This section begins by presenting the Conceptual framework, which identifies the explanatory and latent variables that influence the adoption of PV and/or EV. Subsequently, the Modelling approach, Data, and Sample description are described.

### Conceptual framework

Contents

In this paper, consumer choice to adopt PV and/or EV is explained using the exogenous explanatory variables and endogenous latent variables presented in the conceptual framework in Fig. 1. The choice is presented as a nominal dependent variable with four categories: (1) only adopting PV, (2) only adopting EV, (3) adopting both PV and EV, and (4) adopting none.

Figure 1

Based on the literature review, a set of socio-demographic and two latent variables representing the environmental attitude and technology attitude were used as determinants of the main outcome variable (PV or/and EV adoption). Sociodemographic characteristics are divided into individual-level (gender, age, and employment status), household-level (income, household size [continuous measure of the total number of individuals within each household], dwelling type, dwelling ownership, current change in work location, and residential location), and household energy and appliances (ownership of smart meter, energy management system, and electricity intensive appliances, such as a pool or multiple refrigerators) variables.

Constructs representing attitudes towards the environment and technology were extracted based on a factor analysis of eight attitudinal items elicited in the survey using 5-level Likert scales. The first latent variable, pro-environmental attitude, is used to capture how important climate change is to the consumer and their belief of having the power to change this issue by acting differently. This latent variable is relevant because it reflects the growing awareness and concern about environmental sustainability among individuals. As the effects of climate change become more apparent, consumers are increasingly recognising the need to adopt greener technologies and practices to mitigate its impact. Those with a stronger pro-environmental attitude are more likely to prioritise sustainable choices and seek out environmentally friendly alternatives. The second latent variable represents an individual’s interest in technology, specifically related to the adoption of new technologies and use of smart energy management. This latent variable is relevant because both PV and EV are emerging technologies, and it is expected that individuals with a positive technology attitude are more likely to embrace new technologies and recognize their potential benefits, making them more inclined to adopt PVs and EVs. By incorporating these latent variables into the analysis, we can examine the influence of environmental and technology attitudes on PV and EV adoption. Gaining insights into the underlying psychosocial factors that drive consumer behaviour enables policymakers and other stakeholders to design targeted interventions and strategies that encourage the adoption of sustainable technologies.

### Modelling approach

Considering the nominal discrete nature of the outcome and the latent constructs, we utilise an integrated choice and latent variable (ICLV) modelling approach. This model incorporates the effects of latent variables on choice behaviour, allowing researchers to explore how unobserved factors, such as attitudes or preferences, influence individuals’ decision-making processes. The ICLV model consists of two components: a discrete choice model and a latent variable model11. The components of the modelling framework are presented in Fig. 1. Next, we will present the mathematical formulation of the ICLV model39,40.

In our application, we have four distinct adoption groups and the discrete choice component of the model estimates the utility associated with belonging to each of these groups, taking into account the explanatory and latent variables. The utility derived by individual \(n\) when belonging to group \(i\) is described by Eq. (1).

$${U}_{n,i}= {V}_{n,i}+ {\epsilon }_{n,i}$$

(1)

Traditionally, in a discrete choice model, \({U}_{n,i}\) is the stochastic utility that is a function of the systematic utility \(({V}_{n,i})\) and an error term \({(\epsilon }_{n,i})\) following a type I extreme value distribution. However, in an ICLV, \({V}_{n,i}\) is also stochastic because of the random effects incorporated via latent variables, as represented in Eqs. (2) and (3).

$$V_{n,i} = \delta_{n,i} + \beta_{i} x_{n,i} + \lambda_{i} \alpha_{n,i}$$

(2)

where \({\delta }_{n,i}\) is an alternative specific constant, \({x}_{n,i}\) is the vector of observed variables, for example, sociodemographic variables (in this study we only have individual related explanatory variables and no alternative specific variables). \({\alpha }_{n,i}\) refers to latent variables, and \({\beta }_{i}\) and \({\lambda }_{i}\) are vectors of estimated coefficients.

