Examining the influence of structural ambiguity and reverse causality

As explained in Chapter 2 and 3, the major SEM drawback is its structural ambiguity. SEM structural path overcomes issues such as multicollinearity and endogeneity in regressions but requires assumptions on the dependencies of variables. These assumptions are mainly made based on the theories from literatures but sometimes are required to be tested specifically when the reverse causality is suspected.

In our case, the major structural ambiguity rests in the direction of the dependency between car ownership and travel distances; whether it is car ownership defining distance of travel as one of the travel outcomes (refer to Figure 2) or travel distance as a measure of accessibility, in conjunction with built form characteristics, affecting car ownership (refer to Figure 5 below).

In this dissertation we adopted the former structure as in theory travel distance is mainly the function of people decision on where to live, work, do shopping, visiting friends, etc; these decisions are more fundamental and less sensitive to car ownership than the other way around.

Figure 5 The alternative structure to test reverse causality

The comparison of the two model structures could provide practical evidence on the stronger direction of the effect. Moreover, it is beneficial to compare the influences of built form in the

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two alternative model structures. Considering the main goal of this study in determining built form influences, this helps evaluating the potential effect of structural ambiguity on our findings.

Both structures are modelled by using path-diagram based SEM. More detailed discussion on the specification of built form latent variable, and the significance and inference of the influences from path-diagram based SEM will be provided in Section 5.2. Here, we use the same covariates determined as important in Section 5.2 to compare the alternative model structures. Table 5 below provides the comparison of model coefficients which are called ST1 and ST2 respectively. The numbers in parentheses are the P-Values.

Table 5 The comparison of model structures

Direct Effect ST1- Car

Bus Frequency 1.095 (0.000) 1.094 (0.000) Population Density 1.76 (0.000) 1.757 (0.000) Built form latent

variable regressed ON

Male -0.013 (0.076) -0.013 (0.087)

Full time working 0.102 (0.000) 0.104 (0.000) 1 adult households 0.202 (0.000) 0.203 (0.000) Manual workers -0.05 (0.010) -0.048 (0.014) Skilled manual workers -0.199 (0.000) -0.197 (0.000) Professionals -0.183 (0.000) -0.182 (0.000) Household income less

Full time working -0.006 (0.797) -0.007 (0.755) 1 adult households 0.533 (0.000) 0.585 (0.000) Manual workers 0.413 (0.000) 0.356 (0.000) Skilled manual workers -0.284 (0.000) -0.329 (0.000) Professionals -0.298 (0.000) -0.277 (0.000) Household income less

£25k 0.541 (0.000) 0.505 (0.000)

Household income

more than £50k -0.235 (0.000) -0.201 (0.000)

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variable 0.609 (0.000) 0.556 (0.000)

Commuting travel

distance N/A -0.021 (0.000)

Shopping travel

distance N/A -0.138 (0.000)

Other travel distance N/A -0.026 (0.000)

Threshold 1.689 (0.000) 1.392 (0.000)

Commuting travel distance regressed ON

Male 10.65 (0.000) 10.66 (0.000)

Full time working 16.87 (0.000) 16.9 (0.000) 1 adult households 2.9 (0.000) 2.41 (0.000) Manual workers -3.21 (0.000) -3.54 (0.000) Skilled manual workers -4.45 (0.000) -4.29 (0.000)

Professionals 2.6 (0.000) 2.72 (0.000)

Household income less

Intercepts 10.5 (0.000) 10.3 (0.000)

Shopping travel distance

regressed ON

Male -3.13 (0.000) -3.12 (0.000)

Full time working -0.91 (0.000) -0.89 (0.000) 1 adult households 0.71 (0.001) 0.33 (0.112) Manual workers -1.46 (0.000) -1.72 (0.000) Skilled manual workers -1.17 (0.000) -1.04 (0.000)

Professionals -0.09 (0.688) 0.01 (0.978)

Household income less

distance 0.001 (0.691) 0.001 (0.497)

intercepts 13.8 (0.000) 13.6 (0.000)

Other travel distance regressed ON

Male 14.95 (0.000) 15.03 (0.000)

Full time working 2.53 (0.002) 2.66 (0.001) 1 adult households 20.37 (0.000) 17.34 (0.000) Manual workers -19.92 (0.000) -21.89 (0.000) Skilled manual workers -20.14 (0.000) -19.1 (0.000)

77 Professionals 13.56 (0.000) 14.31 (0.000) Household income less

£25k -10.3 (0.000) -12.6 (0.000)

Household income

more than £50k 17.03 (0.000) 17.33 (0.000) Built form latent

variable -12.06 (0.000) -13.86 (0.000)

No car in household -24.33 (0.000) N/A

Commuting travel

distance -0.138 (0.000) -0.134 (0.000)

Shopping travel

distance 0.334 (0.000) 0.353 (0.000)

intercepts 60.78 (0.000) 58.64 (0.000)

It is reassuring to observe that the direction and absolute values of almost all significant influences across the two models, specifically that of built form, are very similar. This can be due to the fact that built form latent variable is a good representative of the accessibility influences. This in essence diminishes the effects from travel distances reverse causality on car ownership. This suggests that the potential simultaneity biases from SEM structural ambiguity is minimal.

Comparing the influences of car ownership on travel distance (from ST1) with those in the reverse direction (from ST2) also reveals some interesting results. Table 6 shows the percentage change in travel distance when the reference group²⁰ forgo household car (second column)²¹; it compares that with the percentage change in the odds of having no access to household car for the equivalent change in the travel distances (third column). The latter is estimated by the ratio of the probability²² of not having a household car for the reference group with mean Built form factor score and travel distances set to the values of intercepts²³ with the

20 The coefficients of the reference variables are by definition zero. As shown in the right most column of Table 8, the reference segment of employed adults consists of part-time female workers of white collar clerical occupation living in middle income (£25-50,000), car owning households with more than one adults.

21 This is calculated for each travel purposes by dividing the coefficient value of “No car in Household” (i.e. the marginal effect of having no car) by the intercepts. The intercept is the total travel distance by the reference group and the coefficient of “No car in Household” represents the difference between the travel distance of the reference group with them when they have no access to the household car (i.e. marginal effect). The land use latent variable is assumed to be at its mean (i.e. 0.018-refer to appendix B)

22 As we have used probit regression to model car ownership, the probability is estimated by calculating the standard normal cumulative density of the sum of the descriptive variables multiplied by their respective coefficients minus ‘No car in Household’ threshold (i.e. 𝐹(∑ 𝛽𝑋 − 𝜏) ).

23 For estimating the Travel distance of the reference group in ST1 and car ownership probability for reference group in ST2 we assumed that all dummy variables have the coefficients of zero. We also assume that the Land

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otherwise same group who additionally experience changes in their travel distances equivalent to the coefficient of the influences of “No Car in Household” on travel distances from ST1.

Table 6 The comparison of model structures Car Ownership substantially stronger when compares to the reverse directional influence. For instance, non-car owner commute 3.91 miles or 37% shorter than the non-car owners (from ST1). However, having shorter travel distance to work by 3.91 miles would shows only 1.8% increase in the probability of having no car. This would justify the choice of ST1 as the basis for this research study.