arXiv CSopen access

The causal relation between off-street parking and electric vehicle adoption in Scotland

The causal relation between off-street parking and electric vehicle adoption in Scotland Bernardino D’Amicoa,c,d,∗, Achille Fonzoneb,d , Emma Hartc,d a

arXiv:2604.09271v1 [cs.LG] 10 Apr 2026

Digital Built Environment Group (DiBEG), UK b Transport Research Institute, UK c Centre For Artificial Intelligence and Robotic, UK d School of Engineering and the Built Environment, Edinburgh Napier University, 10 Colinton Road, Edinburgh EH10 5DT, UK

Abstract The transition to electric mobility hinges on maximising aggregate adoption while also facilitating equitable access. This study examines whether the ‘charging divide’ between households with and without off-street parking reflects a genuine infrastructure constraint or a by-product of socio-economic disparity. Moving beyond conventional predictive models, we apply a probabilistic causal framework to a nationally representative dataset of Scottish households, enabling estimation of policy interventions while explicitly neutralising the confounding effect of other causal factors. The results reveal a structural hierarchy in the EV adoption process. Private off-street parking functions as a conversion catalyst: enabling access to home-charging increases the probability of EV ownership from 3.3% to 5.6% (a 70% relative, 2.3 percentage point absolute increase). However, this effect primarily accelerates households already economically positioned to purchase an EV rather than recruiting new entrants. By contrast, household income operates as the fundamental affordability ceiling. A causal contrast between lower- and higher-income strata, shows a reduction in market non-participation by 23.1 percentage points, identifying financial capacity as the principal gatekeeper to entering the EV transition funnel. Crucially, the analysis demonstrates that standard observational models overstate the isolated effect of off-street parking infrastructure. The apparent effect emerges from selection bias: higher-income households are disproportionately likely to possess both private parking and the means to purchase EVs. These findings support a dual-track policy strategy: lowering the affordability ceiling for non-participants through financial instruments, while addressing EV home-charging access for the ‘latent intent’ cohort in high-density urban contexts. Keywords: Electric vehicle, Causal ML, Bayesian networks

∗

Corresponding author Email addresses: [email protected] (Bernardino D’Amico), [email protected] (Achille Fonzone), [email protected] (Emma Hart)

1. Introduction Despite the awareness that decarbonisation of mobility requires rethinking priorities among modes [1], the transition to electric vehicles (EVs) remains a cornerstone of many government climate strategies, including the UK’s and Scotland’s legally binding commitments to net zero [2, 3]. However, recent empirical analyses and systematic reviews suggest that aggregate adoption rates are an insufficient indicator of a just transition, which requires equitable access to charging infrastructure across diverse communities in order to avoid reproducing existing socio-economic disparities [4, 5]. As the EV market expands beyond early adopters, current adoption patterns reveal a stark driveway ‘charging divide’: off-street parking enables homeowners to install domestic chargers, thus acting as a primary catalyst for EV adoption. According to a recent survey report by the Electric Vehicle Association (EVA) [6], 90% of current EV owners in England have access to off-street parking, with 81% of these utilising a home charger. This infrastructure gap may represent an important barrier: residents of multi-unit dwellings (e.g., blocks of flats) may face significant physical, financial, and regulatory hurdles (such as the requirement for third-party legal consents) that frequently preclude home-charging installation [7, 5]. Beyond practical convenience, this may reflect an underlying financial disparity: according to EVA England, while 87% of surveyed EV drivers with driveways report lower running costs compared to internal combustion engines, only 50% of those without off-street parking access find their EVs cheaper to operate [6]. 1.1. Determinants and barriers to EV adoption According to existing literature, households’ EV adoption is shaped by a combination of socio-demographic, economic, behavioural, and infrastructural factors. Empirical studies consistently identify income [8, 9, 10, 11, 12, 13, 14], education [8, 9, 11, 15], home ownership [16, 12, 17], and multi-vehicle household status [9, 12, 18] as strong predictors of adoption, reflecting both financial capacity and lifestyle compatibility with electric mobility. Psychological factors such as environmental concern [11, 16] and technology affinity [11, 12, 19, 20] also seem to influence adoption decisions. Among structural determinants, housing characteristics and access to residential charging infrastructure have also been recognised as particularly influential. In line with Eva England statistics mentioned above, access to home charging capability is one of the strongest covariates [21], explaining why detached housing and dedicated parking consistently predict ownership [11]. Home charging capability is also reported to be a more important determinant of EV adoption than the availability of public charging infrastructure [12]. 1.2. Research gap Albeit the above-reviewed literature consistently reports the existence of a statistical association between dedicated parking provision and EV uptake, no study has yet attempted to estimate the independent causal effect that parking access may have on EV uptake. Although the absence of off-street parking may constitute a structural constraint on home charging, it remains unclear to what extent the observed adoption gap reflects the infrastructural barrier itself rather than the socio-economic characteristics that systematically correlate with a lack of off-street parking. This leaves a critical policy question unresolved: is the lower adoption 2

rate among on-street parking households primarily driven by charging access constraints, or by broader socio-economic disparities that shape vehicle ownership and purchasing capacity (as well as access to off-street parking)? International evidence indicates that affluent and lower-density areas are disproportionately favoured in charging station deployment, generating a ‘spatial disparity’ that overlaps with existing demographic privilege [22]. Disentangling these effects is essential for effective policy design. Historically, UK strategies have prioritised vehicle purchase incentives; however, if the principal barrier faced by the 40% of UK households without driveway access [23] lies in charging availability, reliability, and convenience rather than upfront vehicle cost, a reorientation of policy towards sustainable and equitable infrastructure provision may be required. Crucially, policies supporting residential charging must navigate a trade-off: incentivising parking-based infrastructure may conflict with urban planning goals aimed at increasing density and promoting mixed land use to reduce sprawl. We therefore clarify that this study does not evaluate the expansion of off-street parking as a viable policy lever. Such an intervention would be physically infeasible in dense urban areas and counterproductive to broader decarbonisation objectives when applied to new housing developments. Following the logic of causal inference for non-manipulable causes, we treat off-street parking provision as a structural diagnostic rather than a literal policy lever. Just as quantifying the causal link between obesity and morbidity helps target taxation policies at sugary drinks rather than mandating weight loss itself [24], estimating the ‘driveway effect’ can help calibrate compensatory policy interventions aimed at replicating the advantages that driveway access confers. In practice, these advantages operate through two primary mechanisms: a price mechanism, whereby domestic charging enables access to cheaper electricity tariffs compared with public charging; and a temporal mechanism, which enables a transition from highfriction active charging to passive, zero-wait-time background activity. While we do not model these mechanisms explicitly, identifying the causal effect of parking provision provides a useful proxy for the scale of cost reductions and convenience improvements required to bridge any existing adoption gap without compromising urban density. In this context, Scotland has been piloting one-off schemes to address the off-street charging gap, such as the Energy Saving Trust’s cross-pavement charging initiative, which facilitates the installation of cable gullies for households reliant on on-street parking [25, 26]. In parallel, regulatory levers are also being considered as additional policy avenues, including the possibility to remove existing restrictions to expand on-street and pavement charging as part of permitted development rights [27]. In order to ensure such targeted policy interventions are effective, policymakers must move beyond standard correlations and apply a causal framework capable of disentangling physical infrastructure from socio-economic privilege. To this end, the primary aim of this research is to quantify the causal effect of private off-street parking on EV adoption in Scotland, moving beyond traditional correlational analyses to address a critical void in the literature. 1.3. The necessity of causal inference for policy analysis In research domains concerning policy analysis and evaluation (or decision making in general), the objective shifts from predicting existing patterns to predicting the effects of interventions. While machine learning excels at estimating conditional probabilities, such as the likelihood of EV ownership given a set of covariates, these models are fundamentally 3

Figure 1: Causal graphical structure of the parking provision and EV ownership toy example. The presence of household wealth (Z) creates an undirected back-door path (X ← Z → Y ), inducing a spurious correlation between dwelling type (X) and EV ownership (Y ) that biases the true causal effect of interest, X → Y .

optimised for statistical association rather than causal identification [28, 29]. As argued by Chauhan et al. in the context of travel mode choice [30], even high-accuracy predictive models (e.g., neural networks or random forests) may succeed in capturing complex data patterns while failing to reflect the underlying causal mechanisms required for robust policy design. This discrepancy arises from the critical distinction between observing a state and intervening upon it. To illustrate, let us consider the relationship between dwelling type (X) and EV ownership (Y ). A purely predictive model might find a strong positive association between the two, as a detached house is significantly more likely to have a private driveway than an apartment. However, household wealth (Z) may act as a critical confounder, causally influencing both the capacity to afford a dwelling with a driveway (X) and the financial ability to purchase an EV (Y ). In causal graphical terms (Figure 1), the variable Z creates an undirected ‘backdoor’ path (X ← Z → Y ), which induces a spurious correlation between X and Y [31]. Without ‘closing’ this path by conditioning on Z, any observed difference in EV ownership between households with and without off-street parking will conflate the true causal effect with a bias driven by underlying economic status. 1.4. Research questions and causal estimands Building on the distinction between observational associations and interventional effects, we formalise our policy problem in explicitly causal terms. Rather than asking whether offstreet parking or income are associated with EV adoption, we evaluate the shift in outcomes under hypothetical interventions. Given that the relationship between parking and adoption is fundamentally entangled with socio-economic status, we formulate three primary research questions to disentangle these drivers: RQ1: What is the causal effect of providing access to off-street parking on EV adoption status and purchase intentions? RQ2: How does household income influence the EV adoption pipeline, acting both as a direct driver of affordability and as a primary determinant of residential parking access? RQ3: To what extent does the observational difference in EV adoption probabilities diverge from the actual probability shift under intervention, and what specific policy bias results from mistaking the former for the latter? 4

