Are Trustworthiness and Legitimacy ‘Hard to Win, Easy to Lose’? A Longitudinal Test of the Asymmetry Thesis of Police-Citizen Contact

Test the asymmetry thesis of police-citizen contact that police trustworthiness and legitimacy are affected more by negative than by positive experiences of interactions with legal agents by analyzing changes in attitudes towards the police after an encounter with the police. Test whether prior attitudes moderate the impact of contact on changes in attitudes towards the police. A two-wave panel survey of a nationally representative sample of Australian adults measured people’s beliefs about police trustworthiness (procedural fairness and effectiveness), their duty to obey the police, their contact with the police between the two waves, and their evaluation of those encounters in terms of process and outcome. Analysis is carried out using autoregressive structural equation modeling and latent moderated structural models. The association between both process and outcome evaluation of police-citizen encounters and changes in attitudes towards the police is asymmetrical for trust in police effectiveness, symmetrical for trust in procedural fairness, and asymmetrical (in the opposite direction expected) for duty to obey the police. Little evidence of heterogeneity in the association between encounters and trust in procedural fairness and duty to obey, but prior levels of perceived effectiveness moderate the association between outcome evaluation and changes in trust in police effectiveness. The association between police-citizen encounters and attitudes towards the police may not be as asymmetrical as previously thought, particularly for changes in trust in procedural fairness and legitimacy. Policy implications include considering public-police interactions as ‘teachable moments’ and potential sources for enhancing police trustworthiness and legitimacy.

1 3 et al. 2016 ;Slocum 2018;Tyler 2017;Tyler and Fagan 2008). But even these studies either excluded people without recent experience with police from the analysis or excluded such individuals from the design itself (surveying only people with recent experience with the police). As a result, they could not compare attitudinal changes among individuals influenced by well-and poorly-handled encounters with the police with individuals who had had no contact whatsoever. Given the centrality of police-citizen contact to policing policy and research, this is a surprising gap in the literature that needs to be filled.
In this paper we present the first longitudinal test of the asymmetry thesis of policecitizen contact. Drawing on data from a two-wave panel study of Australian citizens, 1 we provide the most complete empirical assessment of the asymmetry thesis that has hitherto been attempted. On the one hand, we break down key constructs into a number of dimensions related to perceived police trustworthiness (differentiating between trust in police procedural fairness and trust in police effectiveness) and normatively grounded sense of duty to obey (legitimacy). On the other hand, we fit two complementary statistical models to (a) test the asymmetry thesis of police-citizen contact using longitudinal data and (b) assess whether prior levels of attitudes towards legal authorities moderate the impact of contact on changes in trustworthiness and legitimacy.
The remainder of the paper proceeds as follows. First, we clarify the concepts of trustworthiness and legitimacy in the context of public attitudes towards legal authority. This is an important preliminary step, because there has been a good deal of recent debate over these concepts and how they should be measured (Bottoms and Tankebe 2012;Hamm et al. 2017;Jackson 2018;Jackson and Bradford 2019;Jackson and Gau 2015;Trinkner 2019;Tyler and Jackson 2014). Second, we review evidence from cross-sectional surveys that assessed the impact of police-citizen encounters on attitudes towards the police. Third, we review evidence from panel studies. Fourth, we identify the gaps in the literature and how our study extends research in the field. Fifth, we present the methods and results of our study. Finally, our conclusions focus on the implications of our findings as well as future directions for research in this important area of criminological debate.

Clarifying Concepts: Trustworthiness and Legitimacy in Police-Citizen Relations
Studies of public attitudes towards the police often employ concepts loosely related to police effectiveness and procedural fairness. Previous studies have called them (1) perceived fairness and perceived effectiveness, (2) public confidence in policing, (3) trust in the police, (4) trust in procedural justice and trust in police effectiveness, and (5) legitimacy (differentiating between procedural justice, distributive justice, effectiveness and lawfulness). For example, procedural justice theory specifies that perceived fairness and perceived effectiveness are potential sources of legitimacy (Sunshine and Tyler 2003), while Tankebe (2013) assumes that they are constituent components of legitimacy (for discussion, see Jackson and Bradford 2019;Trinkner 2019;Sun et al. 2019). In our view, the most important conceptual distinction is between (a) task-specific public evaluations and expectations of police conduct (e.g., people's perceptions of the effectiveness and fairness of officers) that we call 'perceived trustworthiness', ascribed states and qualities that mean that they can be trusted to do what they are expected to do (cf. Hardin 1996) and (b) judgements about the legitimacy of the police (the belief that police have a valid claim to exercise power and therefore have the authority to enforce the law and dictate appropriate behavior).
Perceived trustworthiness relates to the core characteristics and actions of the police that lead them to be more or less trusted to do the things that they are tasked to do (under conditions of uncertainty). Two key dimensions of police conduct are fairness (particularly in relation to process) and effectiveness (particularly in relation to the outcomes police produce). When citizens have positive evaluations and expectations that officers treat people with respect and dignity, make neutral, transparent and accountable decisions; and when citizens have positive evaluations and expectations that officers turn up quickly in emergencies, deter crime, and catch criminals, those citizens will be more likely to act in ways that manifest a willingness to assume risk and be vulnerable. While prior studies might have employed concepts such as confidence, trust, and perceived police fairness and effectiveness, we premise that they are all referring to the perceived trustworthiness of police. 2 That being said, we will use expressions such as 'trust in procedural fairness' and 'trust in police effectiveness' throughout the paper to keep the prose crisp-the reader should be clear that we are referring to the perceived trustworthiness of police here.
We test the asymmetry thesis using panel data in regard not only to trust in police fairness and effectiveness, but also to perceptions of police legitimacy. Legitimacy is the overarching judgment regarding the institution's credible, or otherwise, claim to exercise power (appropriateness) and govern citizen behavior (entitlement). So while public assessments of police fairness and effectiveness relate to positive and negative evaluations and expectations regarding whether officers can be trusted to do what they are tasked to do-where one or both of these might be important sources of legitimacy-legitimacy relates to the ascription of appropriateness and entitlement by citizens to the institution that officers represent. Appropriateness judgements (perceived right to power) are sometimes operationalized as institutional trust, or confidence, or normative alignment, while entitlement judgements (perceived right to dictate appropriate behavior) are invariably operationalized as felt obligation to obey. We focus in the current study on obligation to obey police, since the survey did not measure the other constituent component of legitimacy, namely appropriateness judgements. 2 We are not implying that perceived trustworthiness of police is a second-order latent construct reflected by constructs such as trust in procedural fairness and trust in police effectiveness. These are separate constructs, both theoretically and empirically -as we demonstrate in Appendix A.1. We use 'trustworthiness' as an alternative label to 'perception', i.e. rather than call people's attitudes towards the procedural fairness and effectiveness of the police as 'perceived procedural fairness' and 'perceived effectiveness', we treat them as the extent to which police are seemed as trustworthy in the context of acting in procedurally just and effective ways.

