MNL base specification

Assuming that the IIA property holds for the error term 𝜀_𝑖𝑛, the choice probabilities are given by the MNL model (equation 4.6), which for the joint charging and parking choice takes the following form:

𝑃_𝑖𝑛 = 𝑒^{𝛽𝐶𝑃𝐶𝑃𝑖𝑛+ 𝛽𝑊𝑇𝑊𝑇𝑖𝑛+𝛽𝐶𝐷𝐶𝐷𝑖𝑛+𝛽𝐶𝐼𝑆𝐷𝐸𝐶𝐼𝑆𝐷𝐸(𝑡0,𝑖𝑛)}

∑_{𝑗∈𝐶𝑛}𝑒^{𝛽𝐶𝑃𝐶𝑃𝑗𝑛+ 𝛽𝑊𝑇𝑊𝑇𝑗𝑛+𝛽𝐶𝐷𝐶𝐷𝑗𝑛+𝛽𝐶𝐼𝑆𝐷𝐸𝐶𝐼𝑆𝐷𝐸(𝑡0,𝑗𝑛)}

(4.34)

where 𝐶_𝑛 is the choice set for individual 𝑛. The limitation of the IIA property in the present context lies in the fact that the substitution rates between alternatives are the same, regardless if their attributes (e.g. charging duration, walking times) have adjacent values or not. For example, if a higher tariff is introduced in a facility located half a mile from the destination to

discourage drivers from plugging-in their EVs there, this will cause a proportionate increase in the choice probability of a charging post 2 miles away and a charging post 5 miles away from the destination. The reasonable expectation is that the drivers will disproportionally choose to move to the closest available charging post, i.e. the one located in a 2 miles distance.

Figure 4.5: Example of a choice situation from the charging game

The MNL might be limiting in this perspective, yet it is very useful for a preliminary estimation of the sample to gain insights into the significance, the signs and the relative magnitude of the charging parameters. Flexible substitution patterns and taste heterogeneity are introduced later with more advanced specifications.

The MNL estimates from the base specification of 4.33 are presented in Table 4.1. The overall fit of the model is indicated by the likelihood ratio index 𝝆³⁶. All the estimated parameters are statistically significant. The parameters for price, walking time and CISDE have the expected negative sign while the parameter for charging duration is positive, suggesting an implicit

36 The likelihood ratio index 𝝆is a statistic that measures the goodness-of-fit of a model. It is defined as 𝜌 = 1 −

𝐿𝐿(𝛽)

𝐿𝐿(0), where 𝐿𝐿(𝛽) is the final log-likelihood, i.e. the log-likelihood calculated with the estimated parameters 𝛽 after convergence, and 𝐿𝐿(0) is the null log-likelihood, which is calculated for all parameters set to zero. For linear-in-parameters specifications, this statistic measures how well the model performs compared to a model assigning equal probabilities to all alternatives. The adjusted likelihood ratio 𝝆̅ index is defined as 𝝆̅ = 1 −

𝐿𝐿(𝛽)−𝐾

preference for longer charging durations. The sign of the charging duration parameter is discussed in more detail later but it is noted at this point that it could be attributed to endogeneity as a result of measurement error. Finally, the ASC for option A is positive and statistically significant, indicating that the respondents tend to choose the alternative that is located on the top part of the reservation screen.

Table 4.1: MNL charging choice, “charging game” – base model specification

Variables Coefficient Std error t-test p-value

ASCA 0.187 0.0677 2.77 0.01^**

Two asterisks (**) indicate that the coefficient for this parameter is statistically significant at the p<0.05 level while one asterisk (*) indicates that the coefficient is statistically significant at the p<0.10 level.

In Chapter 3, it was shown that 263 respondents completed the EV-PLACE survey. However, taking into account that the instructional video for the charging game lasted three minutes, all individuals that completed the exercise in less than four minutes were not further processed, since it would be difficult to argue that they made actual trade-offs between the charging alternatives. As a result, the final sample size consists of 118 individuals and, considering that each of them responded to nine choice situations, they correspond to 1062 observations.

Examining if there are systematic patterns among the respondents that were excluded from the analysis, it was observed that the proportion of young, employed and individuals that live in London is slightly increased compared to the initial sample.