We translate the first two questions into formal causal estimands, whilst the third evaluates the discrepancy between interventional and standard observational probabilities. Together, this framework enables us to determine whether the provision (or absence) of off-street parking functions as a catalyst (or barrier) within the EV adoption pipeline; whether household income represents a more fundamental prerequisite for market entry; and to what extent purely observational metrics may misdirect policy interventions aimed at accelerating the transition to electric mobility. 2. Methods Our methodology is grounded in probabilistic causation [32], whereby external interventions are understood as factors that shift the likelihood of an outcome rather than as deterministic mechanisms. Specifically, we employ a causal Bayesian network framework [31], representing the system as a directed acyclic graph (DAG), such as the one illustrated in Figure 1. The topology of such graphs, denoted by G, can be established through two primary approaches. The first is knowledge-based specification, in which causal relationships are defined based on prior domain expertise [33]. The second approach is automated structure learning, whereby the graph is inferred directly from observational data. In this study, we adopt a multi-stage hybrid strategy. First, domain expertise is exercised in the selection of the feature space; by determining which variables are included in the model, we encode prior knowledge regarding the known socio-economic and infrastructural determinants of EV adoption. Second, we learn the causal structure from data while enforcing domain-specific constraints during the automated search process, followed by a post-hoc manual refinement of the resulting graphical output. The algorithm details and refinement steps are described in section 2.3. In a causal Bayesian network, nodes represent random variables, and directed edges encode direct causal relationships. As for non-causal Bayesian networks, each observed variable Vi ∈ V is associated with a conditional probability distribution, which is denoted as P (Vi = vi | P a(Vi ))G , and specifies the probability that Vi = vi given the values of its parent1 variables P a(Vi ) in the graph G. The implementation of Bayesian networks relies on two fundamental assumptions that connect the graphical structure to the observed statistical data: - Faithfulness condition: it assumes that every statistical independence found in the data is a direct result of the underlying data-generating process, as modelled by the graph’s structure, therefore assuming that different causal influences do not perfectly cancel each other out across different pathways. - Causal Markov condition: this assumption states that, conditional on its direct parents in the causal graph, each variable is statistically independent of all its non-descendants. In essence, once the immediate causes (i.e., parents) of a variable are accounted for, no additional information from its ancestors or other non-descendant nodes contributes further to its probability belief. 1

Parents are the set of nodes in G from which a directed edge points toward Vi .

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To illustrate this latter with an example, consider the causal chain: weather (X) → traffic (Z) → being late (Y ). In this causal chain, the Markov condition implies that if we already know the current state of traffic (Z = true), knowing the weather provides no additional information about the probability of being late. The causal influence of weather X = rainy on arrival time is entirely captured by the traffic congestion it creates, hence, once the state of traffic is observed, knowing the weather becomes redundant for predicting lateness: P (Y | Z, X) = P (Y | Z), thus implying that Y ⊥ X | Z, meaning, the outcome Y is independent of its ‘grandparent(s)’ X once we condition on its parent variable(s) Z. A critical implication of the causal Markov condition is the possibility to factorise the full joint probability distribution over the entire set V of observed variables. In the absence of a structured graph, representing the full joint distribution explicitly would require specifying dependencies across the entire variables’ state space, yet as the number of variables increases, this task becomes computationally and statistically intractable due to the curse of dimensionality, that is, the exponential blow-up in the degrees of freedom required to represent the full joint.2 Conversely, in a Bayesian network, the probability of a generic event assignment {V1 = v1 , V2 = v2 , . . . , Vn = vn } can be implicitly encoded as a product of local conditional probabilities [34]: P (v1 , v2 , ..., vn )G =

n Y

P (vi | P a(Vi ))G

(1)

i=1

As such, any observational probability distribution (whether marginal or conditional on observing a set of covariates) can be queried from the network’s local probability distributions via Eq. (1). 2.1. Parameter estimation Once the DAG structure G is specified (see section 2.3), the model can then be trained to represent the specific joint distribution of the system (a procedure known as parameter estimation), which involves quantifying the local conditional probability distributions on the r.h.s. of Eq. (1). For discrete variables, as used in this study, these local distributions can be represented via Conditional Probability Tables (CPTs), hence training the network essentially entails a frequency estimation of each entry assignment in these tables. For each node Vi , the likelihood of each state vi conditioned on every possible configuration paj of its parent set was computed via Maximum Likelihood Estimation: count(vi , paj ) + α P (vi | paj ) = P [count(vi , paj ) + α]

(2)

vi ∈Vi

where the numerator, count(vi , paj ), denotes the frequency of the joint occurrence of variable Vi in state vi and of its parents in state paj , whereas the denominator sums these counts across the entire set Vi of possible outcomes for the child variable Vi , thus acting as a normalisation 2

For the specific variable set V used in this study (n = 15), an explicit representation of the full joint distribution would require specifying 15,482,880,000 distinct Q15 joint state configurations, computed as the product of the cardinalities of all variables’ state spaces: i=1 |Vi |

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factor to ensure that all probabilities within each row in the CPTs sum up to 1. The Laplace smoothing term in Eq. (2) was set to α = 10−5 . The term is required to address the “zerofrequency” problem, that is, when a parent-child state {vi , paj } is not present in the training dataset, its count would be zero on the r.h.s. of Eq. (2), which would yield a zero probability for P (vi | paj ). Regarding notation, it is important to note that the subscript vi in the above summation in Eq. (2) is not a standard numerical index, but a placeholder for P the elements of the set Vi . For the sake of brevity we will henceforth adopt the shorthand v to represent summations P v∈V across all subsequent equations. 2.2. Variable selection, data sourcing and preprocessing The selection of variables for our causal model followed a systematic, domain-informed approach. We began by defining the primary causal relationship of interest: the treatment and outcome variables. From this core link, we expanded the variable set by identifying factors documented in the literature as influencing both treatment and outcome. This expansion was guided by a synthesis of transport economics and urban sociology research. To support systematic literature mining, we used Elicit [35], an LLM-based research tool, to identify empirically grounded determinants in prior EV adoption studies (see literature review section 1.1 for a detailed summary). To ensure the technical validity of the generated outputs, we followed a verification protocol where each identified determinant was manually cross-referenced against the original source papers to confirm empirical significance and the direction of the reported effect. Only variables with a consensus of support across multiple studies were retained for the final model specification. We idealised the system as comprising of decision-making agents embedded within material and infrastructural constraints. Accordingly, the resulting variable set can be conceptually partitioned into two ontologically distinct categories: (1) socio-economic household characteristics, representing agent-level attributes such as net annual income, household composition, and working status; and (2) dwelling and infrastructure characteristics, representing structural and spatial constraints, including architectural dwelling type, dwelling age, and regional charging infrastructure density. This distinction between household characteristics and structural constraints is reflected in our data sources. To populate these variables with empirical observations, we integrated two complementary national datasets that together capture the intersection of social behaviour and physical housing conditions in Scotland, namely: the Scottish Household Survey (SHS) [36] and the Scottish Housing Condition Survey (SHCS) [37]. SHS and SHCS data was enriched with information about availability of public charging facilities as explained below. The latest SHS and SHCS data releases at the time of writing were used for this study, referring to the 2022 survey year. The SHS contains approximately 10,500 household entries, reporting on a range of socio-economic characteristics and behaviours, including information indicating whether the selected random adult within the household has access to (or intends to buy) an electric car or van. Data from the SHS were cross-linked with those from the SHCS for the same year via a unique-household ID variable, mapping surveyed households to their corresponding dwelling characteristics. The latter represents a much smaller subset (≈3,000 entries). While the SHS focuses on social and economic data, the SHCS provides an expertled physical assessment of the Scottish housing stock, reporting on dwelling fabric, energy 7