Evidence from Cross-Sectional Surveys
It was Skogan (2006) who first popularized the idea of asymmetry in the impact of policecitizen encounters on public attitudes. 3 On the one hand, people who have had a 'bad' recent police-citizen encounter tend to have more negative attitudes towards the police, compared to people with no recent experience. On the other hand, people who have had a 'good' recent police-citizen encounter are either no different in their attitudes, or only slightly more positive, compared to people with no recent experience. Skogan (2012) speculated that negativity bias may be at play here (for reviews of the psychological literature, see Baumeister et al. 2001;Rosin and Soyzman 2001). People may more readily attend to-and learn more powerful lessons from-negative experiences, either dismissing good experiences as exceptions to the norm, or treating good service as a given. Whether or not this is correct, if teachable moments only count when they go against the police, then the implications for policing policy are not very optimistic-as Skogan (2006, p. 119) says: "The empirical message is unfortunately: 'You can't win, you can just cut your losses'." Yet, according to procedural justice theory police can improve matters by acting in fair and respectful ways, making neutral, accountable and transparent decisions, conveying trustworthy motives, and allowing citizens a voice in their interactions with officers. If it is only procedural injustice that counts, then this is a major challenge to the theory.
In the first test of the asymmetry thesis, Skogan (2006) drew on data from eight crosssectional surveys-telephone surveys in Chicago (2003), City of Indianapolis (1996), New York City (2002), St Petersburg, Florida (1997), Seattle (2003 and Washington DC (1999 and2000), and face-to-face surveys in England and Wales (1992) and St Petersburg, Russian Federation (2003). Skogan fitted a series of linear models to estimate the partial association between contact (whether people had come into contact with the police recently and if they did, whether they were satisfied or dissatisfied with the officer or officers) and confidence in police (attitudes towards the effectiveness and public engagement of the police). 4 Conceptualizing evaluations of the police along a single dimension, public opinion was measured as a uni-dimensional construct, ranging from negative views to positive views towards the police.
Distinguishing between police-initiated encounters and citizen-initiated encountersand controlling for various socio-demographic factors in the modeling- Skogan (2006) found that people with a negatively-received recent contact were, on average, much less confident in the police (i.e. they tended to believe that officers were ineffective and did not engage properly with their community) compared to people without any recent contact. Strikingly, however, people with a positively-received recent contact were only slightly more confident in the police (on average) compared to people without recent contact. While the statistical effect of police-initiated contact was a little more asymmetric than citizen-initiated contact (i.e., the difference between positively-and negatively-received contact was a little bigger for citizen-initiated contact), Skogan inferred from the analysis 1 3 of the eight surveys that negatively experienced contact may reduce confidence, while positively experienced contact may at best only weakly improve confidence. 5 An alternative approach is to break public attitudes down into a number of core constituent parts. Bradford et al.'s (2009) face-to-face survey of Londoners (fielded in 2005 and 2006) focused on perceived police trustworthiness and differentiated between: (a) perceived effectiveness at fighting crime and meeting the needs of victims; (b) perceived fairness when interacting with citizens (procedural and distributive fairness); and (c) perceived engagement with the community. They found that asymmetry was present in the statistical effect of contact on perceptions of police effectiveness, but the statistical effects were more symmetrical for perceptions of police fairness and community engagement. 6 Considering that Skogan's measures focused on effectiveness rather than fairness, this may partly explain the difference in findings (although both studies included measures of community engagement). Like Skogan (2006), Bradford et al. (2009) found greater asymmetry in police-initiated contact compared to citizen-initiated contact.
Overall, similar results have been found in a number of different studies in the US and UK (Bradford 2017;Bradford et al. 2009;Jackson et al. 2012Jackson et al. , 2013Rengifo et al. 2019;Skogan 2006;Slocum 2018;Trinkner et al. 2018). People who have had unsatisfactory interactions with legal officials tend to have less positive attitudes towards the police than people with satisfactory interactions. There are two slight complications. First, the distinction between police-and public-initiated encounters seems to be important. When the focus is on police stops or invasive and involuntary interactions, the relationship between contact and attitudes seems to be strongly asymmetrical, but when the focus is on voluntary citizen-initiated interactions, the relationship seems more symmetrical. When citizens initiate an interaction, police behavior could at least slightly boost perceived trustworthiness and legitimacy. Second, unpacking the concept of perceived trustworthiness seems to make some difference. While police-citizen encounters appear to have a strong asymmetrical relationship with trust in police effectiveness, slightly more symmetrical relations are found in terms of trust in police fairness (Bradford 2017;Bradford et al. 2009;Jackson et al. 2012Jackson et al. , 2013. Yet, and this is the launch-pad for the current study, cross-sectional studies do not take the all-important temporal ordering into account. The asymmetry thesis is a theory of change, in that it predicts shifts in people's attitudes caused by positively-received and/ or negatively-received police-citizen contact. People's prior levels of perceived police trustworthiness and legitimacy could play a key role, but cross-sectional surveys cannot take into account people's previous attitudes into account. They cannot assess whether encounters are indeed associated with change. Skogan (2012) suggests that people might have already formed ideas about the police before they come into contact with them, thus bringing 'priors' into any interactions, and that the "path towards untangling the impact of prior expectations would be to gather over-time or panel data" (2012, p. 276). It could, for example, be the case that respondents with more negative views of the police prior to the encounter tend to be more dissatisfied with the experience, while respondents with more positive views of the police prior to the encounter might expect the encounter to be positive and therefore discount such experience. What, we believe, is actually at stake in the debate regarding contact and public attitudes towards the police is the extent to which there is an association between interactions with legal officials and changes in public opinion. In order to assess whether police-citizen encounters are associated with changes in attitudes towards the police, panel studies are necessary.

Evidence from Panel Studies
A number of panel studies have in fact addressed the link between contact and attitudes towards the police. But, crucially, not a single study has assessed whether the impact of perceived quality of police behavior during police-citizen encounters on changes in trustworthiness and legitimacy is the same for satisfactory and unsatisfactory interactions in comparison with no contact.
There are two groups of panel studies that focused on the relationship between perceived police behavior and public opinion about legal institutions 7 : (a) those that model change in public opinion but exclude from the analysis respondents with no contact with police, so they did not test the asymmetry thesis because they could not compare positive and negative encounters with no contact (Bradford et al. 2014;Gau 2010;Rosenbaum et al. 2005;Sargeant et al. 2018;Tyler 2017;Tyler and Fagan 2008); those that included all respondents in the analysis, thus providing some basis for the assessment of the asymmetry thesis, but did not model change in opinion (Slocum et al. 2016;Slocum and Wiley 2018;Tyler and Fagan 2008).
Among studies in the first group, the most common empirical strategy involves drawing on data from two-wave panel surveys, with researchers analyzing only respondents who had contact with police between waves 1 and 2. Often fitting autoregressive models (wherein one includes a lagged dependent variable as one of the covariates), such studies account for changes in attitudes towards legal institutions. However, by excluding respondents with no contact, they are not able to assess whether the impact of encounters is asymmetrical. One of the first studies to rely on panel data, Rosenbaum et al. (2005) rely on the high coefficients of lagged response variables to suggest that public attitudes towards the police are highly stable over time. The authors also speculate that a negative predisposition may simply cause someone to selectively interpret encounters with the police as more negative (Rosenbaum et al. 2005, p. 359). A similar conclusion was reached by 7 There are of course a number of longitudinal studies that focused on the development of attitudes towards the police and the law over time, especially drawing on data from the Pathways to Desistance (Mulvey 2016). However, these studies do not focus on the link between perceived quality of police behavior during contact and changes in attitudes towards the police. Some studies focused on changes in legal attitudes over time and did not include information regarding police-citizen encounters (Kaiser and Reisig 2019;Piquero et al., 2005;Schubert et al., 2016), whereas others investigated the legal socialization process while taking into account previous arrests (Augustyn, 2016;Fine et al., 2016;Fine et al., 2017) and whether respondents had been picked up by the police (Fine and Cauffman, 2015;McLean et al., 2018) -but none of them engaged in comparisons of expected changes in attitudes between respondents who satisfactory, unsatisfactory, and no police contact.
1 3 Sargeant et al. (2018) using a similar analytic strategy. Drawing on panel data, the authors assessed whether pre-existing defiant attitudes shaped citizens' satisfaction with police-citizen encounters in Australia and concluded that respondents who were more defiant toward police before their contact with police were less likely to be satisfied with the process of their police interaction.
Another two-wave study that modeled changes in attitudes towards the police after dropping respondents with no contact with police between waves 1 and 2 was Tyler and Fagan's (2008) panel survey of New York City residents. The authors sought to disentangle the effect of process (specifically, citizen perceptions of the fairness of treatment and decisionmaking) from the effect of outcome (specifically, citizen perceptions of the favorability of the outcome) on perceived police legitimacy (measured using indicators of obligation, trust and confidence, and identification with the police). While their findings suggest that satisfaction with process is far more important than outcome favorability in shaping changes in perceived legitimacy, they do not speak to a potential symmetry in the impact of contact.
As examples of the second group of studies, Tyler and Fagan's (2008) second set of analyses included all respondents and attempted to test the asymmetry thesis by comparing levels of perceived legitimacy at Time 2 with quality of contact, but did not include respondents' prior levels of legitimacy. Comparing levels of trustworthiness or perceived legitimacy between people who had positive and negative contact with people with no contact, but without taking into account people's prior attitudes towards the police, was also the strategy employed by Slocum et al. (2016) and Slocum and Wiley (2018). While their goal was not to assess asymmetry in the impact of police-citizen encounters, they grouped respondents based on their satisfaction with contact and used respondents with no policeinitiated contact as the reference group-but the focus was not on change in public opinion from before to after the encounter.
To our knowledge, only one study has modeled changes in public opinion and compared perceived quality of police contact with a group of people with no contact. Drawing on data from a two-wave panel using a sample of 16 neighborhoods in England, Myhill and Bradford (2012) grouped respondents on the basis of 'type of contact' they had between wave 1 and wave 2. They then modeled changes in trust in police effectiveness by fitting autoregressive linear regression models. Results indicate a somewhat symmetrical relationship between citizen-initiated contact and trustworthiness, but a strong asymmetrical relationship both in terms of satisfaction with police stops and contact after being a victim of a crime. Unfortunately, Myhill and Bradford only had measures related to perceived police effectiveness. So they could not model changes in other psychological constructs such as trust in procedural fairness and judgements about the legitimacy of the police.

