Examining the effects of residential self-selection on internal and external validity: an interaction moderation analysis using structural equation modeling

Abstract

Empirical studies on the land use–travel relationship have begun to consider the confounding or moderating effect of residential self-selection on the relationship. The studies were mainly focused on how to control for selection bias in relation to its threat to internal validity, but the bias also harms external validity through its interaction with explanatory variables. This study further considers this interaction moderation using partial least squares structural equation modeling, which compared to its covariance-based counterpart, can easily specify a large number of interaction indicators and include both reflective (compact land use) and formative (life situation inclined to automobile travel) constructs. Tested in Seoul, South Korea, structural equation models find that a considerable proportion of the land use effect on travel time is attributed to the self-selection. Regarding the interaction moderation, it turns out to significantly affect external validity: in a study area with more automobile-inclined residents than Seoul, compact land use may exert a stronger effect on automobile travel reductions and transit travel increases.

Keywords:

• Residential self-selection
• validity
• interaction moderation
• structural equation modeling

Acknowledgements

The author is grateful to Ryan Dash, Carolina Ajeng, Nurlin Amirudin, Seung-hwan Chun, Dong Yun Shin, Su Kim, Juri Kim, Sang Mook Shin, and Daejin Kim for their assistance. The two anonymous reviewers’ helpful comments greatly improved the paper.

Notes

1. All data used for PLS-SEM were made available online: https://drive.google.com/open?id=0B7BjwkPI35r1S2hGM2pab21mRDg.

2. Notably, in the trade-off relationship between them, this study agrees with the argument that internal validity should be considered prior to external validity (Imbens and Rubin 2015).

3. The relationship between the daytime and nighttime populations is as follows: daytime population = nighttime population (i.e. residents) − outbound commuters + inbound commuters. Except for commuting workers and students, travelers for other purposes (e.g. business, shopping, and leisure) are not counted.

4. Administrative neighborhood is the finest administrative division in Korea and the TAZ (traffic analysis zone) of the MHTS.

5. According to previous studies on land use balance (Brown et al. 2009; Christian et al. 2011), this study identified four land uses, which, respectively, comprised six classes of residential use (single-family, multi-family, row housing, condominium, other housing, and housing open space), four classes of office use (office, business, other business, business open space), three classes of commercial use (commercial, other commercial, and commercial open space), and two classes of recreational use (parks/others and leisure facilities/others) while the other three classes – unidentified, unidentified open space, and others – were dropped out of the calculation.

6. In fact, as reviewed by Van Acker and Witlox (2010), previous studies put the number of automobiles either as an explanatory variable of life situation on travel behavior or as an outcome travel behavior variable that is explained by life situation and land use characteristics. Van Acker and Witlox (2010) acknowledged the status of the automobile variable as an explanatory as well as an outcome variable and specifying it as an intermediary (i.e. the life situation–automobile ownership–travel behavior relationship). They found that such a model specification leads to larger explained variations (R²). In relation to the estimation of the land use effect, they suspected that the model specification makes the land use effect larger because compact land use can reduce automobile travel not only directly, but also indirectly by discouraging the intention to purchase the automobile. This suspicion – a greater impact of land use through the mediating effect of automobile ownership – was empirically supported in a different area (Næss 2009). However, following a convention of earlier and the most recent Korean studies (Cho and Lee 2016; Choi, Choo, and Jang 2016; Gim 2011a, 2011b, 2013b, 2016; Kim, Ahn, and Kwon 2014; Lee and Ko 2014; Lee, Won, and Ko 2015), this study included the automobile variable in the life situation construct insomuch as the mediating effect of automobile ownership has not been confirmed in Korean settings.

7. Readers should be mindful of biases that could be brought about by the use of the travel time measure. Speed equals distance divided by time, that is, time increases as speed is reduced regardless of the distance variation. While speed differs by mode, causes for the speed difference such as traffic regulation and congestion vary in different parts of the city. As another alternative that has been frequently investigated, trip frequencies were not analyzed in this study because while it used data from the one-day MHTS, their variations were not enough for inferential statistics. Future studies may use other travel measures including travel distances and trip frequencies considering Ewing and Cervero’s argument (2001) that the magnitude of the land use–travel relationship hinges also on the type of the travel measure itself.

8. In CB-SEM, the issue of the multivariate non-normality can be addressed, using alternative estimators to ML (maximum likelihood), such as ADF/WLS (asymptotically distribution-free/weighted least squares), WLSM/WLSMV (mean-adjusted/mean- and variance-adjusted WLS), and Bayesian approaches.

9. Through simple linear regression, commuting time can be expressed as a function of land use balance, which has been reported as an important determinant of commuting patterns (Lee and Suzuki 2016; Lin, Allan, and Cui 2015): (1) C_TM_SUM-hat = −10.563 ENT (p = 0.000) + 49.890 (p = 0.000), (2) CA_TM_SUM-hat = −8.526 ENT (p = 0.000) + 45.930 (p = 0.000), and (3) CT_TM_SUM-hat = −7.073 ENT (p = 0.000) + 53.937 (p = 0.000), where C_TM_SUM = total commuting minutes, CA_TM_SUM = automobile commuting minutes, CT_TM_SUM = transit commuting minutes, and ENT = land use balance. (In this study, land use balance was consistently found to have a negative coefficient in reflecting the construct of compact land use.).

10. As Brambor, Clark, and Golder (2006) argued, in E(Y) = a + bX + cZ + dXZ [where Y = travel time, X = compact land use, and Z = (residents with) automobile-inclined life situation, for example], ‘(a)bsent any knowledge about the distribution of condition Z, the only clear way to gage the average effect of X on Y is to run an unconditional model in which X is not included in a multiplicative interaction term’ (72). Thus, this study ran simple models with the LU–TB path, which evaluated the land use effects (as misestimated because the models did not control for the self-selection at all). Then, according to Brambor, Clark, and Golder (2006), the effects were compared with those that were estimated by the research models because the final model estimates present the land use effects when ‘condition Z is absent’ (64) or ‘when Z is zero’ (72) [as if the study area has no self-selected residents (by definition, no residents have automobile-inclined life situation characteristics)]. In the meantime, regarding an accurate way of determining the range of Z, Brambor, Clark, and Golder (2006) suggested that because ‘the observed range of the modifying variable is [not always] the most substantively meaningful or informative’ (75), ‘[t]he specific question being addressed by the analyst should determine the relevant range’ (75).

11. One might try to remove the moderation construct (and automatically, its indicators) to estimate how strongly residential self-selection lowers external validity; as discussed above, this study has removed the life situation construct – it subsequently removed the moderation construct, also – to evaluate the overall degree of residential self-selection. However, this is not an appropriate approach; statistically, if the removal leads to significant differences in individual coefficients, then it suggests that the land use and life situation constructs have the collinearity issue. When this study excluded the moderation construct, the coefficient differences were at a minimal level, ranging 0.000–0.002 (detailed results are not shown).

12. The magnitude of the self-selection effect could also be differentiated by variations in the geographical scale (local vs. regional) and the composition of explanatory land use variables; as stated in ‘Partial least squares structural equation modeling’, this study did not analyze the shape and centeredness variables among others.