performance, and external property features. By doing so, we were able to assemble a merged dataset reporting on both household and dwelling variables, such as dwelling type, dwelling age, and most importantly, parking provision. This latter variable, as originally reported in the SHCS, comprises nine separate categories. These were remapped into two categories (see Table A1 in Appendix A) to obtain a binary classification for our parking provision treatment variable: specifically, distinguishing between those who can park off-street and those who cannot. Similar data cleaning and mapping procedures were applied to other variables. For instance, the SHC variable regarding EV ownership and intent included a category for individuals who stated they do not drive/need a vehicle, regardless of engine type; these respondents were subsequently excluded from the sample. To prevent information loss during model discovery and training phases, the original 8-fold classification for household net annual income (termed V1 in here —see Table A2 in Appendix A) was retained in its original form. However, for causal estimation purpose the inferred post-intervention distributions P (Y | do(V1 )) were later aggregated into two categories, namely: V1 = low-income for bands 1 to 6 and V1 = high-income for bands 7–8. This binary discretisation was achieved by averaging the specific post-intervention probability of each band, weighted by their respective marginal probabilities P (v1 ), (reported here in Table 1) that is, for V1 = low-income for instance we have: P6 P (Y | do(v1,i ))P (v1,i ) (3) P (Y | do(V1 = low-inc.)) = i=1 P6 i=1 P (v1,i ) By re-discretising V1 approximately at the median (48.5%), we obtain an almost perfectly balanced binary partition to contrast the effect of income between control group (≤ £30,000) and treatment group (> £30,000). The resulting full observational set, V = {Y, V1 , . . . , V14 }, comprises 15 variables, the majority of which were retrieved from the SHS and the SHCS dataset collections, with the exceptions of V10 and V11 , which represent the density of workplace and public EV charging stations, respectively. These two infrastructure density metrics were derived for each of Scotland’s 32 local authorities by calculating the ratio between charging station projects completed by the end of 2022 and the total resident population within each jurisdiction. Charging station statistics were retrieved from the Department for Transport [38, 39], whereas the demographic data used to normalise these figures were sourced from the National Records of Scotland [40]. This real-valued density data was subsequently normalised per 100,000 residents and discretised into five ordinal bands, as detailed in Table A2 in Appendix A, before being cross-linked to individual household units in the primary training dataset using the Local Authority code as a unique spatial identifier. 2.2.1. Population weighting and resampling To ensure that the final model is representative of Scotland’s broader dwelling and household population, the unweighted dataset resulting from the aforementioned preprocessing and cleaning procedures was subjected to a weighted resampling routine. Specifically, the original sample (N = 1, 802) was resampled with replacement using selection probabilities proportional to the paired sampling weight variable (tsWghtP_n) provided by the SHCS. This

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procedure adjusts for the complex survey design by approximating a representative pseudopopulation; by doing so, the structural dependencies and conditional probabilities learned by the network better reflect the population distribution across the weighted dimensions. While this approach mitigates the inherent biases of the sampling frame, we acknowledge that it corrects for non-response only relative to the auxiliary variables used in the weight construction. We tested this resampling across various random seeds to assess the stability of the results and observed no discernible change in the estimated post-interventional distributions. With the training dataset thus obtained, the next phase of the analysis involves uncovering the causal structure of the network’s graph (G) governing the dependencies between these 15 variables. We hence move on to describe the adopted causal discovery framework in the following section. Table 1: Marginal probabilities and cumulative sample distribution for the eight classification bands of household income (V1 ).

Household income band, v1 1: < £6000 2: £6001-10,000 3: £10,001-15,000 4: £15,001-20,000 5: £20,001-25,000 6: £25,001-30,000 7: £30,001-40,000 8: > £40,000

Marginal probability P (v1 ) 0.0202 0.0364 0.0786 0.1358 0.1079 0.1064 0.1602 0.3546

Cumulative sample total 0.020 0.057 0.135 0.271 0.379 0.485 0.646 1.000

2.3. Causal discovery Causal discovery aims to learn causal relationships among random variables directly from observational data. To discover the causal structure of our graphical model, we employed the Multivariate Information-based Inductive Causation (MIIC) framework [41, 42]. MIIC was selected for its ability to handle the relatively limited sample size of our dataset. By quantifying the strength of dependencies rather than just their existence, MIIC effectively balances explanatory power with model complexity, outperforming classical constraint-based methods [42], particularly when dealing with small-sample datasets, where a high noise-to-signal ratio can undermine the reliability of statistical independence testing as typically employed in constraint-based methods. A technical note describing the theoretical foundations underpinning the MIIC algorithm, is detailed in Appendix B. Within this framework, the MIIC algorithm starts from a fully connected graph and iteratively prunes edges while orienting the remaining ones using information-theoretic metrics together with adaptive complexity thresholds. By expressing the complexity threshold as a ratio relative to the sample size, the method provides a formal mathematical implementation of Occam’s Razor, penalising overly flexible models that may otherwise over-fit limited data. For instance, a fully connected graph can represent virtually any arbitrary distribution, thereby mistaking sampling noise for genuine structural dependencies. Unlike traditional constraint-based approaches, which rely on fixed and often somewhat arbitrary 9

significance thresholds (e.g., p-value < 0.005), the adaptive complexity threshold allows the algorithm to resolve increasingly subtle dependencies as the sample size grows, while maintaining structural parsimony in data-sparse regimes. Following the pruning of the graph skeleton, the algorithm then orients the remaining edges and identifies potential latent confounding to produce a Maximal Ancestral Graph (MAG) by evaluating interaction signatures and applying logical propagation rules, as detailed in Appendix B.3. 2.3.1. Blacklisting edges To ensure logical consistency of the discovered structure, we imposed a set of a priori structural constraints during the iterative pruning and orientation phases. Specifically, we defined a ‘blacklist’ of prohibited causal directions. For example, edges such as Household income → Household working status were blacklisted, as it is the occupational status that determines the flow of earnings rather than the reverse. Notably, the causal discovery algorithm did not detect causal links between public (workplace) infrastructure charging densities (V11 and V10 , respectively) and individual EV ownership status & intentions, Y (see Figure 2-b). This was likely due to the coarse granularity of the infrastructure data, which was measured as the average density at the local authority level, i.e., count of public (workplace) charging stations per 100,000 residents. 2.3.2. Post-hoc refinement The automated discovery phase described above resulted in the MAG illustrated in Figure 2-b which provides a graphical representation of the Markov Equivalence Class, i.e., the class

Figure 2: Causal discovery workflow. (a) Initial, fully connected skeleton. (b) Maximal Ancestral Graph discovered via the MIIC algorithm, featuring directed (→), bi-directed (↔) and undirected (−) edges. The isolated variable subset {V6 , V10 , V11 , V14 } is statistically independent of the main network. (c) Final refined DAG: fully specified model after omitting the disconnected subset and incorporating post-hoc a latent confounder between V8 and Y .

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of all causal structures that are statistically indistinguishable based on the conditional independence relationships found in the data. Notably, all of the undirected edges the algorithm was unable to orient in the orientation-propagation phase (see Appendix B.3) were confined to an isolated four-variable cluster (as shown in Figure 2-b), which shared no connectivity with the rest of the model, i.e., the two subgraphs are statistically independent. To this end, we were thus able to simply omit this four-variable subset from the final model, hence successfully recovering a fully specified DAG from the Markov Equivalence Class. Additionally, a latent (unobserved) confounder was discovered by the algorithm between the household income variable (V1 ) and the variable reporting on No. of vehicles (V2 ), represented as a bi-directed edge in Figure 2-b. Because this dependency could not be explained by any other variables in our dataset, it implies the influence of an external factor not captured in our study. We hypothesise that this latent confounder likely captures the effect of occupational classification (denoted as U1 in Figure 3), that is, specific work occupations inherently dictate both a household’s income as well as its mobility requirements —for example, trade-based occupations (e.g., self-employed contractors, electricians, or plumbers)— thereby acting as a common parent to both variables. A further bi-directed edge was manually introduced post-hoc between Dwelling type (V8 ) and EV ownership status & intention (Y ) to account for the potential latent confounding effect of household’s overall financial capacity. This latent factor, denoted as U2 in Figure 3, represents accumulated wealth in the form of liquid assets and non-income financial reserves. We assume that both the choice of housing type and the purchase of premium vehicles, such as EVs, depend on a household’s overall financial capacity, including their savings and longterm wealth (U2 ) as well as their annual income flow (V1 ). Although no bi-directed edge V8 ↔ Y was detected via the MIIC algorithm, this absence of evidence does not implies evidence of absence: it is entirely possible that such confounding influences exist, yet the association V8 − Y might have been too weak (or the sample size too small) to surpass the complexity threshold leading the algorithm to treat it as statistically indistinguishable from noise. The final, manually refined, graph G (as shown in Figure 2-c and Figure 3) provides the necessary set up to perform causal effect identifiability and estimation. 2.4. Causal effect identification & estimation Having established the causal structure G, we now focus on estimating the causal effect of specific interventions. Within the framework of causal graphical models, this amounts to computing the post-intervention distribution P (Y | do(X)). This quantity represents the distribution of the outcome Y when the treatment variable X is externally set to a specific value x. Graphically, such an intervention corresponds to removing all incoming edges to X, which encode the natural causal mechanisms that would otherwise determine its value. As mentioned in the introduction, a central difficulty is that the post-intervention distribution P (Y | do(X)) generally differs from the observational conditional distribution P (Y | X) available in the data —with the latter reflecting how Y behaves when we merely observe X = x, with all underlying causal mechanisms intact. In contrast, P (Y | do(X)) characterizes the response of Y when those mechanisms influencing X have been deliberately severed through intervention.

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Figure 3: Final DAG (G) representing the causal mechanisms of EV ownership status and intentions (Y ). The model integrates automated causal discovery results with post-hoc manual refinements to account for latent confounding (Ui ). Directed solid edges indicate causal effects, dashed edges denote unobserved common causes. The DAG structure provides the formal basis for identifying sufficient adjustment sets Z required to estimate post-treatment distributions from observational data via the back-door criterion (section 2.4).