One significant characteristic of the survey sample is that it consists of both EV drivers and people that do not have experience with driving an EV (although they have considered buying one during the last 12 months). The charging preferences are expected to have dissimilarities

specification, later, a dummy variable for owning/leasing an EV is interacted with the charging attributes in order to capture its effect. The estimated parameters for the two sub-samples are presented in Table 4.2.

The goodness-of-fit for the “EV drivers” model is higher than the goodness-of-fit for the “EV considerers” model, indicating a larger variability across individuals in the utility parameters for the latter. The parameters have the same sign and similar values as above, yet the charging duration is not statistically significant for the “EV considerers” group. It is also observed that EV drivers have a higher sensitivity to price and time of arrival while EV considerers are slightly more sensitive to walking time.

Table 4.2: MNL charging choice, “charging game” – sample split among EV drivers and EV considerers

EV drivers EV considerers

Variables Coefficient Std error t-test p-value Coefficient Std error t-test p-value

ASCA 0.173 0.0920 1.88 0.06^** 0.212 0.101 2.09 0.04^** consists of multiple data sources and hence it is important to check for taste homogeneity and variance differences among them. For this reason, the MNL model is estimated separately for the respondents that have been recruited by the researchers and for those that have been recruited by Panelbase.com. The results are presented in Table 4.3.

It can be seen that there is a significant difference in the goodness-of-fit for the two data sources, suggesting a higher degree of error associated with the Panelbase respondents. The

estimated parameters have the same sign, but they are of different scale while the main inconsistency is the statistical significance of the alternative specific constant for Option A.

Table 4.3: MNL charging choice, “charging game” – sample split among different recruitment channels

Internal recruitment Panelbase

Variables Coefficient Std error t-test p-value Coefficient Std error t-test p-value

ASCA 0.0193 0.141 0.14 0.89 0.253 0.079 3.20 0.00^**

Hensher et al. (1998) suggest that if the parameter vector of one model is plotted against the parameter vector of the other model and the graph exhibits a positive, proportional relationship between the two then the hypothesis for equal taste parameters and unequal variances should hold. The ratio of variances, in this case, is equal to the slope of the underlying curve. Figure 4.6 illustrates this plot and reveals that the expected relationship holds for all parameters apart from the alternative specific constant for option A, which is of greater relative importance for Panelbase respondents than for the rest of the sample. This visual test is similar to a t-test of the difference between the estimates; however, it is useful in this case to demonstrate that the ASCA is an outlier.

In order to combine the observations from the two sub-samples, considering the increased variance of the error term for Panelbase, it has been decided to take account of the difference in scale of their corresponding utilities. This is achieved by estimating a scale parameter that is multiplied with the utility of the Panelbase sub-sample. The effect of this scale parameter is that the utility of this dataset is forced to have the same scale with the utility of the other respondents. Here, the internally recruited sub-sample was set as the reference environment

since it can be considered to reflect a more realistic behaviour and the scale factor was fixed as equal to one. The main reason for this assumption is that it includes only EV drivers, who should be more familiar with the hypothetical situations. The MNL model with the additional scale parameter is presented in Table 4.4. The results show that the scale parameter is significant, and after its inclusion, the goodness-of-fit for the base specification has improved.

Figure 4.6: Plot of MNL attribute coefficients for different recruitment channels Table 4.4: MNL charging choice, “charging game” – accounting for scale differences

Variables Coefficient Std error t-test p-value

ASCA 0.217 0.107 2.04 0.04^**

ASCB 0 fixed *** ***

CP [£] -0.918 0.120 -7.66 0.00^**

WT [mins] -0.0666 0.0118 -5.65 0.00^**

CD [mins] 0.0046 0.0021 2.22 0.03^**

CISDE(t0)[mins] -0.0269 0.0048 5.66 0.00^**

Scale for recruitment channel (𝜼) 0.469 0.0829 5.66 0.00^**

Number of estimated parameters Number of individuals Number of observations Null log-likelihood Final log-likelihood Likelihood ratio index 𝝆 Adjusted likelihood ratio index 𝝆̅

6 118 1062 -736.122 -637.989 0.133 0.125