The latent variable component of the model contains structural and measurement models. The structural model part is shown in Eq. (3) and it estimates a vector of parameters (\({\gamma }_{l})\) showing how sociodemographic variables \({(z}_{n})\) influence attitudes and preferences, which are represented by the latent variables (\({\alpha }_{n,l}\)), while \({\eta }_{n,l}\) is the associated random disturbance that follows a standard normal distribution across individuals (\(l\) =1,…, L, where L is the total number of latent variables, in our case 2).

$$\alpha_{n,l} = \gamma_{l} z_{n} + \eta_{n,l}$$

(3)

The measurement model part uses an ordered logit model to construct the latent variables based on the responses to 5-level Likert scale attitudinal indicators (\(s\)). The measurement model is presented in Eq. (4).

$$L_{{I_{n,s} }} = \mathop \sum \limits_{p = 1}^{5} \delta_{{I_{n,s,p} }} \left( { \frac{{e^{{\tau_{{I_{s,p} }} – \zeta_{l,s} \alpha_{n,l} }} }}{{1 + e^{{\tau_{{I_{s,p} }} – \zeta_{l,s} \alpha_{n,l} }} }} – \frac{{e^{{\tau_{{I_{s,p – 1} }} – \zeta_{l,s} \alpha_{n,l} }} }}{{1 + e^{{\tau_{{I_{s,p – 1} }} – \zeta_{l,s} \alpha_{n,l} }} }}} \right)$$

(4)

\({L}_{{I}_{n,s}}\) represents the likelihood of the observed value of an individual’s response \({I}_{n,s}\) to an indicator (\(s\)). \({\delta }_{{I}_{n,s,p}}\) takes the value of 1 if individual n selects response p (p: 1…,5) for indicator s. The parameter \({\tau }_{{I}_{s,p}}\) is estimated as the threshold value, where the normalisation condition for \({\tau }_{{I}_{s,0}}\) is set to -∞ and \({\tau }_{{I}_{s,5}}\) is set to + ∞ so that we estimate the four intermediate values. \({\zeta }_{l,s}\) estimates the impact of \({\alpha }_{l}\) on \({I}_{s}\). A significant estimate for \({\zeta }_{l,s}\) shows that the latent attitude \({\alpha }_{l}\) has a statistically significant impact on the answers provided to the attitudinal question \({I}_{s}\).

Equation 5 represents the equation that calculates the likelihood of individual n belonging to group \(i\), conditional on \({\alpha }_{n}\) and \(\beta\).

$$L_{{C_{n} }} \left( {\beta ,\alpha_{n} } \right) = \frac{{e^{{V_{n,i} }} }}{{\mathop \sum \nolimits_{j = 1}^{4} e^{{V_{n,j} }} }}$$

(5)

The joint log-likelihood of all model components is given in Eq. (6). Both of the model components, the component relating to the choice and the component related to attitudinal questions are a function of latent variable. This is why to jointly estimate these models, the entire likelihood function is integrated over the random component in the latent variable (\({\eta }_{n}\)). The Apollo R-programming package is utilized for estimating the ICLV model41.

$${\text{LL}}=\sum_{n=1}^{N}{\text{log}}\int {L}_{{C}_{n}}(\beta ,{\alpha }_{n})\prod_{s=1}^{8}{L}_{{I}_{n,s}} \Phi ({\eta }_{n})d{\eta }_{n}$$

(6)

To mitigate the potential for reaching local maxima during estimation, we utilised a search strategy recommended in the Apollo package41. This involved employing multiple starting points to systematically eliminate unlikely solutions and enhance the probability of discovering the optimal one.

### Data

The data used for this analysis is open source and were collected through a web-based survey conducted by Essential Research for Energy Consumers Australia in 2022. The target group for the survey consisted of individuals who are heads of households, aged 18 and above, and actively involved in decision-making regarding electricity and gas matters within their households across Australia. This survey is conducted annually and explores the attitudes and activity of residential energy consumers by asking questions about how they use power and energy technologies, their attitude to new technology, and their view on the future of energy. For further information, please refer to the details provided by Energy Consumers Australia on their website42. In this section, we highlight the survey aspects pertinent to the present analysis, as listed in section “Method and data”.