This distinction naturally raises the question of identifiability, that is, under what conditions can the interventional distribution be recovered from purely observational data. An effect is said to be identifiable if the interventional distribution can be expressed entirely in terms of observational probabilities. In a Markovian model, i.e. where all variables are fully observed and no unmeasured confounding is present, such identification is in principle always possible from the joint observational distribution. However, this guarantee no longer holds when the graph contains latent variables, such as U1 and U2 in our case (so-called semi-Markovian case). Unobserved confounders may induce spurious associations between observed variables by creating unblocked back-door paths, and since these latent variables cannot be conditioned on directly (as we have no data for them), it may be impossible to express the interventional distribution solely in terms of observational quantities. 2.4.1. The back-door criterion To address this issue, we employ Pearl’s back-door criterion [31], which consists in identifying a set of adjustment variables Z satisfying the following two conditions: 12

- No variable in Z is a descendant of X; - The set Z blocks every back-door path between X and Y . Unlike directed paths that represent the flow of causal influence, a back-door path is any non-causal path between X and Y that begins with an arrow pointing into X. Such paths introduce spurious non-causal correlations between the two variables. The objective of applying the criterion is therefore to identify a set of observed variables Z such that, when conditioned on, the causal effect of X on Y can be estimated from observational data. Conceptually, Z acts as a filter that blocks all back-door paths, that is, all non-causal pathways through which spurious associations between X and Y may arise —thereby emulating the conditions of a randomised controlled trial. If such a set Z exists, our post-intervention distribution of interest can thus be recovered from purely observational probability distributions using the following adjustment formula [31]: X P (Y | X, Z)P (Z) (4) P (Y | do(X)) = z

The formula effectively re-weights the observational data distribution P (Y | X, Z) to remove the bias introduced by the variables in Z. 2.4.2. d-separation To formally determine whether a set Z ‘blocks’ all back-door paths in our causal graph G (shown in Figure 3), we employ the rules of d-separation (directional separation) [43]. These rules define how information flows through the three fundamental types of patterns in a causal network: - Chains (X → Z → Y ; X ← Z ← Y ) and forks (X ← Z → Y ): information flows between X and Y unless the intermediate variable Z is conditioned on. - Colliders (X → Z ← Y ): information is naturally blocked at Z. However, conditioning on Z (or its descendants) ‘opens’ the path, creating a spurious association between X and Y . To find a suitable adjustment set, we therefore examine the mutilated graph, denoted as GX , which is the original graph G where we remove all edges directed out of the treatment X. In this sub-graph, any surviving path between X and Y is a back-door path. A set Z is thus a sufficient adjustment set if it d-separates X and Y within GX , that is, if it blocks all chains and forks while avoiding conditioning on colliders, in accordance with the rules outlined above. 2.4.3. Treatment effect of parking provision (V7 ) To answer our primary research question, namely, assessing the causal effect of parking provision (V7 ) on EV ownership status and intentions (Y ) we identified Z = {V8 , V9 } to be a sufficient adjustment set to recover the post-treatment distribution P (Y |do(V7 )), thus yielding to the following adjustment formula: X P (Y | do(V7 )) = P (Y | V7 , V8 , V9 )P (V8 , V9 ) (5) v8 ,v9

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Proof. Following the rules of d-separation, we identify a total of 24 simple3 back-door paths between V7 and Y in the mutilated graph GV7 , with this latter shown in Figure 4-a. The 24 paths are reported in Appendix C.1. Crucially, every one of these paths is comprised of one of two distinct topological segments located immediately adjacent to the treatment V7 : - Chain segments (12 paths): these follow the pattern V7 ← V8 ← . . . Y . In these instances, V8 acts as a non-collider intermediate variable (a mediator). Hence, conditioning on V8 is necessary and sufficient to block the flow of non-causal information along these specific segments. - Collider segments (12 paths): these involve a junction where V8 acts as a collider: V7 ← V9 → V8 ← . . . Y . These segments are naturally blocked in the observational distribution by the collider at V8 . While controlling for V8 successfully blocks the first class of back-door segments, it simultaneously ‘opens’ the second class due to collider bias. To resolve this, we include Dwelling age (V9 ) in the conditioning set. Since V9 is a non-descendant of the treatment and acts as a fork (common cause) in this second class of segments, its inclusion re-establishes d-separation. Consequently, the set Z = {V8 , V9 } is sufficient to block all 24 back-door paths, satisfying the independence condition: (6) V7 ⊥ Y | {V8 , V9 } in GV7 This confirms that the back-door criterion is met for identification.

Figure 4: Mutilated graphs used for the identification of causal effects via the back-door criterion. (a) Subgraph GV7 used to identify the effect of parking provision (V7 ) on EV intentions, Y . (b) Sub-graph GV1 used to identify the effect of household income (V1 ) on Y . 3

A simple path is one in which no node is visited more than once.

14

Notably, an initial attempt to establish causal identifiability involved adjusting solely for Household income, Z = {V1 }. As visualised in the mutilated graph GV7 (Figure 4-a), conditioning on V1 successfully blocks the majority of back-door paths. However, it fails to intercept the non-causal association flowing through the latent confounder Household wealth & assets (U2 ), specifically along the path: V7 ← V8 ← U2 → Y

(7)

Indeed, such path could be blocked by conditioning on the common-cause variable U2 if we had observational data for it. 2.4.4. Treatment effect of Household income (V1 ) To answer our secondary research question, namely, assessing the causal effect of household income (V1 ) on EV ownership status and intentions (Y ) we identified Z = {V5 } as a sufficient adjustment set to recover the post-treatment distribution P (Y |do(V1 )), thus yielding to the following adjustment formula: X P (Y | do(V1 )) = P (Y | V1 , V5 ) P (V5 ) (8) v5

Proof. We identify, via d -separation algorithm, a total of 27 undirected back-door paths between V1 and Y in the mutilated graph GV1 , shown in Figure 4-b. These paths (reported in Appendix C.2) can be grouped into three distinct topological classes based on their initial segments adjacent to the treatment node V1 : - Chain segments (9 paths): these paths follow the pattern V1 ← V12 ← V5 → . . . Y . Here, V5 acts as an ancestor to the treatment through variable V12 (Household working status). - Fork segments (9 paths): these follow the pattern V1 ← V5 → . . . Y , where V5 (Household composition) is a direct common parent of both the treatment and subsequent causal chains. - Collider segments (9 paths): these include the pattern V1 ← U1 → V2 ← . . . Y , and as such are characterised by a v-structure at the node V2 (No. of vehicles), where the latent U1 , Occupational classification, and other variables converge. By conditioning on V5 , we successfully d-separate V1 from Y in the subgraph GV1 across the first 18 paths (first and second class above), as V5 acts as a common-cause intermediate node in every instance. The remaining 9 paths (third class above) are naturally blocked by the collider at V2 . Because our adjustment set Z = {V5 } does not include V2 or any of its descendants, these paths remain closed. Consequently, the single variable V5 is sufficient to satisfy the back-door criterion, which implies the following conditional independence condition is verified: V1 ⊥ Y | {V5 } in GV1 (9)

15

2.5. Observational distributions All of the required observational distributions appearing on the r.h.s. of Eq. (5) and Eq. (8) where derived by direct querying of the Bayesian network, including the conditional probability distribution P (Y | V7 ), shown here in Figure 5 for comparison with its postinterventional counterpart P (Y | do(V7 )). To ensure the precision of these results, these observational queries were computed using Variable Elimination (VE), a recursive algorithm designed for inference in probabilistic graphical models [44]. VE simplifies the computation of marginal and conditional probabilities by iteratively marginalising out non-queried variables and combining the resulting potentials until only the target distribution remains. For this study, the Bayesian network modelling and the VE exact inference algorithm were implemented using the pyAgrum Python library [45]. Unlike approximate inference methods such as those based on Markov Chain Monte Carlo (MCMC) sampling, VE yields exact results, meaning that the output is a closed-form solution derived directly from the network’s factorised joint distribution (Eq. (1)). As such they are not subject to approximation errors arising from sampling variability or convergence criteria. 3. Results 3.1. Causal effect of parking provision The causal effects of providing off-street parking across the four categories of EV ownership status and intention (Y ) are illustrated in Figure 5. These results provide the empirical basis for addressing RQ1 regarding the structural influence of parking provision on EV adoption. Specifically, Figure 5-a visualises the overall post-treatment probability distribution P (Y | do(V7 )) whereas in Figure 5-c it is shown the treatment effect ∆T E , measured as a contrast (difference) between the control state do(V7 = off-street) and treatment state do(V7 = on-street): ∆T E = P (Y | do(V7 = off-street)) − P (Y | do(V7 = on-street))

(10)

With reference to Figure 5-c, we can therefore observe that enabling a household to access off-street parking yields a +2.3 percentage point (pp) probability lift in the “Already own” category, alongside a +2.7 pp lift in immediate intent (“Thinking to buy one soon”). Conversely, this intervention produces a distinct -5.5 pp contraction in the “Thinking to buy in the future” category. Notably, the probability score for the “Not considering to buy one” category remains essentially stable, with an almost negligible shift of approximately +0.5 pp from a baseline probability of 48.7% (i.e., ≈ 1% change in relative terms). We interpret this negligible shift as statistical noise inherent to the network’s sensitivity rather than a meaningful causal effect (see section 4.1.1). Although these estimated lifts of +2.3 pp (already own) and +2.7 pp (thinking to buy soon) may appear modest in absolute terms, their magnitude is substantial when evaluated relative to the corresponding baseline probabilities: as shown in Figure 5-a, in the absence of off-street parking, the probability of already owning an EV (in Scotland, 2022) is only 3.34%; enabling off-street parking would increase this to 5.63%, which corresponds to an approximate 70% relative increase in EV ownership probability. A similar proportional amplification is observed for immediate purchase intent. Hence, while the absolute probability shifts are 16

numerically small, they represent sizeable relative gains within categories that are initially characterised by low baseline prevalence within the population. Importantly, these proportional increases do not arise in isolation, but correspond to a systematic reallocation of probability mass across EV adoption categories. The distribution of the treatment effects ∆T E therefore indicates a clear directional shift towards earlier EV adoption. Specifically, the combined +5.0 pp increase in immediate intent (2.7 pp) and ownership (2.3 pp) is largely offset by a -5.5 pp contraction in the “Thinking to buy in the future” category under the intervention. This pattern is consistent with a redistribution of probability mass from latent, long-term intent toward more advanced intentions of adoption, rather than a decline in overall interest. As a result, the near-zero treatment effect for the “Not considering to buy” category suggests that, at the aggregate level, lack of off-street parking is unlikely to be an important constraint for households that report no intention to adopt an EV. This distinction becomes critically apparent when comparing the causal treatment effect against the raw observational metrics, a comparison necessitated by RQ3. If, instead of estimating ∆T E , we had based our analysis on the observational probability shift of EV uptake conditional on parking provision: ∆obs. = P (Y | V7 = off-street) − P (Y | V7 = on-street)