Summary and Literature Gap
It seems on the basis of extant evidence that: (a) the association between trust in police effectiveness and satisfaction with the encounter is more asymmetrical than it would be for police fairness (Bradford et al. 2009); (b) people evaluate their encounters with legal officials in terms of process and outcome as two distinct dimensions (Bradford et al. 2014;Tyler and Fagan 2008); and (c) the impact of involuntary police-initiated contact is more asymmetrical than self-initiated contact (Jackson et al. 2012;Myhill and Bradford 2012). In this study, we extend the literature by presenting what is, to our knowledge, the first longitudinal test of the asymmetry thesis using a relatively comprehensive set of trustworthiness and legitimacy measures-i.e. we analyze whether police-citizen encounters are associated with changes in satisfaction with police when compared to respondents who did not experience contact between two waves of data.
The current study advances previous work in a number of ways. We model no contact, good contact, neutral contact, and bad contact as predictors of change in public attitudes towards the police (considering two waves of data, lagged dependent variable models are fitted considering police-citizen encounters that happened between wave 1 and wave 2). Public attitudes are measured as perceived police trustworthiness (which is disaggregated into effectiveness and procedural fairness) and judgements about police legitimacy (as represented by respondents' normatively grounded duty to obey the police). Perceived quality of police-citizen encounters ('good', 'neutral', or 'bad') is measured as evaluations of both the procedural fairness enacted by the officer and the outcome favorability. We rely on two complementary statistical models to: (a) test the asymmetry thesis; and (b) assess the extent to which previous levels of police trustworthiness and legitimacy moderate the impact of different police-citizen encounters on changes in attitudes.
The asymmetry thesis posits that the impact of unsatisfactory encounters is stronger in magnitude than the impact of satisfactory encounters on attitudes towards the police. If this is true, when 'no contact' is the reference group the absolute value of the (expectedly negative) coefficient of 'negative' contact will be greater than the absolute value of the (expectedly positive) coefficient of 'positive' contact. We test this hypothesis in relation to (1) trust in procedural fairness, (2) trust in police effectiveness, and (3) duty to obey the police, while disentangling contact evaluation between process (A) and outcome (B). A diagram displaying all the theorized relations being tested can be found in Fig. 1. For each response and explanatory variable, we examine the predicted values of attitudes controlling for prior attitudes and in comparison with people with no contact with police during the relevant period.
• Hypothesis 1A: the association between process evaluation and trust in procedural fairness is asymmetrical. • Hypothesis 1B: the association between outcome evaluation and trust in procedural fairness is asymmetrical. • Hypothesis 2A: the association between process evaluation and trust in police effectiveness is asymmetrical. • Hypothesis 2B: the association between outcome evaluation and trust in police effectiveness is asymmetrical. • Hypothesis 3A: the association between process evaluation and duty to obey the police is asymmetrical. • Hypothesis 3B: the association between outcome evaluation and duty to obey the police is asymmetrical.
Additionally, we draw on Skogan's (2012) discussion that people might bring 'priors' that could influence how they perceive an encounter. If people perceive the quality of police behavior during an encounter differently, based on expectations formed from prior attiudes (Sargeant et al. 2018), then the impact of police-citizen encounters could vary conditional on those prior attitudes. Based on procedural justice theory, however, we would expect that the impact of perceived quality of police behavior during encounters on changes in public opinion would be broadly the same regardless of one's prior levels of perceived police trustworthiness and legitimacy. If this were not the case then the change in attitudes predicted by theory-based on evaluations of process fairness which vary across encounterswould be much less likely to occur.
In order to assess this further, a second group of hypotheses was established. A second theorized diagram can be found in Fig. 2. Each hypothesis relates to a potential interaction effect between perceived quality of police contact and attitudes towards the police before such encounter took place while predicting changes in attitudes after the encounter. If the interaction effect is different from zero, that means that prior levels of perceived police trustworthiness and/or legitimacy moderate the impact of contact on changes in public opinion-the effect would thus be heterogeneous, i.e. different for people with different Theorized diagram: is the impact of police-citizen contact moderated by prior attitudes?. Note: Three models were fitted based on this theorized diagram, one checking for heterogeneity effects on changes in trust in procedural fairness (hypotheses 4A and 4B), one for changes in trust in police effectiveness (hypotheses 5A and 5B), and one for changes in duty to obey (hypotheses 6A and 6B) levels of prior attitudes. Again, we test this hypothesis in relation to trust in procedural fairness (4), trust in police effectiveness (5), and duty to obey the police (6) while disentangling contact evaluation between process (A) and outcome (B).
• Hypothesis 4A: homogeneous effect of process evaluation on changes in trust in procedural fairness (i.e., interaction term is zero). • Hypothesis 4B: homogeneous effect of outcome evaluation on changes in trust in procedural fairness (i.e., interaction term is zero). • Hypothesis 5A: homogeneous effect of process evaluation on changes in trust in police effectiveness (i.e., interaction term is zero). • Hypothesis 5B: homogeneous effect of outcome evaluation on changes in trust in police effectiveness (i.e., interaction term is zero). • Hypothesis 6A: homogeneous effect of process evaluation on changes in duty to obey the police (i.e., interaction term is zero). • Hypothesis 6B: homogeneous effect of outcome evaluation on changes in duty to obey the police (i.e., interaction term is zero).

