Network models of driver behavior

Psychological mechanisms and latent variables in traffic psychology

Consider the above-cited assertion that dimensionality reduction produces insights about psychological mechanisms. This is unlikely, since a mechanistic explanation of a cognitive process involves accounting for the component operations of the process and their interaction (Lappi & Rusanen, 2011; Bechtel, 2008), while PCA and factor analysis are—stated simply—procedures for grouping correlated variables. In fact, offering violation- and error-proneness as explanations for why individuals break rules and commit errors amounts to reified circular reasoning (Boag, 2011) insofar as the “pronenesses” refer to nothing but being likely to behave in said manner. Furthermore, it has been argued that a detailed analysis of psychological mechanisms should precede the generation of psychometric instruments instead of being used as a post hoc explanation for the correlational structure of the instrument in the data analysis stage (Embretson, 1994). When latent variable models have been constructed in this manner, based on theories of cognitive psychology, it has been observed that several psychological mechanisms may contribute to a given latent variable score (Borsboom, Mellenbergh & Van Heerden, 2003; Embretson, 1994).

Further, the individual DBQ errors and violations are of such a wide variety that it is unclear how they could all be implemented by a single cognitive or psychological mechanism. For instance, the errors include missing an observation, forgetting the road one was travelling, ending up on an often-used route when intending to travel elsewhere, etc. Accordingly, it has been argued that these errors are differentially related to top-down and bottom-up attention, updating of a mental model of the driving situation and resolving conflicts between schemas in memory (Mattsson, 2012). Similar considerations apply to individual violations. Network models, with their focus on the interactions between traffic behaviors, may prove useful in practice in encouraging the researcher to focus on the psychological underpinnings of individual traffic behaviors.

Causal and statistical assumptions of latent variable models and network models

When discussing latent variable models, a distinction is often drawn between measurement models and structural models (Kline, 2011). Measurement models describe the relationships between latent variables (e.g., errors) and observed variables (e.g., miss observing a pedestrian, misestimate the speed of another vehicle). Structural models concern interrelationships between latent variables (and observed variables assumed to be measured without error). Now, as the name suggests, in a measurement model, the relationship between the latent and observed variables is understood as one of measurement. This idea is most readily compatible with giving the latent variables a realist interpretation, that is, understanding them as existing independently of the act of measurement (Borsboom, Mellenbergh & Van Heerden, 2003). Even though the matter is rarely explicitly discussed in traffic psychology, the realist interpretation seems in line with how latent variables are used in practice: separate psychological processes are taken to underlie the latent variables (errors and violations), and causal language is used when describing the relationships between the latent and observed variables (Mesken, Lajunen & Summala, 2002; Lajunen, Parker & Summala, 2004; Stephens & Fitzharris, 2016). Under the realist interpretation, the relationship between the latent variable (the measured quantity) and observed variables is seen as one of causation: the measured quantity is seen as causing variation in the observed variables similarly to how temperature causes variation in thermometers (Schmittmann et al., 2013). It is naturally possible to interpret latent variables in a non-realist fashion, for example, as mere statistical summaries, in which case the relationship can be understood as a logical one instead of a causal one (Borsboom, Mellenbergh & Van Heerden, 2003). However, if one is committed to ideas such as estimating the values of parameters, evaluating the position of a subject on the latent variable or assessing the truth of a claim involving a latent variable, it appears that latent variables need to be given a realist interpretation (Borsboom, Mellenbergh & Van Heerden, 2003).

The realist interpretation of latent variables is naturally compatible with viewing variation in the observed variables as being due to either the latent variables or measurement error, and allowing no covariance among the observed variables once these effects are accounted for Borsboom, Mellenbergh & Van Heerden (2003). Such relationships are schematically depicted in Fig. 1. Attributing causal power to latent variables in this manner renders the observed variables inert, interchangeable reflections of the latent properties being measured (Borsboom, Mellenbergh & Van Heerden, 2003; Schmittmann et al., 2013). The idea that observed variables are rendered statistically independent when conditioning on the latent variable(s) is known as the assumption of local independence (Borsboom, Mellenbergh & Van Heerden, 2003) and it is problematic in at least two cases: (1) when several latent variables prove to influence a given set of observed variables (lack of unidimensionality) and (2) when direct causal connections exist among the observed variables.

The problematic nature of the unidimensionality assumption is concretely reflected in the common practice of representing errors and violations as unweighted or weighted (De Winter, Dodou & Stanton, 2015) sum scores. The following example is related to the unidimensionality (or the lack thereof) of items related to the subscale of violations in the DBQ. Consider two imaginary persons filling in the DBQ: John, known for his quick temper, answers the three items related to aggressive behavior with the option “nearly all the time,” and reports performing no other violations, thus obtaining the sum score of 21. Bill, on the other hand, known for his careful nature, chooses the option “never” to the aggression-related items and the option “hardly ever” or “occasionally” to the other violation items. As there are many more items related to non-aggressive violations than to aggressive ones, both respondents receive identical scores, even though their behavioral profiles are quite different. It is naturally possible to react to this challenge within the latent variable framework by creating a more complex model. For instance, “ordinary violations” and “aggressive violations” can be modelled as separate latent variables (Mattsson, 2012). Still, the unidimensionality of the items related to these further latent variables remains an open research question.