(11)

we would have erroneously concluded that off-street parking access exerts an influence (however small) in pulling households away from the “Not considering to buy” category. As visualised in Figures 5-b and 5-d, the observational difference ∆obs. yields a -2.2 pp reduction for this cohort. However, this is merely a spurious association arising from confounding bias, due to the influence of variables like income (V1 ) and wealth (U2 ) which simultaneously affect both housing choice and vehicle preference. This divergence confirms the hypothesis in RQ3; that relying on observational data alone would mislead policymakers to overestimate the impact of policies aimed at recreating the off-street charging ‘experience’ (such as cross-pavement charging grants) on the most disengaged households while underestimating the deeper socio-economic barriers to market entry. 3.2. Causal effect of income While the effect invariance of the “Not considering to buy” cohort to parking interventions indicates that off-street parking availability is not a major barrier, it also points toward a more fundamental constraint. As the DAG in Figure 3 illustrates, the total causal effect of household income (V1 ) on EV adoption (Y ) is bipartite: first, there is a direct causal influence (V1 → Y ), representing the raw financial capacity to clear the higher entry cost of an electric vehicle; second, there is an indirect influence mediated by parking provision (V1 · · · → V7 → Y ). This latter path reflects a critical socio-economic reality: higher income is a common cause of residing in a dwelling type (V8 ) that facilitates off-street parking (V7 ), which in turn enables EV adoption (Y ). With reference to Figure 6, by estimating the total causal effect of an income intervention as: ∆T E,Inc. = P (Y | do(V1 = high-inc.)) − P (Y | do(V1 = low-inc.)) 17

(12)

Figure 5: Probability distributions of EV adoption status and intentions (Y ) as a result of intervening or observing parking provision (V7 ). (a) Post-intervention probability distributions comparing households with and without off-street parking. (b) Raw observational probability distributions. (c) Causal treatment effects (∆T E ), illustrating the redistribution of probability mass from future intent toward immediate intent and ownership. (d) Observational shifts (∆obs. ), highlighting the selection bias in the “Not considering to buy one” category (-2.2 pp) which is absent in the causal estimation.

we observe a substantial -23.1 pp contraction in the probability of the “Not considering to buy” category. Crucially, and in marked contrast to the parking provision results, this probability mass is mostly converted into future intent (+13.3 pp), thus signalling that income is the primary lever for shifting households from non-participation to latent interest. These findings highlight a clear structural hierarchy that addresses RQ2: while parking provision acts as a catalyst to accelerate and convert latent intent into realised ownership, income serves as the fundamental prerequisite for entering the EV adoption pipeline. This confirms that for the “Not considering” cohort, the primary barrier is not the so-called charging divide but an 18

Figure 6: Total causal effect of household income (V1 ) on EV adoption (Y ). (a) Post-intervention distributions comparing high vs. low income. (b) Total treatment effect (∆T E,Inc. ) accounting for both direct affordability (V1 → Y ) and indirect mediation (V1 · · · → V7 → Y ). The -23.1 pp drop in non-participation and +13.3 pp rise in future intent indicate income as the primary driver for joining the EV adoption process.

affordability ceiling that must be cleared before infrastructural interventions become relevant. 4. Refutation tests Estimating causal effects relies on structural assumptions about the underlying datagenerating process (see Methods section 2). Crucially, even when a causal graph is discovered from data, the resulting graph structure remains a model-based hypothesis of the invariant laws governing reality. These laws are, by definition, inaccessible; we only have access to the data they generate. This creates a distinct challenge compared to predictive machine learning. In prediction, cross-validation allows for performance evaluation against observed labels 19

(the ground ‘truth’). In causal inference, such direct validation is impossible because the underlying data-generating process —i.e., the ground-truth mechanism we aim to benchmark our model against— is never directly observed. To address this challenge, we follow on the work by Sharma et al. [46], which builds on the philosophical principle of falsifiability [47]. According to this principle, scientific claims cannot be definitively proven; instead, their credibility increases when they withstand systematic attempts at refutation. Following this perspective, we implement a series of refutation tests to assess the robustness of our causal model. These tests examine whether the estimated treatment effects align with the theoretical expectation required for the model to yield valid causal conclusions. The specific expectations vary by test and are detailed in the subsections that follow. 4.1. Placebo treatment test We conduct a placebo treatment test [48] by randomly permuting the values of the treatment variable V7 within the training dataset. Specifically, each household unit is assigned a treatment value v7 drawn at random from the original dataset, thereby redistributing treatment values across units. This procedure replaces the original treatment variable V7 with a randomized counterpart, V7,placebo , effectively ‘breaking’ any causal relationship between V7 and its child variables Y, V2 , while maintaining its marginal probability distribution: P (V7,placebo ) = P (V7 ) P (Y, V2 | V7,placebo ) ̸= P (Y, V2 | V7 )

(13)

We then assess the estimated causal effect of parking provision on EV uptake within this placebo framework. Under valid causal assumptions, the theoretical expectation is that the model should produce a null treatment effect, ∆T E , when the treatment is randomised. Although this test does not directly evaluate the estimated treatment effect, ∆T E , finding a significant effect where none should exist would call the model’s validity into question, and thus its estimate as well. Formally, we state the following null hypothesis: the estimated true treatment effect of parking provision on the probability increase of owning an electric car or van (δT E = +2.3 pp) is not statistically distinguishable from the effect of a random noise (placebo) treatment, δplacebo . To evaluate this hypothesis, we repeat the random reassignment procedure n times, generating n = 1000 separate placebo datasets. For each i-th dataset, we estimate the corresponding placebo treatment effect, δi,placebo . These estimates are then used to construct a reference distribution under the null hypothesis. A p-value is then calculated by comparing the magnitude of δT E with the empirical distribution of the placebo effects: P 1 + ni=1 I(|δi,placebo | ≥ |δT E |) (14) p-value = 1+n where I(·) is the indicator function that counts the number of i instances of δplacebo that are as extreme as the estimated true effect, δT E . In other words, the p-value represents the probability of observing a placebo treatment effect at least as large as δT E under the null hypothesis that the treatment has no causal effect on the outcome. As such, the resulting pvalue = 0.024 (second column of Table 2) provides strong evidence against the null hypothesis. 20

Table 2: Robustness checks for the estimated treatment effect of parking provision on the probability lift of owning an electric car or van (δT E ) and the lift in probability of not considering to buy one (δT′ E ). The placebo test (columns 2–3) evaluates whether a treatment effect persists when the treatment values are randomly reassigned. The subsample test (column 4) assesses the stability of the estimate across random subsamples (≈ 80% of the full training dataset). Columns 5–6 report the baseline estimates of the true causal effect.

Mean Median Perc. (1st; 99th) p-value Sample size n

δplacebo

′ δplacebo

δsub.

δT E (baseline)

δT′ E (baseline)

−0.021 pp −0.020 pp (−2.48; +2.34) 0.024 1000

+0.008 pp −0.011 pp (−4.98; +5.48) 0.817 1000

+2.292 pp +2.303 pp (+1.20; +3.41) 0.983 1000

+2.3 pp

+0.5 pp

Additionally, Table 2 reports the mean and median of the empirical distribution of δplacebo , both close to zero (≈ −0.02 percentage points), whereas the estimated true effect, δT E = +2.3 percentage points, is substantially larger in comparison. 4.1.1. Sensitivity analysis of non-significant probability shift While the low p-value (= 0.024) for the “Already own electric car/van” category validates the presence of a robust causal signal, we apply the same placebo test to the negligible shift observed in the “Not considering to buy one” category (δT′ E = +0.5 pp). In this context, we state the following null hypothesis: the estimated treatment effect of parking provision on the most disengaged cohort (δT′ E ) is not statistically distinguishable from the effect of ′ . Unlike the previous placebo treatment test, a random noise (placebo) treatment, δplacebo whereby the objective was to reject the null hypothesis via a low p-value, now we seeks to demonstrate that the estimated true effect δT′ E is statistically indistinguishable from zero. Accordingly, the theoretical expectation for this negative control is a high p-value, indicating that the observed shift falls well within the high-density region of the null distribution. This p-value is computed again via Eq. (14) but substituting the categorical treatment effect δT E ′ . with δT′ E and the placebo effects δi,placebo with δi,placebo Upon re-execution with n = 1000 placebo datasets, the equation yields a p-value = 0.817, meaning that a probability shift as extreme as ±0.5 pp occurs in approximately 82% of the randomly permuted datasets, where no causal relationship exists. Consequently, we fail to reject the null hypothesis for this category, thus supporting our interpretation that the +0.5 pp lift is due to sampling variance within the learned network parameters (CPTs) rather than the result of an invariant causal mechanism. 4.2. Data subsample test This refutation test evaluates the robustness of the estimated effect of parking provision by assessing its sensitivity to variations in the training dataset through repeated random subsampling. Specifically, we generate n = 1000 random subsamples from the full training dataset, each containing approximately 80% of the household units, and compute the corresponding treatment effect estimate, δi,sub. , for each iteration. This procedure yields an empirical distribution of subsample-based estimates, δsub. , against which the full-sample estimate, δT E , is compared. The underlying intuition is that a stable 21