The choice variable is not the outcome of a direct question in the survey and is defined based on respondents’ PV and EV adoption status. PV and EV adoption were elicited separately using four possible options: (1) currently own, (2) intending to purchase in the next 12 months, (3) considering, but not intending to purchase in the next 12 months, and (4) not intending to purchase. To define the outcome variable of our model, respondents who owned, intended, and considered buying PV and EV were categorised as adopting both PV and EV, respondents who owned, intended, or considered buying EV but did not intend to purchase PV were categorised as only adopting EV. Analogously, respondents who owned, intended, or considered buying PV but did not intend to purchase an EV were categorised as only adopting PV. Lastly, respondents who did not intend to buy an PV nor an EV were categorised as adopting none. The decision to merge current adopters/owners with those intending and considering adoption was driven by the aim of obtaining a comprehensive understanding of the adoption landscape and the factors influencing adoption decisions across different stages. By solely focusing on current owners, we would miss out on understanding the needs and motivations of individuals who are considering and intending to adopt PV and/or EV technologies (and we would have a myopic perspective of early adopters only). By including them in the same category as current owners, we can develop more effective policies that consider the necessities of prospective adopters, potentially accelerating the overall adoption process. Additionally, merging these categories increases the sample size of the different groups, resulting in improved statistical power and analysis reliability (helping to mitigate biases that may arise from small sample sizes). This is particularly crucial in Australia, where the current number of EV owners is relatively low.

### Sample description

Table 1 presents the descriptive statistics of dependent and explanatory variables for the final clean sample, consisting of 2219 respondents. Most respondents are still not willing to adopt PVs or EVs, with the smallest group being those who are willing to adopt only EVs and not PVs. This pattern is expected in Australia, where EV adoption is lagging but PV adoption rates are relatively high (33%, according to the Australian PV Institute7).

Table 1 Descriptive statistics of dependent and explanatory variables.

According to the data providers, the sample is considered representative of the population of household heads in terms of age and gender. However, it is worth noting that we do not have access to the specific distribution of this population from Census data. Therefore, we compare the distribution of selected sociodemographic characteristics in the sample with that of the Australian driving age population43,44. The sample shows a slightly higher share of women and a lower share of young adults (between 18 and 34 years old) compared to the driving age population. This is an expected difference considering that the survey targeted individuals who make electricity-related decisions in the household. While the share of home owners and renters is equivalent to the population, we observe an underrepresentation of multi-unit building dwellers45. This limitation is particularly relevant to the problem investigated in this study because both PV installation and EV charging face more significant barriers in apartment complexes. An aggregate analysis based on this sample would thus be biased, but by using a disaggregate model that can capture both observed and unobserved individual heterogeneity we expect to extract important insights even for this underrepresented group.

Regarding household energy and appliances related variables, smart meter ownership rates are much higher than home energy management system ownership rates, with 40.7% of respondents having a smart meter and only 9.6% having an energy management system. The discrepancy in ownership rates between smart meters and home energy management systems in Australia can be largely attributed to the extensive rollout of smart meters facilitated by government initiatives and utility companies, especially in Victoria46. Additionally, the perceived benefits of smart meters, such as accurate and real-time energy usage information, maybe more widely recognized and valued by consumers compared to the advanced features offered by home energy management systems. A relatively low percentage of households own electricity-intensive appliances, with 11.8% owning swimming pools or spa pools and 22.5% having three or more refrigerators.

Table 2 displays the attitudinal indicators and their response distributions, which were measured on a five-point Likert scale. Respondents were asked to choose from five levels of agreement, from strongly disagree to strongly agree. For analysis purposes, we assigned a value of 5 to the highest level of favourable attitudes toward the environment and technology, and a value of 1 to the least favourable level. The last four indicators of environmental attitudes had their scale inverted to ensure that they were all capturing the underlying construct monotonically. Respondents generally express a desire for action on climate change issues. Regarding technology attitudes, only 6% consider themselves early adopters, while around 20% are strongly inclined to use technology to manage bills and learn about new ways of generating, storing, and distributing electricity.

Table 2 Frequency of response to ten attitudinal indicators.

### Factor analysis

We conducted an exploratory factor analysis using Principal Axis Factoring to examine the relationships among the indicators and identify latent variables. Two factors emerged, both demonstrating strong consistency, as all loadings surpassed the threshold of 0.4. We labelled the first factor ‘Pro-Environmental Attitude,’ as it comprised all five indicators related to environmental attitudes. The second factor, which included all three indicators associated with technology attitudes, was named ‘Technology Interest.’ The outcomes of the factor analysis, including the two resulting factors and the rotated factor loadings after Varimax rotation, are presented in Table 3. It is important to note that the factor analysis coefficients were not utilized in the model; the factor analysis was solely conducted to identify the optimal indicators for the latent constructs.

Table 3 Factor analysis on two latent variables.