Data
To assess the linkages between public encounters with the police and attitudes towards legal authorities, we draw on both waves of data from The Crime, Safety and Policing in Australia Survey (Murphy et al. 2010a, b). In 2007, a nationally representative mail survey of adults in Australia was conducted on the extent of respondents' experiences and beliefs about crime and policing in their community. Participants were drawn from Australia's publicly available electoral roll. All electors aged 18 + in Australia are required by law to register their name and home address on the roll; the roll thus consists of a representative subject pool. Selection was stratified by State and Territory jurisdiction. 5700 residents were sent a survey booklet by mail-after several reminders and weeks, an adjusted response rate of 40% was achieved (n = 2120). Two years later, a follow-up panel survey was undertaken in 2009 aiming to examine whether attitudes and experiences of crime and policing had changed over the two-year intervening period. After a series of reminders, a total of 1190 usable responses were returned. Considering the adjusted response rate (for respondents who had died or moved address between waves 1 and 2), an attrition rate of 35% was achieved. 8 Some 46% of the respondents in the final sample were male, 52% had post-secondary education; respondents were on average 54 years of age in 2007 and had an average selfreported household income of approximately AUD$80,000. Using the 2006 Australian Census data as a benchmark, we conclude that older and more educated respondents in the sample were slightly over-represented, but overall the sample was largely representative of the Australian population. For instance, 49% of the population are male, 46% had postsecondary education, and the average household income is approximately AUD$54,000.

Measures and Measurement Model
Following previous work (Bradford et al. 2009;Jackson et al. 2012) we unpack perceived trustworthiness into trust in procedural fairness and trust in police effectiveness. We also consider one part of people's judgements about the legitimacy of the police: namely, a normatively grounded sense of duty to obey the police. All questions were measured on a fivepoint Likert scale ranging from "strongly disagree" to "strongly agree" (except the indicator of perceived police effectiveness, which ranges from "very poor job" to "very good job"). The exact wording for each question asked, their assigned latent construct, and their descriptive statistics can be found in Table 1.
Unless otherwise mentioned, all measures were coded in such way that higher values indicate more positive evaluations of the construct measured. In order to assess the scaling properties and empirical distinctiveness of our measures, we use confirmatory factor analysis (CFA) with categorical (ordinal) indicators, focusing on the two components of trust and felt duty to obey the police commands. As expected, questions tap into the three theorized constructs sensibly, indicating that our empirical indicators can be empirically distinguished in the three premised dimensions. A full analysis of the empirical distinctiveness of the three latent constructs and their equivalence across waves can be found in the Appendix (A.1 and A.2, respectively).

Measuring Attitudes Towards Encounters with the Police
Most previous work on the impact of police contact on perceived trustworthiness assumed a single dimension of satisfaction with the encounter. Skogan (2006), for instance, used six questions evaluating respondents' perceived politeness, helpfulness, and fairness of police officers to create an indicator of positive versus negative encounter. In the same vein, Slocum et al. (2016) asked respondents the extent to which they were satisfied with the encounter and created an indicator with three groups-dissatisfied, neutral, or satisfied with the encounter. However, there might be more than one underlying dimension of contact evaluation, and we distinguish between respondents' perceived fairness in the procedures used in the contact and their satisfaction with the outcome's favorability (Bradford et al. 2014;Tyler and Fagan 2008).
In the wave 2 survey, respondents were asked how many times they had contact with police in the previous 12 months. Some 38% ( n = 440 ) of wave 2 respondents had at least one encounter (i.e., encounters that happened at some point in between the first and the second waves of data collection)-57% of those contacts were citizen-initiated, while 43% were police-initiated (mostly involving some type of police stop). The sub-sample of respondents who did experience an encounter with the legal officials at some point in between waves 1 and 2 were further asked five follow-up questions evaluating the process and four follow-up questions evaluating the outcome favorability of such encounter-these questions can be found in Table 1.
In order to confirm that process and outcome evaluations are indeed empirically distinguishable as suggested in the procedural justice literature, we first use CFA to assess the scaling properties of the nine indicators simultaneously. Considering only the 440 respondents who experienced at least one encounter with the police between waves 1 and 2, we fit two models with one and two factors and all indicators set as categorical. Despite being correlated (r = 0.66), the two theorized dimensions-process and outcome evaluationsseem to be empirically distinguishable given that the two-factor solution has the best model fit. We then fit a third two-factor CFA model after dropping one of the questions measuring process evaluation as it was weakly correlated with the latent construct 9 -we thus use four questions to measure process evaluation and four questions to measure outcome evaluation in all subsequent analyses. Standardized factor loadings, model fit statistics, and a full account of the measurement models can be found in the Appendix A.3. After confirming that we can treat process and outcome evaluations as two distinct constructs, for each dimension we need to somehow classify respondents' most recent encounter with the police as positive or negative, so that their scores for trustworthiness and legitimacy can be compared with the scores of the respondents who did not have any recent contact with police. One solution for that is handpicking the 'positive' and 'negative' categories based on responses on the Likert scale. However, cutoff decisions for this formative approach are arbitrary. Instead, we adopt a data-driven approach and fit latent class models on items concerning respondents' evaluation of their most recent encounter regarding both process and outcome. This approach is preferable as it permits the modeling of unobserved heterogeneity underlying the two dimensions of contact evaluation (see Na et al. 2015;Nylund et al. 2007).
For each process evaluation and outcome evaluation, we fit three models with two, three, and four latent classes. In both cases, the three-class solution emerged as the preferred solution-see details on deciding the number of classes in the Appendix A.4. Roughly, the three classes indicate negative, neutral, and positively experienced contact with police. Our interpretation is that these classes represent encounters that went 'worse than expected' (negative), 'as expected' (neutral-note that this category includes encounters rated 'OK'), or 'better than expected' (positive). It is important to be clear what we mean here. Considering that Australia is by and large a high-trust country (see Table 1; see also Hinds and Murphy, 2007), we assume that expectations of the behavior of officials who represent key institutions in society are broadly positive. Most people expect to be treated relatively well by police officers, and for police to achieve positive outcomes more often than not. Encounters that go 'OK' are therefore experienced as 'neutral', since that is what is expected. It is only when they are better than expected that the experience shifts into the positive. Given this assumption, it is not surprising that the second class-the 'neutral' group, when encounters go as expected-is composed of respondents who mostly answered "agree" with the statements (as opposed most pertinently to "strongly agree" to every question posed to them). By contrast, an encounter with police wherein respondents classify most of the indicators as anything lower than the fourth point in the Likert scale (e.g., "neither agree nor disagree" with a given statement, or worse) we assume to indicate a negative (i.e., worse than expected) contact, since 'neither/nor' indicates at best uncertainty about whether police behaved in line with expectation. Mostly ticking the fifth point to answer the questions (i.e., "strongly agree") would indicate an encounter that went better than expected (i.e., positive)-see results in probability scale in Figs. 1 and 2.