estimate should not be overly influenced by any specific subset of the data and should, therefore, lie well within the range of the subsample-based distribution. Formally, we test the null hypothesis that the full-sample effect is not significantly different from the effects estimated across these random draws. In this context, a high p-value is desirable as it indicates that the full-sample estimate’s position relative to the mean of the subsamples is consistent with random sampling variability. The p-value is calculated as: P ∗ ∗ 1 + ni=1 I(|δi,sub. − δsub. | ≥ |δT E − δsub. |) (15) p-value = 1+n where: - δi,sub. is the treatment effect estimated from the i-th subsample dataset; ∗ - δsub. is the mean of effect estimates of the n subsample datasets;

- δT E is the effect estimate obtained from the full dataset; - I(·) is the indicator function that counts how many subsample deviations from the mean equal or exceed the deviation of the full-sample estimate from that same mean. Retaining the null hypothesis (evidenced by a high p-value, possibly close to 1) strengthens the credibility of the causal estimate by demonstrating that it is not hypersensitive to any particular partition of the training data. As reported in the fourth column of Table 2, the estimated full-sample effect of δT E = +2.3 pp lies well within the empirical distribution and is nearly identical to the distribution’s mean and median. The resulting p-value of 0.983 confirms that the full-sample estimate is not an outlier relative to the observed subsample variability; consequently, we fail to reject the null hypothesis, providing strong evidence of the estimate’s stability. 4.3. Sensitivity analysis to omitted variable bias While the placebo and subsample tests provide empirical evidence of robustness within the observed data and assumed unobserved confounders, a more fundamental issue concerns the possibility of having omitted a confounded. By definition, such confounder cannot be tested directly, yet it may still bias causal estimates if an omitted variable affects both treatment assignment and outcomes (V7 ← U → Y ). To assess this risk, we conduct a sensitivity analysis that examines how strong such a confounder would need to be to fully explain away (i.e., eliminate) the estimated treatment effect ∆T E , Eq. (10). Although the presence of such a confounder is purely hypothetical and ultimately unknowable (potentially representing one, multiple, or no factor at all), for the sake of argument we might posit that Environmentalism (U ) functions as a latent confounder, simultaneously increasing the likelihood of EV ownership and the propensity to reside in more rural areas, where off-street parking is structurally more common. To note: this skeptical line of reasoning runs counter to the (arguably more convincing) view that environmentally conscious individuals choose dense urban areas in order to minimise their ecological footprint. If this is the case, the true causal effect of parking provision on EV ownership would be even larger than our current estimate ∆T E . 22

We now express the identified causal effect of parking provision on EV ownership as a risk ratio (RR), defined in terms of post-intervention probabilities: RRP arking =

P (Y = already-own | do(V7 = off-street) 5.63% = = 1.685 P (Y = already-own | do(V7 = on-street) 3.34%

(16)

To test this ≈ +70% causal effect increase we use the E-value metric introduced by VanderWeele & Ding [49]. This approach is particularly powerful because it is fully non-parametric, hence making no assumptions about the functional form of the association between U and the treatment (and outcome) variables. The E-value is defined as the minimum strength of association an unmeasured confounder must have with both the treatment and the outcome, on the risk ratio scale, to explain away the RR as a null effect: E-value = RR +

p RR(RR − 1)

(17)

By plugging in the above formula the RRP arking value obtained via Eq. (16) we obtain an E-value = 2.76. This means that for a hypothetical confounder like Environmentalism to explain away our results, it would need to increase the likelihood of both having off-street parking and owning an EV by more than 270%. To evaluate the plausibility of such a magnitude, we benchmark it against the estimated causal effect of income, the primary socio-economic driver in our model, expressed this time on the risk ratio scale: RRIncome =

7.47% P (Y = already-own | do(V1 = high-inc.) = = 3.73 P (Y = already-own | do(V1 = low-inc.) 2.00%

(18)

While the required bias (2.76) is numerically lower than the effect of income on EV ownership (3.73), it still represents a prohibitive threshold for any latent factor (such as environmentalism) to overcome. For a hypothetical confounder to nullify the observed effect of parking provision, it would need to exert a simultaneous causal influence on both EV ownership and parking provision equivalent to nearly three-quarters of a household’s financial capacity. Furthermore, because the graph discovery algorithm failed to detect a latent signature (V7 ↔ Y ), it is highly improbable that an omitted variable could be sufficiently strong to overturn the identified direct effect of parking provision (V7 → Y ) as a primary causal determinant of EV adoption. 5. Conclusions The transition to electric mobility represents a critical pathway toward achieving net-zero emissions, yet its success hinges on equitable access rather than mere aggregate adoption. This study addressed a fundamental gap in the existing literature: determining whether the stark ‘charging divide’ observed between households with and without off-street parking is primarily a function of physical infrastructure constraints or a by-product of underlying socio-economic disparities. Methodologically, this research represents a novel departure from traditional transport modelling. By framing the problem within a probabilistic causal framework and applying it to a nationally representative dataset of Scottish households, we moved beyond predictive associations to quantify the interventional effect of residential parking provision. This 23

approach allows for a level of analytical rigour that traditional regression analysis cannot achieve: the ability to simulate policy interventions directly from observational data while explicitly neutralising the influence of confounding variables (whether latent or observed). Our causal analysis directly addressed the three primary research questions outlined in this study through a clear structural hierarchy: - The conversion catalyst (RQ1): we demonstrated that the absence of private off-street parking imposes a distinct, quantifiable ‘adoption penalty’ on households. By controlling for back-door paths, the model confirms that parking access is not merely correlated with EV uptake, but acts as a direct causal catalyst. Specifically, enabling off-street parking yields a 70% relative increase in the probability of EV ownership (moving from 3.3% to 5.6%). However, this effect is largely a conversion mechanism; the +5.0 pp gain in immediate intent and ownership is almost entirely offset by a -5.5 pp contraction in future intent to buy an EV, suggesting that parking access accelerates those already embarked on the EV conversion journey rather than recruiting new participants. - The affordability ceiling (RQ2): while parking provision facilitates the final stages of EV adoption, our findings indicate that household income serves as the fundamental gatekeeper for entering the EV market. An simulated intervention on income produced a substantial -23.1 pp drop in the “Not considering to buy [an EV]” category, with the majority of that mass shifting into future intent to buy (+13.3 pp). This identifies a clear affordability ceiling: for the nearly 50% of the Scottish population not engaged with the EV market, the primary barrier is financial capacity rather than the immediate lack of an off-street parking spot. - The necessity of causal inference (RQ3): our comparison between observational probabilities and interventional probabilities highlights the risks of relying on purely predictive (and often black-box) algorithms for decision making. Machine learning models trained with the sole purpose of predicting observational outcomes would erroneously suggest that investing in on-street home-charging infrastructure would reduce nonparticipation in the EV market. Our model reveals this is a statistical artifact of confounding bias; wealthy households are simply more likely to possess both the income to consider an EV and the dwelling type to park it. Mistaking this correlation for a causal effect risks leading policymakers to over-invest in infrastructure for cohorts who have not yet cleared the financial hurdles of entering the EV market. These findings suggest that a one-size-fits-all approach to EV promotion may be inefficient. Instead, Scottish policy could reflect the different structural barriers faced by households at different stages of the EV adoption journey. For households currently outside the market, the results suggest that affordability remains the primary bottleneck. Until the high entry cost of EVs is addressed (perhaps through broader secondary market support or targeted financial incentives) infrastructural interventions like on-street charging grants may see limited engagement from this cohort. Conversely, for the ‘latent intent’ group (those who intend to buy but are stalled in the ‘future’ category) the charging divide is the definitive barrier. In high-density urban environments like Glasgow or Edinburgh, where tenements currently preclude domestic charging, qualitative policy shifts toward expanding public charging 24