The latter idea, the possibility of direct causal connections among observed variables is less often discussed, and it motivates applying network models in the first place. For instance, driving under the influence of alcohol or driving fast may predispose the driver to other violations and errors, and the consequences of these two violations are likely to be different. Assuming the existence of such direct associations between observed variables is in fact quite a drastic move, since it necessitates viewing the relationship between the latent and observed variables as something else than measurement, perhaps as one of constitution (Cramer et al., 2012b). The metaphor of interacting birds forming a flock has been used to describe the nature of the relationship (Cramer et al., 2012b).

Finally, previous research has indicated equivocal factorial structures for the DBQ. This is evidenced by

1. Different factor structures being obtained for the same version of the instrument. For instance, the often-used 27-item questionnaire is thought to reflect two (De Winter, 2013; De Winter & Dodou, 2010), three (Parker et al., 1995) or four (Rowe et al., 2015) different psychological processes, with exploratory analyses sometimes indicating even more latent variables (Stanojević et al., 2018);

2. Typically high cross-loadings of items on factors (Mattsson, 2012; Mattsson et al., 2015);

3. Complex factor structures needed to adequately fit the data, either by specifying second-order factors (Lajunen, Parker & Summala, 2004) or a general factor (Stanojević et al., 2018) and

4. Failures of the test of measurement equivalence across certain subgroups (Stephens & Fitzharris, 2016; Mattsson, 2012; Mattsson et al., 2015).

Observations such as these function as an empirical motivation for creating the network models reported in the present paper.

Figure 1 shows schematically the fundamental assumptions of latent variable models. Individual behaviors, such as speeding or misjudging speed, are assumed to reflect the level of the underlying latent variable and measurement error. Background factors such as enjoying speed figure as predictors of the latent variables. Importantly, background factors are unrelated to individual driver behaviors, which are assumed causally inefficacious. Typically, a dependent variable of interest, such as the number of crashes, is regressed on sum variables representing violations and errors (De Winter, Dodou & Stanton, 2015). One distinct benefit of such models is their simplicity: if the latent variables indeed manage to capture the important commonalities among the individual behaviors, they provide an extremely parsimonious representation of the data. In addition, the model shown in Fig. 1 is, on purpose, a rather simple example of a structural equation model; these models are a flexible tool that would allow the researcher to add more latent variables and to represent much more complex relationships among them. Further, the model shown in Fig. 1 is not intended to summarize theoretically or practically important findings in traffic research, but rather, together with Fig. 2, to illustrate the kinds of relationships that may obtain between the different types of variables in latent variable models and network models, respectively.

Network models, such as the hypothetical model shown in Fig. 2, are naturally suited to investigating direct associations among traffic behaviors. Individual behaviors are also assumed to be directly affected by background factors. Further, two background variables, stress and congestion, that were not included in Fig. 1, are shown in Fig. 2. This illustrates the possibility that there may exist background factors that are related to only one of the observed variables. Such relationships can be more naturally accommodated in network models than in latent variable models. In network models, the absence of an edge between two nodes is interpreted as showing that when the effects of all other nodes in the network are controlled, the two nodes are rendered statistically independent (Epskamp & Fried, 2018). The non-zero edges can be interpreted as potential causal connections (Epskamp & Fried, 2018), logical relationships of entailment (Kossakowski et al., 2016), reflections of the influence of an unmodeled latent variable affecting both nodes (Epskamp, Kruis & Marsman, 2017), conditioning on a collider (a common effect of both nodes) (Epskamp et al., 2018) or perhaps semantic relationships of the nodes being close to each other in meaning. Finally, a cluster of nodes may reflect the effect of a latent variable influencing all the nodes in the cluster (Golino & Epskamp, 2017).

Network models are valuable tools in exploratory analysis of the data: they enable representing pairwise associations among variables quickly, intuitively and efficiently. However, network models assume that the relationships among the observed variables (in this case, the driver behaviors) are not due to latent variables at all, which is a remarkably strong assumption. In this sense, latent variable models and network models can be seen as having complementary strengths and weaknesses (Epskamp, Rhemtulla & Borsboom, 2017).