Analytical Strategy
In order to assess the relationship between police-citizen encounters and public attitudes toward the police, we use a similar strategy as the one commonly found in the literaturei.e. we compare positive, neutral, and negative encounters with the group of respondents who did not experience contact with police as the baseline category. Unlike almost all previous studies, however, we now focus on changes in attitudes towards the police over time, and distinguish perceived quality of police behavior in encounters in terms of process and outcome. We thus fit two autoregressive structural equation models (SEM), one assessing the association between process evaluation and changes in trustworthiness and legitimacy  10 A single model including both process evaluation and outcome evaluation was too computationally intense (e.g. it did not converge). Considering that the two evaluation variables are also regressed on T1 constructs, a single model including both process evaluation and outcome evaluation would entail two multinomial logistic regressions being estimated simultaneously. For the sake of simplicity and clarity, we estimated the two models separately. 11 The inclusion of a lagged dependent variable as a covariate allows for the modeling of change without confounding with regression towards the mean provided that the treatment is applied at some point between t = 1 and t = 2 (Allison, 1990). Even though it was not randomly assigned, the intervention we are modeling (i.e., an encounter with the police) happened between waves 1 and 2. Additionally, we follow Keele and Kelly's (2006, p. 203) advise in that, in this case, it is reasonable to theoretically assume that past levels of perceived police trustworthiness and legitimacy affect current levels of perceived police trustworthiness and legitimacy -and therefore lagged dependent variable models are a good choice.
Based on the theorized diagram shown in Fig. 1, we fit two autoregressive SEMs: (a) one with the four 'contact' groups (i.e., no contact; negative contact; neutral contact; positive contact) indicating process evaluation (testing the hypotheses 1A, 1B, and 1C) and (b) another with the four 'contact' groups indicating outcome evaluation (testing the hypotheses 2A, 2B, and 2C). In both models, all hypotheses are tested keeping the group of respondents who had no encounter with the police between waves 1 and 2 as the reference group-i.e. three dummy variables indicating negative, neutral, and positive contact are displayed. All coefficients are standardized, which allows for comparisons.
Each model includes three aspects of interest. First and foremost, arrows departing from each of three dummies indicating negative, neutral, and positive contact reflect expected changes in attitudes depending on the type of contact with police in relation to people with no contact. This is the crucial aspect of the models and is used to test hypotheses 1A, 2A, 3A, 1B, 2B, and 3B. Second, both models include a set of autoregressive parameters-the arrows departing from attitudes towards the police before an encounter to attitudes after an encounter. Those parameters speak to the stability of the variables-as psychological constructs, perceived police trustworthiness and legitimacy are expected to be highly stable over time. Finally, both models include multinomial logistic paths regressing contact evaluation on T1 measures of trustworthiness and legitimacy. This aspect of the models account for different odds of having an (un)satisfactory contact with police given different prior attitudes. For the multinomial logistic paths only, we use the 'neutral contact' group as the reference category-we are thus estimating the association between prior attitudes and the odds of having a positive or a negative encounter in comparison with a neutral encounter. 12 Both models include age at T1 (difference between 2007 and year of birth), gender (1 = male), and national identity (1 = Australian non-Aboriginal) as control variables.

Results
Estimated parameters of the panel model considering respondents' process evaluation can be found in Fig. 5. The model was estimated on Mplus 7.11 using maximum likelihood with robust standard errors to handle non-normal indicators and full information maximum likelihood to handle missing data. For visual ease, measurement models and covariates are not displayed, and only paths significant at the 5% level are displayed. All displayed coefficients are standardized and therefore comparable.
As expected, all lagged values are statistically significant and yield relatively large coefficients, which speaks to the stability of such psychological constructs over time, as noted by Rosenbaum et al. (2005). Every unit increase in trust in police fairness at T1 is associated with an increase of 0.45 standard deviations in trust in police fairness at T2. Similarly, every unit increase in trust in police effectiveness at T1 is associated with an increase of 0.40 standard deviations in perceived police effectiveness at T2, and the analogous increase in duty to obey yields an increase of 0.35 at T2. This is not surprising: it means that respondents with high levels of trustworthiness and legitimacy at T1 tend to have high levels of trustworthiness and legitimacy at T2-although T2 scores are by no means determined by T1 scores. There was change over time. 12 Odds of no encounter in relation to a neutral contact were also estimated as part of the model, but these are not discussed as they make no substantive sense. A table displaying all estimated coefficients can be found in Appendix A.5.
Results also show that the experience of an encounter with the police is associated with changes in attitudes towards legal authority. Controlling for previous levels of trustworthiness, respondents who had a positive contact experience in terms of process have scores in trust in procedural fairness 0.52 standard deviations higher on average than respondents with no contact; likewise, respondents who had a negative experience of process have scores of 0.26 lower on average. In contrast to the prediction of the asymmetry thesis, contact perceived as better than expected does more than just "cut the losses"-it is associated with an increase in trust in police fairness of a similar magnitude to the association between unsatisfactory contact and (a decrease in) trustworthiness. Table 2 below displays 95% confidence intervals of standardized coefficients, which can be helpful for comparing effect sizes and assessing the asymmetry hypothesis. Not only are both standardized coefficients significantly different from zero, but-in terms of absolute values-there is an overlap between the two confidence intervals, which indeed suggests a similar effect size albeit in opposite directions. In contrast to the prediction of hypothesis 1A, the association between process evaluation and changes in trust in procedural fairness seems to be symmetrical. Similarly, experiencing procedurally fair encounters is associated with somewhat symmetrical changes in perceived police legitimacy. Respondents who had a positive contact encounter have an average change in duty to obey 0.72 standard deviations higher than respondents with no contact, while respondents who had a negative encounter have an average change of 0.20 standard deviations lower than those with no contact. The absolute values in both confidence intervals do not overlap, meaning that the effect size of satisfactory encounters is greater than the effect size of unsatisfactory encounters. In terms of changes in judgements about the legitimacy of the police, the impact of police-citizen encounters resembles hypothesis 3A as it appears to be asymmetrical-but in the opposite direction as originally suggested by the asymmetry thesis: positive contact is more strongly associated with changes in one's normative duty to obey the police than negative contact.
Finally, changes in trust in police effectiveness are the closest to Skogan's (2006) original results, though not as asymmetrical as originally expected. While respondents who experienced a negative encounter with the police process-wise have predicted scores of trust in police effectiveness 0.32 lower than those with no contact, having experienced a positive encounter is not associated with positive changes in trust in police effectiveness. As predicted by hypothesis 2A, the impact of police-citizen encounters is somewhat asymmetrical when it comes to changes in trust in police effectiveness. The asymmetry thesis seems to be true for changes in people's sense of trust that the police are doing a good job in solving and preventing crime and keeping order.
When it comes to process evaluation of public interactions with the police, then, the relationship between contact and trustworthiness seems very symmetrical when it comes to trust in procedural fairness and asymmetrical when it comes to trust in police effectiveness.
In terms of judgements about the legitimacy of the police, the relationship seems asymmetrical, but in the opposite direction to that predicted by the asymmetry thesis: positive encounters process-wise are more strongly associated with increases in duty to obey than negative encounters are associated with decreases.
Finally, previous levels of trustworthiness and legitimacy are partly associated with the perception of fairness of an encounter. Every unit increase in trust in procedural fairness at T1 is associated with a decrease in the odds of having a negative rather than a neutral encounter by 39% ( ̂= −0.49 , thus an odds ratio of 0.61). Similarly, every unit increase of duty to obey at T1 multiplies the odds of having a positive rather than neutral encounter by 86% ( ̂= 0.62 , thus an odds ratio of 1.86). Finally, every unit-increase of trust in police effectiveness at T1 multiplies the odds of having a positive rather neutral encounter by 61% ( ̂= 0.48 , thus an odds ratio of 1.61). Figure 6 shows the results of the second panel model, now focusing on outcome evaluation. As expected, some of the relationships remain virtually unaltered. All three attitude constructs (i.e. procedural fairness, police effectiveness, and duty to obey the police) are quite stable over time, with regression coefficients for the lagged dependent variables being relatively high. Previous attitudes towards the police are also partly associated with how respondents perceive an encounter in terms of its outcome. The more people feel a sense of duty to obey the police, the more likely it is that they perceive the outcome of an encounter as positive rather than neutral ( ̂= +0.55 , thus an odds ratio of 1.73); and every unit increase in trust in police effectiveness at T1 is associated with a decrease in the odds of having a negative rather than a neutral encounter by 39% ( ̂= −0.4 9, thus an odds ratio of 0.61).
Turning to the association between contact and changes in trustworthiness and legitimacy, results indicate similarities in comparison with the first model in Fig. 5. Not only is negative contact associated with decreases in trust in procedural fairness ( ̂= −0.37 ), but positive contact is also associated with increases ( ̂= +0.27 ). The comparison of effect sizes based on the overlap of absolute values in confidence intervals suggests similar influences from negative and positive contact. Contra hypothesis 1B, the impact of outcome evaluation on changes in trust in procedural fairness seems to be symmetrical.
In terms of changes in trust in police effectiveness, the relationship is as asymmetrical as expected (as per hypothesis 2B): while experiencing a 'bad' contact is associated with a decrease in trust of 0.54 standard deviations, experiencing positive contact is not associated with changes in trust in police effectiveness. Again, in terms of expected effectiveness of the police the relationship between outcome favorability of encounters and trustworthiness is as asymmetrical as Skogan's (2006) original study.
Finally, results indicate outcome favorability is strongly associated with changes in judgements about the legitimacy of the police: respondents who experienced an encounter that went better than expected have an average increase in their scores of duty to obey of 0.58 standard deviations, while those who experienced contact that went 'as expected' (i.e., neutral) have an average decrease in their scores of duty to obey of 0.16 standard deviations. Finally, those who experienced contact that went worse than expected have an average decrease of 0.28. As hypothesis 3B predicted, the relationship between outcome evaluation and changes in perceived police legitimacy is asymmetrical, however in the opposite direction expected-positive contact is more strongly associated with positive changes than negative contact is associated with negative changes.
Together these results show that contact matters. Even considering how stable in time psychological constructs such as trustworthiness and legitimacy are, and taking prior attitudes into account, people's perception of how the police handle an interaction is associated with attitudinal changes. Experiencing procedural fairness is associated with higher values of trustworthiness and legitimacy over time, while experiencing unfairness is associated with lower values. Hence, by: (a) analyzing panel data to account for changes in attitudes as suggested by Skogan (2012) and Tyler and Fagan (2008); (b) unpacking police Standardized coefficients displayed. Measurement models not displayed for visual ease. All T2 latent constructs were regressed on gender, age, and national identity. Only significant paths ( p < 0.05 ) displayed for visual ease. n = 1102. Full model available in the Appendix (A.5) trustworthiness into different dimensions of trust in procedural fairness and police effectiveness and including measures of police legitimacy as suggested by Bradford et al. (2009) and Jackson et al. (2012); (c) considering process and outcome as two different dimensions of contact evaluation as suggested by Tyler and Fagan (2008) and Bradford et al. (2014); and (d) adopting a more appropriate measurement model to account for an unobserved heterogeneity of contact evaluation wherein three rather than two categories emerge-we find some quite strongly symmetrical relationships between police-citizen contact and attitudes towards the police.
Interestingly, prior levels of trust in procedural fairness are associated with how one experiences the process of an interaction with the police, whereas prior levels of trust in police effectiveness and duty to obey the police are associated with how one assesses both the outcome and the process of an interaction. Such associations could challenge our claims that there could be an impact of police-citizen encounters on changes in trustworthiness and legitimacy. In order to investigate this more deeply, we estimated three further statistical models assessing the extent to which prior attitudes towards the police moderate the association between police-citizen encounters and changes in trustworthiness and legitimacy. Skogan (2012) says that people bring 'priors' to bear when they experience contact with the police which "could independently color how they view specific features of an encounter'' (p. 276-see also Jackson and Pósch 2019;Rosenbaum et al. 2005;Sargeant et al. 2018). Although controlling for prior levels of trustworthiness and legitimacy, results displayed in Figs. 5 and 6 do not rule out the possibility that the impact of encounters is different for citizens with different levels of trust and legitimacy before the interaction. Prior attitudes towards legal authority might play an important role in conditioning how fairness is perceived. It could be the case, for instance, that the impact of police-citizen encounters on changes in trustworthiness and legitimacy are actually moderated by citizens' prior attitudes.