density and cross-pavement solutions are essential. By recognising income as the gatekeeper and parking as the catalyst, policymakers can design a more nuanced, equitable transition that addresses both the financial prerequisites and the physical constraints of the Scottish dwelling population. 6. Data and code availability All data and code developed for this study are publicly available and can be accessed via the referenced GitHub repository [50]. 7. Acknowledgements The authors express their gratitude to the School of Computing, Engineering & the Built Environment (SCEBE) at Edinburgh Napier University for providing the support and resources necessary for the completion of this research. References [1] Transport Scotland, National Transport Strategy (NTS2) Second Annual Delivery Plan 2021-2022, Tech. rep., Scottish Government, Edinburgh, UK, accessed: 2026-03-10 (2021). URL https://www.transport.gov.scot/publication/national-trans port-strategy-nts2-second-delivery-plan-2022-2023/ [2] G. Hutton, I. Stewart, M. Benson, D. Webb, I. Jozepa, Electric vehicles and infrastructure, Research Briefing CBP-7480, House of Commons Library, London, UK (June 2025). [3] Scottish Government, Scotland’s Climate Change Plan 2026–2040, Draft strategy and consultation, The Scottish Government, Edinburgh, Scotland, iSBN: 978-1-80643-352-0 (November 2025). [4] A. M. Varghese, N. Menon, A. Ermagun, Equitable distribution of electric vehicle charging infrastructure: A systematic review, Renewable and Sustainable Energy Reviews 206 (2024) 114825. [5] M. Kuby, A. Cordova-Cruzatty, N. Parker, D. King, EV charging for multifamily housing: Review of evidence, methods, barriers, and opportunities, Renewable and Sustainable Energy Reviews 210 (2025) 115253. [6] Electric Vehicle Association England (EVA England), Steer the Conversation: EVA England Survey Report 2025, Tech. rep., survey report, published October 2025 (2025). [7] R. Zhang, N. Horesh, E. Kontou, Y. Zhou, Electric vehicle community charging hubs in multi-unit dwellings: Scheduling and techno-economic assessment, Transportation Research Part D: Transport and Environment 120 (2023) 103776.

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PMLR, 2020, pp. 609–612. URL https://proceedings.mlr.press/v138/ducamp20a.html [46] A. Sharma, V. Syrgkanis, C. Zhang, E. Kıcıman, Dowhy: Addressing challenges in expressing and validating causal assumptions, arXiv preprint arXiv:2108.13518 (2021). doi:https://doi.org/10.48550/arXiv.2108.13518. [47] K. R. Popper, The Logic of Scientific Discovery, Routledge, London, 1934. doi:https: //doi.org/10.4324/9780203994627. [48] A. C. Eggers, G. Tuñón, A. Dafoe, Placebo tests for causal inference, American Journal of Political Science 68 (3) (2024) 1106–1121. doi:https://doi.org/10.1111/aj ps.12818. [49] T. J. VanderWeele, P. Ding, Sensitivity analysis in observational research: introducing the E-value, Annals of internal medicine 167 (4) (2017) 268–274. [50] B. D’Amico, Github repository (2026). URL https://github.com/bernardinodamico/Causal_barriers-EV_up take [51] J. Rissanen, Fisher information and the stochastic complexity, IEEE Transactions on Information Theory 42 (1) (1996) 40–47. doi:10.1109/18.481776. [52] C. Meek, Causal inference and causal explanation with background knowledge, in: Proceedings of the Eleventh Conference on Uncertainty in Artificial Intelligence (UAI), Morgan Kaufmann Publishers Inc., 1995, pp. 403–410. Appendix A. Table A1: Mapping between the 9-fold classification for the Parking Provision variable, V7 , (as reported in the SHCS dataset) and the corresponding binary classification {Off-street; On-street}.

9-fold classification Integral/attached garage Garage on plot Space on plot Space/garage elsewhere Adequate, on-street Inadequate on-street No parking provision Not Applicable Unobtainable

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2-fold classification Off-street Off-street Off-street Off-street On-street On-street — — —

Table A2: Set V = {Y, V1 , ..., V14 } of observed variables used to discover and then train the model parameters of the causal Bayesian Network. Variable label

Variable symbol

EV ownership status & intention

Y

Household income

V1

No. of vehicles

V2

No. of adults in household

V3

No. of children in household

V4

Household composition

V5

Urban/rural classification

V6

Parking provision

V7

Dwelling type

V8

Dwelling age

V9

Workplace charging infrastructure density (normalised per 100,000 residents)

V10

Public charging infrastructure density (normalised per 100,000 residents)

V11

Household working status

V12

Value states

Already own electric car/van; Thinking to buy one soon; Thinking to buy one in the future; Not considering to buy one; < £6000; £6001-10,000; £10,001-15,000; £15,001-20,000; £20,001-25,000; £25,001-30,000; £30,001-40,000; > £40,000; No car; One car; Two cars or more; 1; 2; 3; 4; ≥ 5; 0; 1; 2; 3; ≥ 4; Single adult; Small - multiple adults; Single parent; Small - family; Large - family; Large - multiple adults; Small - old adults; Single pensioner; Urban; Rural; Off-street; On-street; Detached house; Semi-detached house; Terraced house; Tenement flat; 4-in-a-block flat; Tower/slab flat; Flat from converted house; < 1919; 1919-1944; 1945-1964; 1965-1982; 1983-2002; > 2002; < 20; 21-40; 41-60; 61-80; > 80; < 50; 51-100; 101-150; 151-200; > 200; One or more working adults; None working;

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Probability distribution P (·) 0.0485 0.0462 0.4149 0.4904 0.0202 0.0364 0.0786 0.1358 0.1079 0.1064 0.1602 0.3546 0.0719 0.6157 0.3124 0.3668 0.5400 0.0705 0.0211 0.0017 0.7764 0.1149 0.0871 0.0161 0.0055 0.1759 0.2149 0.0901 0.1029 0.0289 0.0615 0.2030 0.1227 0.8069 0.1931 0.6516 0.3484 0.2573 0.2276 0.2073 0.1657 0.0765 0.0327 0.0329 0.2114 0.1093 0.1615 0.2214 0.1493 0.1471 0.0821 0.3346 0.4562 0.0910 0.0361 0.2048 0.5949 0.1537 0.0438 0.0028 0.6664 0.3336

Table A2 (continued) Variable name

Variable symbol

Tenancy

V13

Local Authority (LA)

V14

Value states

Owned (outright or mortgage); Part mortgage, part rent; Rented (LA, Co-op, private landlord;) South Ayrshire; South Lanarkshire; Stirling; West Dunbartonshire; West Lothian; Na h-Eileanan Siar; Aberdeen City; Aberdeenshire; Angus; Argyll and Bute; Scottish Borders; Clackmannanshire; Dumfries and Galloway; Dundee City; East Ayrshire; East Dunbartonshire; East Lothian; East Renfrewshire; City of Edinburgh; Falkirk; Fife; Glasgow City; Highland; Inverclyde; Midlothian; Moray; North Ayrshire; North Lanarkshire; Orkney Islands; Perth and Kinross; Renfrewshire; Shetland Islands;

Probability distribution P (·) 0.7354 0.0041 0.2605 0.0266 0.0638 0.0178 0.0205 0.0383 0.0078 0.0466 0.0433 0.0216 0.0211 0.0228 0.0072 0.0266 0.0244 0.0250 0.0183 0.0182 0.0117 0.1077 0.0327 0.0527 0.1038 0.0411 0.0128 0.0172 0.0183 0.0178 0.0594 0.0028 0.0333 0.0316 0.0072

Appendix B. This appendix provides a brief technical note on the information-theoretic causal discovery algorithm introduced in section 2.3. For a comprehensive description of the methodology, the reader is referred to the original works of Verny et al. [41], who introduced the MIIC framework, and Ribeiro-Dantas et al. [42], who further developed and applied it to large-scale datasets. Appendix B.1. Information-theoretic-driven causal discovery The MIIC framework identifies the skeleton of the causal graph by systematically evaluating the information flow between variable pairs using information-theoretic metrics. Mutual information (MI) is a non-negative measure of association (e.g. in units such as bits) shared between two random variables X and Y :   X P (x, y) I(X; Y ) = P (x, y) log (B.1) P (x) P (y) x,y where the ratio inside the logarithm compares the joint probability of the event {X = x, Y = y} to the product of the corresponding marginal probabilities. If X and Y are independent, 31

this ratio equals 1, and hence the logarithm evaluates to 0. The double summation in Eq. (B.1) aggregates the information gain across all possible states (values) of X and Y . Unlike statistical independence tests, which provide a binary ({true, false}) assessment of dependence, MI provides a continuous, non-negative measure of association strength ∈ [0, ∞). Similarly, conditional MI measures the amount of information shared between X and Y given that a third variable Z is being observed:   X P (x, y | z) (B.2) I(X; Y | Z) = P (x, y, z) log P (x | z) P (y | z) x,y,z If X and Y are conditionally independent given Z, then I(X; Y | Z) ≈ 0, reflecting the absence of any shared information between X and Y once the influence of Z has been accounted for, meaning, any dependence between X and Y is entirely explained away by their mutual relationship with Z. Like for mutual information, conditional mutual information is a continuous, non-negative measure. Appendix B.2. Iterative skeleton pruning As for any constraint-based causal discovery algorithm, MIIC starts with a fully connected graph, representing the initial hypothesis that every pair of variables might be dependent upon each other (see Figure 2-a). The algorithm then evaluates the conditional MI for every variable pair to determine if their association is direct or mediated by other variables. Unlike traditional methods that may test all possible combinations of variables to condition on (an approach that becomes computationally unfeasible as the network grows) MIIC employs a greedy, iterative decomposition strategy [42]: for each pair (X, Y ), the algorithm searches for a set of contributors {Zi } that explain away the shared information between them. Crucially, a contributor Zi is only accepted if the value of the interaction information is positive, thus signalling the signature of a chain (e.g., X → Zi → Y ) or common cause (X ← Zi → Y ). To build intuition, let us consider the simplest case of a three-node fully connected skeleton as shown in Figure B.1-a. Here, we can express the MI between X and Y as the sum of a conditional MI contribution and an interaction MI contribution: I(X; Y ) = I(X; Y | Z) + I(X; Y ; Z)