This paper conceptualizes the behavior of newly licensed drivers as an interacting network of component behaviors. First, the dynamics of the relationships between the typical levels of individual violations and errors during the first 3 years post-licensure are represented as the between-person network (Costantini et al., 2019) which enables assessing direct associations between behaviors and judging the centrality of the behaviors in the network. Second, relationships between driver behaviors and background factors are assessed in a cross-sectional analysis using data collected at 6 months post-licensure. Importantly, the background factors are directly linked to individual driver behaviors rather than latent variables or sum scores. Third, individual driver behaviors recorded at 6 months post-licensure are used for predicting crashes occurring during the following 2 ½ years. Different predictive models are compared by building the models in one subset of data and testing them in another one.

Data and participants

This study is based on the archival dataset collected in the longitudinal Cohort II study in 2001–2005 on new and novice drivers in the UK (Wells et al., 2008). The initial sample size was 20,512 with four waves of data collection taking place after the respondents had passed their driving tests. The numbers of responses and response rates were as follows: 10,064 at 6 months (49%), 7,450 at 12 months (36%), 4,189 at 24 months (26%) and 2,765 at 36 months (26%). The age distribution of the respondents corresponded to that of the population of newly licensed drivers, with 59% of respondents under the age of 20 at the first wave of data collection and 76% under the age of 25. Women, on the other hand, were overrepresented: at the first wave, 64% of the respondents were females. The dataset has been previously used in several studies (De Winter, Dodou & Stanton, 2015; De Winter & Dodou, 2010; Rowe et al., 2015; Roman et al., 2015) and is freely available online (Transport Research Laboratory, 2015).

The cross-sectional network analyses were performed on data obtained at 6 months post-licensure. Only cases with non-missing data in all variables were included, resulting in a sample size of 8,858. The respondents included in this analysis had a mean age of 22.51 years (SD = 7.95), and 64% of them were female. Due to the drop-out described above, a much smaller number of cases was available for forming the between-person network: the model was built based on 1,173 cases with no missing data. The between-person network was formed by averaging responses across the four time points. The respondents in the between-person analysis had a mean age of 24.04 years (SD = 9.62), and 71% of them were female. The regression analyses were based on cases with no missing values on any of the predictor variables or the number of crashes variable, resulting in N = 1,152, 69% female.

Measures

Data collected using the Driving Experience Questionnaire (DEQ) that includes a 39-item version of the DBQ was used. In addition to the DBQ items, items referred to as “background factors” were used. The responses to the DBQ items were recorded on a six-point Likert scale (“never” to “nearly all the time”), and were intended to assess the two constructs of violations and errors. Example items include How often do you disregard the speed limit on a motorway and How often do you select the wrong gear when wanting to go into reverse, respectively. The response options for the background factors were as follows. Drivers’ self-image was assessed on a seven-point scale anchored to the end points of a continuum (e.g., “inattentive” to “attentive”). The self-perceived improvement needs were recorded on a three-point scale (e.g., “no improvement needed in controlling the car” to “a lot of improvement needed in controlling the car”). Attitudes were assessed on a five-point scale ranging from “Strongly disagree” to “Strongly agree;” an example item reads Decreasing the motorway speed limit is a good idea. In addition, self-reported age, sex and mileage at 6 months post-licensure were used as predictors of public road crashes (both major and minor crashes) in the Poisson regression analyses.

Procedure

The “Learning to drive questionnaire,” which includes the question items related to attitudes, was filled in after the practical driving test, prior to responding to the DEQ. Informed consent was inferred from returned postal questionnaires in accordance with the social research guidelines of Department of Transport.

Statistical analyses

Network analyses

The results reported below are based on the maximum number of cases available for the respective analyses as described in the Methods section (N = 1,173 for the between-person model and N = 8,858 for the cross-sectional network model, respectively). First, the between-person network is shown in Fig. 3. It illustrates between-person differences in the connectivity of the driver behaviors during the first 3 years of learning to drive. Errors are shown as striped blue nodes and violations as striped red nodes. The presence of an edge between two nodes represents their conditional dependence when controlling for all other nodes.

First, in outline, violations and errors occupy different regions of the graph, and their distinction seems a sensible rough description of the data. However, if all violations and all errors were reflections of respective latent variables, we would expect all violations and all errors to be interconnected (Epskamp & Fried, 2018) and for all violations and errors to be independent. In contrast, thematically related violations are clustered together and connected by strong edges, aggression-related nodes (v2, v4, v9) and speeding-related nodes (v5, v11) being a case in point. The edges are interpreted as showing, for example, that drivers who were more likely than others to exceed speed limits within residential areas (v5) were also more likely to do so on highways (v11). Similarly, nodes related to substance abuse (v8, v12) were connected to each other and few other behaviors, except using the cell phone while driving (v6). Similar considerations apply to errors. For instance, the nodes related to forgetting something (e3, e6) shared a strong edge and were connected to few other nodes except absent-mindedness (v13).