Prior Attitudes and the Impact of Police-Citizen Encounters
To properly assess the extent to which prior attitudes moderate the association between contact and attitudinal changes and test the hypotheses displayed in Fig. 2, we concentrate on the sub-sample of respondents who experienced contact with police between waves 1 and 2. An appropriate strategy for this assessment involves fitting statistical models with an interaction term between constructs at T1 and contact evaluation. The empirical strategy of interacting lagged outcome with a treatment variable is particularly common in the context of lagged dependent variable models (Vickers and Altman 2001). Given that we are dealing with latent constructs, we use latent moderated structural modeling (LMS) to analyze how 'priors' that individuals bring when interacting with the police condition the association between encounters and changes in trustworthiness and legitimacy-LMS models allow for interactions between two latent variables. Our analytic strategy involves fitting three separate models: we first interact respondents' scores of trust in procedural fairness at T1 with evaluations regarding both process and outcome concerns (hypotheses 3A and 3B); we then do the same with trust in police effectiveness at T1 (hypotheses 4A and 4B); and finally with duty to obey at T1 (hypotheses 5A and 5B). We can thus evaluate the impact of police-citizen contact on changes in trustworthiness and legitimacy across different levels of prior attitudes and assess whether the association is independent of the 'priors' people bring when interacting with police.

Estimation Strategy
We use LMS to estimate interaction effects between latent variables in one step using maximum likelihood (Klein and Moosbrugger 2000;Muthén and Asparouhov 2012). By design, the means of all latent variables are constrained to be zero. Therefore, for an interaction term between η and ξ, the main effect of η should be interpreted as the statistical effect of η at an average value of ξ. To make sure that all latent constructs reflect what they are supposed to reflect, we use a two-step approach whereby we first estimate the measurement model and then plug-in the estimated factor loadings in an LMS estimation (this procedure is similar in spirit to what is suggest by Bakk and Kuha 2018 in the context of latent class analysis). We fit three two-step LMS models with full information maximum likelihood to handle missing data assessing the moderating role of prior attitudes: model 1 focuses on trust in procedural fairness, model 2 on changes in trust in police effectiveness, and model 3 on changes in duty to obey.

Results
Results of three LMS models fitted on Mplus 7.11 can be found in Figs. 7, 8, and 9. For visual ease, only the structural part of the model was included in the figures; all models control for age, gender, and national identity, but likewise these paths are not displayed. Non-significant coefficients at the 5% level are represented by dashed arrows. Figure 7 shows the results of the first model, testing whether prior levels of trust in procedural fairness moderate the association between process and outcome evaluations and changes in trust in procedural fairness. At an average level of trust in procedural fairness at T1, it is noticeable that while process evaluation is associated with changes in trust in procedural fairness ( ̂= 0.37 ), outcome evaluation has no statistical effect-most likely due to the fact that we are now solely analyzing respondents who did experience contact with police rather than comparing with respondents with no contact.
The focus, however, should be on the interaction terms. The most important finding is their lack of significance, which suggests that the statistical effect of process evaluation on trust in procedural fairness at T2 does not vary by levels of trust in procedural fairness at T1. As predicted by hypothesis 4A, this statistical effect is homogeneous. The association is on average the same for all respondents regardless of their previous levels of trust in police fairness. Inasmuch as previous attitudes towards the police potentially influence people's experiences when interacting with the police, the subsequent impact of such contact-in terms of fairness in the procedures-is homogeneous.
The same conclusion is true for outcome evaluation, as per hypothesis 4B. This is unsurprising given that, in this subgroup analysis, we found no evidence even of a main effect: considering only the sub-sample of respondents who did experience contact with police, the statistical effect of outcome evaluation on changes in trust in procedural fairness (at an average level of trust in procedural fairness at T1) is homogeneously zero. However, outcome evaluation is particularly central when the focus of the analysis is on changes in trust in police effectiveness- Fig. 8 shows the results of the second LMS model. First, note that the exact opposite associations are found now-in this subgroup analysis we find no evidence of an association with process evaluation, but at an average level of trust in police effectiveness at T1 outcome evaluation does have an association with changes in attitudes ( ̂= 0.27 ). The most important aspect of Fig. 8, however, is that it provides evidence for an interaction effect. In terms of outcome evaluation, the impact of police-citizen encounters does not seem to be homogeneous: the statistical effect is different depending on previous levels of trust in police effectiveness (at T1). Unlike our prediction in hypothesis 5B, the interaction term is negative ( ̂= −0.13 ), which means that the impact of police-citizen contact on trust in police effectiveness is lower among respondents with higher prior levels of trust in police effectiveness. The more one expects the police to be effective, the less outcome evaluation seems to make a difference-alternatively, the impact of contact is stronger among respondents with lower levels of trust in police effectiveness.
Finally, Fig. 9 shows the results of the third LMS model. In terms of perceived police legitimacy, only outcome evaluation is associated with changes in duty to obey ( ̂= 0.17 ) at an average level of duty to obey the police at T1. Crucially, the model indicates little evidence of heterogeneity in the association. The fact that both interaction terms are virtually zero suggests that the impacts of both process and outcome evaluations on changes in one's normative duty to obey the police are the same regardless of people's prior levels of perceived police legitimacy, as predicted by hypotheses 6A and 6B.

