biology, 58(2), 455-476.
Cramer, A. O., van Borkulo, C. D., Giltay, E. J., van der Maas, H. L., Kendler, K. S., Scheffer, M., & Borsboom, D. (2016). Major Depression as a Complex Dynamic System. PLoS One, 11(12), e0167490.
Dalege, J., Borsboom, D., van Harreveld, F., van den Berg, H., Conner, M., & van der Maas, H. L. (2015). Toward a formalized account of attitudes: The Causal Attitude Network (CAN) model.
Dijkstra, E. W. (1959). A note on two problems in connexion with graphs. Numerische mathematik, 1(1), 269-271.
Dunne, J. A., Williams, R. J., & Martinez, N. D. (2002). Network structure and biodiversity loss in food webs: robustness increases with connectance. Ecology letters, 5(4), 558-567.
Eagly, A. H., & Chaiken, S. (1993). The psychology of attitudes. Harcourt Brace Jovanovich College Publishers.
Epskamp, S. (2015). graphicalVAR: Graphical VAR for Experience Sampling Data. R package version 0.1, 3.
Epskamp, S., Cramer, A. O., Waldorp, L. J., Schmittmann, V. D., & Borsboom, D. (2012). qgraph: Network visualizations of relationships in psychometric data. Journal of Statistical Software, 48(4), 1-18.
Erber, M. W., Hodges, S. D., & Wilson, T. D. (1995). Attitude strength, attitude stability, and the effects of analyzing reasons. Attitude strength: Antecedents and consequences, 433-454.
Farley, S. D., & Stasson, M. F. (2003). Relative influences of affect and cognition on behavior: Are feelings more related to blood donation intentions?. Experimental Psychology, 50(1), 55.
Fazio, R. H., Lenn, T. M., & Effrein, E. A. (1984). Spontaneous attitude formation. Social Cognition, 2(3), 217-234.
Flay, B. R. (1978). Catastrophe theory in social psychology: Some applications to attitudes and social behavior. Systems Research and Behavioral Science, 23(4), 335-350.
Freeman, L. C. (1978). Centrality in social networks conceptual clarification. Social networks, 1(3), 215-239.
Haugtvedt, C. P., Petty, R. E., & Cacioppo, J. T. (1992). Need for cognition and advertising: Understanding the role of personality variables in consumer behavior. Journal of Consumer Psychology, 1(3), 239-260.
Haugtvedt, C. P., & Wegener, D. T. (1994). Message order effects in persuasion: An attitude strength perspective. Journal of Consumer Research, 21(1), 205-218.
Himmelfarb, S., & Youngblood, J. (1969). Effects of factual information on creating resistance to emotional appeals. Psychonomic Science, 14(6), 267-269.
Huskinson, T. L., & Haddock, G. (2004). Individual differences in attitude structure: Variance in the chronic reliance on affective and cognitive information. Journal of Experimental Social Psychology, 40(1), 82-90.
Krosnick, J. A., & Petty, R. E. (1995). Attitude strength: An overview. Attitude strength: Antecedents and consequences, 1, 1-24.
Latané, B., & Nowak, A. (1994). Attitudes as catastrophes: from dimensions to categories with increasing involvement.
Lavine, H., Huff, J. W., Wagner, S. H., & Sweeney, D. (1998). The moderating influence of attitude strength on the susceptibility to context effects in attitude surveys. Journal of Personality and Social Psychology, 75(2), 359.
Lewan, P. C., & Stotland, E. (1961). The effects of prior information on susceptibility to an emotional appeal. The Journal of Abnormal and Social Psychology, 62(2), 450.
Lingle, J. H., & Ostrom, T. M. (1981). Principles of memory and cognition in attitude formation. Cognitive responses in persuasion, 399-420.
Lingle, J. H., & Ostrom, T. M. (1979). Retrieval selectivity in memory based impression judgments. Journal of Personality and Social Psychology, 37, 189-194.
Mitchell, M. (2006). Complex systems: Network thinking. Artificial Intelligence, 170(18), 1194-1212.
Molenaar, P. C. (1985). A dynamic factor model for the analysis of multivariate time series. Psychometrika, 50(2), 181-202.
Monroe, B. M., & Read, S. J. (2008). A general connectionist model of attitude structure and change: The ACS (Attitudes as Constraint Satisfaction) model. Psychological Review, 115(3), 733.
Newman, M. E. (2001). Clustering and preferential attachment in growing networks. Physical review E, 64(2), 025102.
Newman, M., Barabasi, A. L., & Watts, D. J. (2011). The structure and dynamics of networks. Princeton University Press.
Petty, R. E., & Cacioppo, J. T. (1986). The elaboration likelihood model of persuasion. In Communication and persuasion (pp. 1-24). Springer New York.
Petty, R. E., Cacioppo, J. T., & Goldman, R. (1981). Personal involvement as a determinant of argument-based persuasion. Journal of personality and social psychology, 41(5), 847.
Petty, D. T. W. R. E., & Fabrigar, N. D. S. L. R. (2004). Multiple routes to resisting attitude change. Resistance and persuasion, 13.
Rothman, A. J., Levina, E., & Zhu, J. (2010). Sparse multivariate regression with covariance estimation. Journal of Computational and Graphical Statistics, 19(4), 947-962.
Shakarchi, C. P. H. R. J., & Liu, B. M. S. K. (2004). Consumer Psychology and Attitude Change. Resistance and Persuasion, 283.
Scheffer, M., Bascompte, J., Brock, W. A., Brovkin, V., Carpenter, S. R., Dakos, V,. &
Sugihara, G. (2009). Early-warning signals for critical transitions. Nature, 461(7260), 53-59.
Scheffer, M., Carpenter, S. R., Lenton, T. M., Bascompte, J., Brock, W., Dakos, V.,& Pascual, M. (2012). Anticipating critical transitions. Science, 338(6105), 344-348.
Sherman, S. J., Zehner, K. S., Johnson, J., & Hirt, E. R. (1983). Social explanation: The role of timing, set, and recall on subjective likelihood estimates. Journal of Personality and Social Psychology, 44(6), 1127.
Tesser, A., & Achee, J. (1994). Aggression, love, conformity, and other social psychological catastrophes.
Van Borkulo, C. D., Borsboom, D., Epskamp, S., Blanken, T. F., Boschloo, L., Schoevers, R. A., & Waldorp, L. J. (2014). A new method for constructing networks from binary
data. Scientific reports, 4, 5918.
Van der Maas, H. L., Kolstein, R., & Van Der Pligt, J. (2003). Sudden transitions in attitudes. Sociological Methods & Research, 32(2), 125-152.
van Nes, E. H., & Scheffer, M. (2005). Implications of spatial heterogeneity for catastrophic regime shifts in ecosystems. Ecology, 86(7), 1797-1807.
Van Overwalle, F., & Siebler, F. (2005). A connectionist model of attitude formation and change. Personality and Social Psychology Review, 9(3), 231-274.
Walls, T. A., & Schafer, J. L. (2006). Models for intensive longitudinal data. Oxford University Press.
West, M. (1996). Bayesian forecasting. John Wiley & Sons, Inc.
Zimbardo, P. G., & Leippe, M. R. (1991). The psychology of attitude change and social influence. Mcgraw-Hill Book Company.