(B.3)

noting that I(X; Y | Z) measures the information ‘flow’ shared via the direct edge X − Y whereas I(X; Y ; Z) accounts for the association between X and Y flowing across the indirect path X − Z − Y . As per Eq. (B.3), when the interaction information term I(X; Y ; Z) is negative, it follows that the conditional information I(X; Y | Z) is larger than the overall MI I(X; Y ). The only case when conditioning on a third variable Z increases the direct flow of association, via the X − Y edge, it is when both X and Y are common-causes of Z, namely, Z is a collider: X → Z ← Y (Figure B.1-c). Since this step aims to identify variables that explain away (reduce) the association between X and Y , colliders are rejected from the conditioning set {Zi } to avoid introducing biased dependencies. In more realistic networks involving a large number of variables, the algorithms generalises this principle, eventually isolating the unbiased direct association I(X; Y | {Zi }) for every X − Y edge in the network. 32

Figure B.1: Information-theoretic signatures of causality in a three-node skeleton. (a) Initial skeleton: the MIIC algorithm starts with an undirected graph where I(X; Y ) represents the total association between X and Y . (b) Interaction information I(X; Y ; Z) > 0 is a signature of a causal chain or common cause. In these patterns, Z explains part of the mutual information, reducing the residual conditional mutual information between X and Y . (c) Interaction information I(X; Y ; Z) < 0 is a signature of a collider (v-structure). Conditioning on Z increases the conditional mutual information between X and Y , leading to its rejection from the conditioning set {Zi } during skeleton pruning.

Having quantified the unbiased association strength for every edge, to determine whether this remaining associations represent genuine causal relations or mere sampling noise, their strength is measured against a dynamic complexity threshold: an edge is retained only if its conditional MI exceeds the cost of adding that specific dependency to the model, namely, if I(X; Y | {Zi }) > CN M L (X, Y | {Zi })/N . The term CN M L denotes the Normalised Maximum Likelihood complexity [51], which quantifies a model’s inherent capacity to fit many data patterns. Appendix B.3. Edge orientation and latent variables identification After obtaining the pruned skeleton, the next step entails determining causal flow via edges orientation. All unshielded node triples ⟨X; Z; Y ⟩ (sets of nodes where X and Y are both adjacent to Z but are not adjacent to each other) are evaluated to identify the presence of a v-structure. Because in those triples X and Y are non-adjacent, Z must act as a mediator, a common cause, or a collider. For each triple, the correct orientation is established based on interaction mutual information signatures. To build intuition, let us reconsider the 3-node example in Figure B.1-a, assuming now the direct edge X − Y was removed during pruning. If the interaction term I(X; Y ; Z) < 0, it follows that X and Y are independent but become dependent upon conditioning on Z, implying a signature of causality for a v-structure, hence arrowheads are placed pointing toward the mid-node (X → Z ← Y ). Conversely, a positive interaction term, I(X; Y ; Z) > 0, would indicate redundancy, meaning Z is either a mediator (X → Z → Y or X ← Z ← Y ) or a common cause (X ← Z → Y ). Because these latter patterns are Markov equivalent, their edge orientation cannot be established via the interaction information signatures, nonetheless, following the local orientation of already identified v-structures, Meek’s rules [52] are applied to propagate the remaining undirected edges. These rules essentially prevent propagating ‘illegal’ v-structures and enforce the acyclicity condition. For example, if the mid-node in the partially directed triple X → Z − Y was already identified not to be a collider, then Z − Y must be oriented as Z → Y in order to prevent the creation of an illegal v-structure. Similarly, if orienting an edge in one direction would create a closed loop, that orientation is rejected, and the edge is oriented in the opposite direction to maintain acyclic causal flow. Crucially, some of the edges may remain undirected even after these propagation rules are applied, representing a fundamental limit of discovering causal structure purely from ob33

servational data. As such, the algorithm preserves the undirected edges in returning the final output, a Maximal Ancestral Graph (MAG), along with directed edges (→) and bi-directed edges (↔). These latter are introduced when a dependency X −Y cannot be explained by any observed variable, yet the orientation signatures for the pair are contradictory. For instance if discovered v-structures and subsequent propagation rules suggest a arrowhead pointing away from both X and from Y in the following pattern: → X − Y ←, rather than forcing a directed relationship which would either introduce illegal v-structures or create cycles, the algorithm assigns a bi-directed edge ↔ to indicate that X and Y share a hidden (latent) parent U (→ X ← U → Y ←). Appendix C. Appendix C.1. Back-door paths in GV7 The following 24 simple back-door paths are identified in the mutilated graph GV7 . They are categorised into two groups based on their initial topological segments. Group 1: paths starting with chain segments (V7 ← V8 ← . . . Y ): 1: (V7 , V8 , V13 , V1 , Y ) 2: (V7 , V8 , V13 , V5 , V1 , Y ) 3: (V7 , V8 , V13 , V5 , V12 , V1 , Y ) 4: (V7 , V8 , V13 , V5 , V2 , V1 , Y ) 5: (V7 , V8 , V13 , V5 , V2 , U1 , V1 , Y ) 6: (V7 , V8 , V1 , Y ) 7: (V7 , V8 , V5 , V1 , Y ) 8: (V7 , V8 , V5 , V13 , V1 , Y ) 9: (V7 , V8 , V5 , V12 , V1 , Y ) 10: (V7 , V8 , V5 , V2 , V1 , Y ) 11: (V7 , V8 , V5 , V2 , U1 , V1 , Y ) 12: (V7 , V8 , U2 , Y ) and Group 2: paths involving a collider segment (V7 ← V9 → V8 ← . . . Y ) with V8 as the mid-node: 13: (V7 , V9 , V8 , V13 , V1 , Y ) 14: (V7 , V9 , V8 , V13 , V5 , V1 , Y ) 15: (V7 , V9 , V8 , V13 , V5 , V12 , V1 , Y ) 16: (V7 , V9 , V8 , V13 , V5 , V2 , V1 , Y ) 17: (V7 , V9 , V8 , V13 , V5 , V2 , U1 , V1 , Y ) 18: (V7 , V9 , V8 , V1 , Y ) 19: (V7 , V9 , V8 , V5 , V1 , Y ) 20: (V7 , V9 , V8 , V5 , V13 , V1 , Y ) 21: (V7 , V9 , V8 , V5 , V12 , V1 , Y ) 22: (V7 , V9 , V8 , V5 , V2 , V1 , Y ) 23: (V7 , V9 , V8 , V5 , V2 , U1 , V1 , Y ) 24: (V7 , V9 , V8 , U2 , Y ) 34

Appendix C.2. Back-door paths in GV1 The following 27 simple back-door paths are identified in the mutilated graph GV1 . They are categorised into three groups based on their initial topological segments. Group 1: paths starting with chain segments (V1 ← V12 ← V5 → . . . Y ): 1: (V1 , V12 , V5 , V8 , V7 , Y ) 2: (V1 , V12 , V5 , V8 , V9 , V7 , Y ) 3: (V1 , V12 , V5 , V8 , U2 , Y ) 4: (V1 , V12 , V5 , V13 , V8 , V7 , Y ) 5: (V1 , V12 , V5 , V13 , V8 , V9 , V7 , Y ) 6: (V1 , V12 , V5 , V13 , V8 , U2 , Y ) 7: (V1 , V12 , V5 , V2 , V7 , V8 , U2 , Y ) 8: (V1 , V12 , V5 , V2 , V7 , Y ) 9: (V1 , V12 , V5 , V2 , V7 , V9 , V8 , U2 , Y ) Group 2: paths involving a fork segment (V1 ← V5 → . . . Y ) with V5 as the mid-node: 10: (V1 , V5 , V8 , V7 , Y ) 11: (V1 , V5 , V8 , V9 , V7 , Y ) 12: (V1 , V5 , V8 , U2 , Y ) 13: (V1 , V5 , V13 , V8 , V7 , Y ) 14: (V1 , V5 , V13 , V8 , V9 , V7 , Y ) 15: (V1 , V5 , V13 , V8 , U2 , Y ) 16: (V1 , V5 , V2 , V7 , V8 , U2 , Y ) 17: (V1 , V5 , V2 , V7 , Y ) 18: (V1 , V5 , V2 , V7 , V9 , V8 , U2 , Y ) and Group 3: paths involving a collider segment (V1 ← U1 → V2 ← . . . Y ) with V2 as the mid-node: 19: (V1 , U1 , V2 , V5 , V8 , V7 , Y ) 20: (V1 , U1 , V2 , V5 , V8 , V9 , V7 , Y ) 21: (V1 , U1 , V2 , V5 , V8 , U2 , Y ) 22: (V1 , U1 , V2 , V5 , V13 , V8 , V7 , Y ) 23: (V1 , U1 , V2 , V5 , V13 , V8 , V9 , V7 , Y ) 24: (V1 , U1 , V2 , V5 , V13 , V8 , U2 , Y ) 25: (V1 , U1 , V2 , V7 , V8 , U2 , Y ) 26: (V1 , U1 , V2 , V7 , Y ) 27: (V1 , U1 , V2 , V7 , V9 , V8 , U2 , Y )

35