Discussion
Criminologists have long studied the link between police-citizen encounters and attitudes towards the police. People want decisions to be made in fair ways, especially for invasive police stops where one potential outcome is arrest and entry into the criminal justice system. People also want their concerns to be taken seriously and they want information to be provided when and where relevant. Contact can also be status-challenging and status-reinforcing: the police protect the boundaries of inclusion and exclusion (Waddington 1999) and officer contact contains status-relevant information concerning the citizen-about the moral worth that the officer assigns to them, as well as their position within the social groups the police both represent and partially define. Positive encounters may help to confirm an individual's social standing, while negative encounters may help to undermine this status, resulting in resentment and consequently damaging opinions of the police.
In this paper we considered the idea that the police cannot enhance public trustworthiness and legitimacy through their interactions with the public, they can only damage public opinion. Skogan's (2006) asymmetry thesis posits that people who experience a negative encounter with the police will have lower, on average, opinions of police compared to people who did not experience an encounter, while those who experience a positive encounter with the police will at best have only slightly higher opinions, on average, compared to people who did not experience an encounter. We approached the issue using two-wave panel data and an empirical strategy that models change over time. This involved comparisons between four groups: (a) no contact between waves 1 and 2; (b) contact that went worse than expected (i.e., negative); (c) contact that went as expected (i.e., neutral); and (d) contact that went better than expected (i.e., positive). Autoregressive SEM allowed us to perform what is, to our knowledge, the first panel analysis test of the asymmetry thesis that has considered both trust, as a multi-dimensional construct, and legitimacy. As well as drawing on longitudinal data to empirically test the asymmetry thesis of police-citizen contact, we built on recent advances in the literature and unpacked attitudes towards the police in terms of legitimacy and trustworthiness as separate constructs (Jackson and Gau 2015)-we also distinguished between trustworthiness as perceived police fairness and perceived police effectiveness (Bradford et al. 2009). Moreover, we built on previous work and differentiated between process and outcome evaluations in encounters with the police (Tyler and Fagan 2008). Finally, we extended prior research and developed a new measurement model of contact evaluation that took into account people's expectations about the encounter to consider 'positive' and 'negative' contact in relation to what is expected.
This set of methodological and substantive advances may have made a difference. On the one hand, the results are relatively close to Skogan's (2006) original thesis when it comes it changes in trust in police effectiveness. While we found some symmetry in the association between police-citizen encounters and changes in expectations that the police are effective in delivering their job, negative experiences during contact with police-both in terms of process and outcome-seem to damage trust in police effectiveness to a greater extent than positive experiences seem to boost it. While policing policy might aim for more than just 'cutting losses,' in terms of trust in police effectiveness the relationship between contact and trust does seem to be asymmetrical.
On the other hand, the relationship between police-citizen encounters and changes in trust in procedural fairness does not appear to be as asymmetrical as previously thought. Indeed our results indicate a very symmetrical relationship. Our study suggests that satisfactory encounters could do more than just prevent damages in public trustworthiness in policing: they could potentially improve trust in police. Results are even more striking in terms of changes in duty to obey the police. If anything, the relationship is asymmetrical in the opposite direction: positive contact boosts changes in perceived police legitimacy to a much greater extent than negative contact damages it.
Our findings are therefore significant for the procedural justice field. Procedural justice research was from the beginning based on a symmetry model, whereby authorities could rely on good practice to build their legitimacy (Tyler 1990). Findings from studies testing the 'asymmetry thesis' seemed to imply that good practice would be pointless; concerns were raised that good practice would make little to no difference in gains to legitimacy. Our findings stand in contrast to such concerns and once again highlight the importance of police being both fair and effective. Policing policy should consider that police-citizen encounters do seem to be teachable moments where citizens infer from the behavior of individual police officers the behavior of police in general and update their recognition of legal authority as a rightful authority. Instead of 'cutting their losses', police-citizen interactions could be the base for policy aiming for enhancing perceived police legitimacy.
In order to investigate the relations between police-citizen encounters and changes in trustworthiness and legitimacy more deeply, a second set of analyses was employed. Drawing on the hypothesis that prior attitudes towards legal institutions might influence one's perception of contact with legal authorities, we removed from the analysis respondents who had had no contact with the police between waves 1 and 2 and focused on estimating change over time using a statistical model that allows for the test of heterogeneity in the effects of police-citizen contact (latent moderated structural modeling)-it was possible to assess the extent to which prior attitudes moderate the association between police-citizen encounters and changes in trustworthiness and legitimacy.
This set of analyses included interaction terms between each psychological construct at T1 (i.e., trust in procedural fairness, trust in police effectiveness, and duty to obey the police) and evaluations about the most recent encounter (both for process and outcome) as predictors of the relevant T2 constructs. In terms of trust in police fairness, only process evaluation is associated with change, and there is no evidence of heterogeneity. The statistical effects of contact on changes in trust in police procedural fairness are the same regardless of previous levels of trustworthiness. Contrariwise, in terms of trust in police effectiveness, only outcome evaluation is associated with change. However, we found evidence for heterogeneity-in the opposite direction as originally expected: outcome evaluation is most associated with changes in trust in police effectiveness for people with lower prior levels of trust in police effectiveness. Finally, in terms of perceived police legitimacy, satisfaction with both process and outcome are associated with changes in duty to obey, but we found little evidence of heterogeneity here: police-citizen encounters seem to enhance perceived police legitimacy regardless of people's prior attitudes towards legal authority.
Overall, our results indicate that the influence of police-citizen encounters on attitudes towards the police can be distinguished between the assessments of process fairness and outcome favorability. It seems that when citizens perceive an encounter to be procedurally fair, they will increase their levels of trust in police fairness and duty to obey. When they perceive an encounter to end favorably, they may increase their levels of trust in police effectiveness-depending on the extent to which they believed the police to be trustworthy in fighting crime before contact-and duty to obey.
Limitations should, of course, be acknowledged. First, there could be omitted variable bias, and we are not engaging in causal inference as we did not randomly assign respondents to satisfactory and unsatisfactory encounters. Nor are we claiming any particular identification strategy. More field and laboratory experiments and other quasi-experimental designs that permit the identification of causal effects are needed in this area. Second, it would have been helpful to have more than two waves of data. With three waves of data, for instance, we could test whether the statistical impact of police-citizen encounters is the same at different moments in time, which would clarify the mechanisms of such impact, as well as include random intercepts to properly account for within-and between-individual changes (Hamaker et al. 2015). Third, the findings only pertain to Australia, which can be considered a somewhat specific context. Both attitudes towards the police and perceptions of police-citizen encounters are overall very positive in Australia, which could partly explain the results we found. Perhaps the impact of contact on changes in trustworthiness and legitimacy is as asymmetrical as previously thought in contexts where police confrontations with the public are more common; we would welcome panel studies in other contexts so as to evaluate the dynamics of the relationship between police-citizen encounters and public attitudes towards the police.