Second, certain violations and errors were connected by relatively strong edges. Notably, drivers who exceeded speed limits within residential areas (v5) were more likely than others to tailgate other drivers (e15). Further, the tailgating drivers were more likely to need to brake or swerve to avoid an accident (e19). Similarly, crossing junctions against a red light (v3, a violation) was connected by roughly equally strong edges to other violations and errors.

Third, not all thematically related nodes were connected by strong edges, the two items related to perceiving traffic signs (e8, e16) being a case in point. Still, both shared strong edges with other errors; for instance, misreading signs (e8) with getting into a wrong lane (e14). Finally, a methodological note is in order: differences between edge strengths can be interpreted only if their confidence intervals are not excessively wide. Bootstrap analyses assessing this are reported in Figs S4–S5).

Interpreting large networks such as those in Fig. 3 becomes easier with examining indices of node centrality and clustering. The interpretability of the indices themselves depends on their stability, which can be judged by calculating the CS coefficient based on bootstrap tests (Table S5). The indices whose CS-coefficient exceeded the recommended value of 0.5 (Epskamp, Borsboom & Fried, 2017) are shown in Fig. 4.

Both strength centrality (associations with immediate neighbors) and closeness centrality (associations with all nodes) of the between-person network indicated the presence of a group of nodes that were especially central in the network. Closeness centrality is perhaps the more revealing in this context, as it capitalizes less on single strong edges. The node with the highest closeness centrality was v5 (speeding within a residential area), followed by nodes v3 (crossing junction on red), e15 (tailgating), e10 (queuing, nearly hit car), e17 (fail to check mirror) and v11 (speeding on motorway); nodes e10, v5, e15 and v3 had also high strength centralities. In addition, nodes e14 (getting into a wrong lane) and e7 (failing to notice pedestrians) had a high strength centrality. In general, the nodes along the path connecting speeding with various errors (v11-v5-v3-e7-e17-e15-e10 or v11-v5-e15, etc.) were central. Figure 4 also shows Zhang’s clustering coefficient, according to which certain nodes, most notably v4 (become angered, give chase) and node e3 (forget where left car) contained little unique information.

The cross-sectional network model (Fig. 5) shows the DBQ variables in relation to various background factors: attitudes (yellow), self-judged improvement needs (green) and self-image as a driver (lilac). The model is based on data collected at the first time point, 6 months post-licensure. It appears at the first sight quite different from the between-person model, but this is largely because the node placements are different due the use of the Fruchterman–Reingold algorithm. Similarities between the two models are revealed by examining the connection strengths and the centrality indices (Fig. 6). The indices whose CS-coefficient exceeded the recommended value of 0.5 (Epskamp, Borsboom & Fried, 2017) are shown in Fig. 6. The speeding-related nodes (v5 and v11) were again central together with node e7. Node e16 (missing give way signs) now had a high strength centrality, while in the between-person network the corresponding centrality value was average; on the other hand, the connectivity patterns of the node were similar. The path v11-v5-e15 was present also in this model, even though node e15 was now slightly less central. A prominent difference between the models was that the aggression-related nodes v2, v4 and v9 were more central in the cross-sectional model.

Looking at the background factors, the self-judged improvement needs were strongly interconnected. They were, however, also related to driving behaviors in a revealing pattern. In general, they shared negative associations with different violations. In particular, the judged need for improvement in changing lanes (in4) was related to less speeding (v11) and less pushing into a lane (v7), while the perceived need of improving controlling the car (in1) was associated with having problems with gears (e1) and car controls (e4). Negative attitudes to speeding (a1) and overtaking on the inside (a2) were related to fewer self-reported behaviors of those kinds (v11 and v1, respectively). On the other hand, perceiving oneself as a fast driver (si2) was positively associated with speeding (v5 and v11) and racing from the lights (v10). The drivers’ self-judgment of themselves as irritable (si1) was closely associated with the anger-related nodes, even though the node was quite redundant as judged by the clustering coefficient. Self-perceived need of improvement in hazard-perception (in3) had a similarly high value of the clustering coefficient.

Regression analysis

The self-reported driving behaviors, age, sex and mileage at the first time point were used in predicting subsequent crashes. As seen in Table 1, the naive Poisson model fit the training data best (as it should), but its performance deteriorated notably in the hold-out data. In fact, the model fit the hold-out data worse than the null model without predictors, offering a dramatic demonstration of how such models sometimes overfit data. The elastic net model fit the training data the worst, but its fit to the hold-out data was almost identical to that of the ridge regression model and is to be preferred due to its parsimony (16 vs. 42 parameters, respectively).

Table 2 shows the regression weights of the elastic net model that are low, partly because of the dual penalization involved. The driving behaviors included in the model comprise various violations and errors. Variables related to failing to notice pedestrians, problems with car controls and different forms of aggressive behavior had the highest regression weights. Hitting something when reversing, which is itself a minor crash, also predicted subsequent crashes.