Conclusion
To close, our findings have positive implications for policing policy and practice. While we cannot engage in causal inference, it seems there is a robust relationship between positively experienced police-citizen contact and positive changes in public opinion. When citizens perceive police officers to be treating them with dignity and respect, making clear and fair decisions, explaining the reasons for every decision, listening to what they have to say, both the belief that the police are trustworthy and public judgements about the legitimacy of the police increase.
Public support is essential for the good functioning of the criminal justice systemthe police, in particular, rely on public confidence to function effectively . Without public support, police work is costly, difficult, and to some extent ineffective. Boosting positive attitudes towards legal institutions is therefore crucial for policy and practice. What we show in this paper is that interactions between citizens and legal officials do seem to be an important source both for boosting and damaging public attitudes towards legal authorities in a symmetrical fashion.
Consistent with Skogan's (2006) asymmetry thesis, it seems like the positive statistical effect of 'good' contact is slightly weaker in magnitude than the equivalent negative statistical effect of 'bad' contact-but only when it comes to changes in trust in police effectiveness. In terms of changes in trust in police fairness and duty to obey, our findings paint a 'good news' story, at least in terms of the police's ability to improve public trust through their interactions with citizens. It seems that procedural fairness during interactions with the public really can enhance trustworthiness and legitimacy.

Appendix 1: Measuring Public Attitudes Towards the Police: Empirical Distinctiveness Between Latent Constructs
We use confirmatory factor analysis (CFA) to assess the scaling properties of our measures, focusing on the two components of perceived police trustworthiness (trust in procedural fairness and trust in police effectiveness) and one of the components of police legitimacy (a normative duty to obey the police). All indicators are set as categorical (ordinal) and the models are estimated using diagonally weighted least squares. In order to assess the empirical distinctiveness of the three theorized constructs, we estimate three models with one, two, and three factors using only first wave data and compare their fit statistics.
Model fit statistics for the three estimated models can be found in Table 3. The onefactor model tests whether all these indicators could actually be reflecting one overall construct representing some sort of normative compass of attitudes towards the police. The two-factor model tests whether legitimacy and trustworthiness are distinguished from one another, but with no further empirical distinction between trust in procedural fairness and trust in police effectiveness within the trustworthiness construct. Finally, the three-factor model tests whether items tapping into the latent constructs that we name 'trust in procedural fairness, 'trust in police effectiveness', and 'duty to obey the police' are empirically distinguishable as theoretically predicted. Multivariate models like this do not signal whether indicators actually measure constructs as this is a purely theoretical claim (Jackson and Kuha 2016), but they can suggest how well each indicator taps into the theorized constructs. Accordingly, results of Table 3 clearly show that a three-factor model is preferred over the one-and two-factor solutions. The three-factor model is the only one with acceptable fit (RMSEA = [0.058; 0.080], CFI = 0.996, TLI = 0.994; the χ2 test tends to be sensitive to sample size). Results speak to the empirical distinctiveness between items loading onto trust in procedural fairness, trust in police effectiveness, and duty to obey the police. Standardized factor loadings of the three-factor solution can be found in Table 4.

Appendix 2: Measuring Public Attitudes Towards the Police: Measurement Equivalence of Latent Constructs
In order to establish measurement equivalence of latent constructs over time, for each latent construct we fit four two-factor confirmatory factor analysis (considering the latent construct at T1 and T2). The first model (configural equivalence) freely estimates all parameters, with residuals of the same indicators at different time points being allowed to correlate. The second model (weak equivalence) constrains the factor loadings to be the same across time, with residuals of the same indicators at different time points being allowed to correlate. The third model (strong equivalence) constrains both the factor loadings and the intercepts to be the same across time, with residuals of the same indicators at different time points being allowed to correlate. The fourth model (strict equivalence) constraints the factor loadings, the intercepts, and the residuals to be the same across time. We then compare the model fit statistics and perform three likelihood ratio tests to assess whether each further constraint improves upon the less restrictive model.
We perform this test separately for trust in procedural fairness and trust in police effectiveness. Given that there are only two indicators of duty to obey, it is not possible to assess the measurement equivalence for this latent construct. Results of the tests can be found in Table 5.

Appendix 3: Measuring Evaluations of Encounters with the Police: Empirical Distinctiveness Between Latent Constructs
In terms of citizens' evaluations of their most recent encounter with the police that happened at some point between the wave 1 and 2 surveys, nine questions were asked-five tapping into process concerns and four tapping into outcome concerns. Standardized factor loadings and model fit statistics of three CFA models with one, two, and two factors can be found in Table 6. The first model assumes that all nine indicators tap into one single latent construct-something like a general index of satisfaction with contact. The second model assumes that process evaluation and outcome evaluation are two, albeit correlated, separate dimensions of one's attitudes towards their most recent encounter with the police. Finally, the third model has the same assumptions as in the second model but removes one of the indicators which has a low factor loading in the first and second models.
Model fit statistics indicate the two-factor solution as a better-fitted model, 13 signaling that the indicators do seem to be empirically distinguishable as the two theorized dimensions of evaluations about the encounter. Interestingly, albeit demonstrating some empirical distinctiveness between satisfaction with process and satisfaction with outcome, these dimensions are strongly correlated with each other (cov(η1, η2) = 0.64). The fifth indicator of perceived fairness ("You feel you were able to influence the decision made by the police") is poorly correlated with its relevant latent construct ( * 51 = 0.662), so a third model was fitted without this question. While all parameters remained virtually unaltered, model fit statistics demonstrate an improvement. The two separate dimensions of satisfaction with contact with four empirical indicators each were used in subsequent models.

Appendix 4: Measuring Evaluations of Encounters with the Police: Latent Class Analysis
With the goal of classifying respondents' encounters with the police as positive or negative but without handpicking how to define the categories 'positive' and 'negative', we use latent class analysis to assess the underlying structure of people's contact evaluation. For each dimension-process and outcome-we fit latent class models with two, three, and four latent classes and compare their fit statistics. Results of such model fit comparison can be found in Table 7. Considering that the number of classes is usually decided in terms of their information criteria, entropy, and substantive contribution (Nylund et al. 2007), a three-class solution is the one with the best performance both for process and outcome evaluations.
Originally, we were hoping to find two latent classes for each process and outcomeroughly, a group of respondents who thought the encounter was positive and another who thought the encounter was negative. However, information shown in Table 7 makes it clear that the two-class solution does not have an appropriate fit: in both cases, it has the highest BIC and AIC and lowest entropy levels. For satisfaction with outcome favorability, the three-class solution clearly has the best fit (lowest AIC and BIC, highest entropy). When it comes to process evaluation, there are some mixed signals: the three-class solution has a higher entropy, but the four-class solution has lower BIC and AIC levels. Nylund et al. (2007) suggest that substantive contributions are equally, if not more important when deciding on the number of latent classes. Despite some mixed signals from the model fit comparison, from a substantive perspective a three-class solution is more appropriate than a four-class. We therefore adopt three latent classes both for process evaluation and outcome evaluation-which indicate encounters that went negative (i.e., worse than expected), neutral (i.e., as expected), or positive (i.e., better than expected).

Appendix 5: Autoregressive Structural Equation Modeling: Full Models
See Table 8.  Table 9 Latent moderated structural models as presented in Figs Table 9.