Multinomial logit (multinomial logistic regression)

In previous research, multinomial logistic regression (MLR) was used as the next step of analysis after factors and clusters are obtained in the initial analysis (Zandvliet et al., 2006). As discussed in Kwak and Clayton-Matthews (2002), MLR is suitable for a nominal dependent variable where the number of levels is more than two. Multinomial regression is a predictive analysis, similar to all linear regressions (Greene, 2003).

However, MLR is used to describe data and to clarify the relationships between one dependent nominal variable and one or more continuous independent variables, which may be either interval or ratio.

MLR models explain the association between a set of predictors and unordered multi-category nominal outcomes. Consistent with common practice, a conditional probability of the logistic model, which is a generalisation of the multinomial outcome of standard logistic regression, is chosen as a reference against which others are compared.

and level are two levels, such that level j is the reference level, and k is the selected level. is the conditional probability that an individual chooses alternative k and is the reference conditional probability that an individual chooses the alternative j. The multinomial logistic regression model is defined by:

where:

is the independent variable;

is the number of independent variables;

is the estimated intercept;

is the estimated coefficient.

Table 3.5 provides brief details of examples of the application of MLR in travel behaviour research. These include Zandvliet et al. (2006), Geraghty and O’Mahony (2015), Wuerzer and Mason (2015), Geng et al. (2017), Gim (2017), Hamersma et al. (2017), Zhao et al.

(2018) and Nutsugbodo et al. (2018).

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dyTopicDetails of the research Dependent variableIndependent variable Destination choice; Space-time ecology; Visitor populations.

Applied MLR for car users to analyse the joint effect of personal and household characteristics using 1998 Netherlands National Travel Survey (NTS) dataset. They concluded that different types of visitor population environments attract different kinds of visitors at different times of the day.

Visitor population environment: 1. Central-place 2. Contemporary-node 3. Self-contained 4. Mobile-children type 5. Local-children

1. Personal variables (gender, age, and educational level) 2. Household variables (car ownership, household income and household type) 3. Workday 4. Day-of-the-week 5. Location ) Urban noise; Transport; Household characteristics.

Conducted MLR to investigate noise levels regarding location, month of the year, weekday, and hour of the day using a database of urban noise measurements collected from April 2013 to March 2014 at 10 sites in Dublin, Ireland. Location emerged as the most significant variable in forecasting urban noise levels, whilst transport and household characteristics were not significant.

Noise levels - Leq(A)dBA1. Location 2. Month 3. Weekday 4. Hour of the day GIS; Cycling; College students; Distance.

Conducted a health survey among college students (n = 949) to explore distance and socio-demographic factors towards susceptibility to cycling. MLR was used to examine their demographic and personal characteristics and distance variable in cycling. The results showed that age and susceptibility to cycling for transportation mediate the adverse influence of distance on the probability of cycling.

Cycling distance 1. Age 2. Gender 3. Healthy weight 4. Cycling for transportation 5. Cycling for recreation e next page

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3.5 (continued) ples of studyTopicDetails of the research Dependent variableIndependent variable l. (2017)Motivation; Sustainable urban transportation; Travel mode choice; Urban residents.

Developed MLR based on survey data from 1244 urban residents in the Jiangsu, China to observe the effects of motivations, government measures and demographic characteristics on residents’ travel mode choice behaviours. The result shows that pro-environment has a significant and positive role in promoting sustainable transportation (walking, bicycling, and PT) compared to car use. Furthermore, the effects of gender, age, income, vehicle ownership, travel distance, and government instruments show significant differences among travel mode choices. The results proposed that in order to warrant sustainable urban transportation, pro- environmental motivation has to be emphasized. Policies targeted to only increase public awareness of the environment are not sufficient. Instead they should be targeted to specific groups with diverse key inspirations.

1. Walking 2. Bicycle 3. Public transport

1. Pro-environmental motivation 2. Self-interested motivation 3. Government instruments 4. Demographic variables, vehicle ownership, and travel distance 2017) Travel utility; Linear regression; Mode choice; Travel time.

Investigated three travel methods – the automobile, public transit, and non-motorised based on the most frequently chosen mode in the year by using survey data collected in Seoul, South Korea in June 2013. MLR results indicated that in comparison to life situation and land- use variables, utility elements are among the strongest travel influencing factors. Non-motorised travel and modal shift (walking/biking) are strongly influenced by services, facilities, and trip timeliness. The results were significant to public health and transportation planners by providing evidence to inform policies that promote more walking or use bicycles in order to achieve modal shift target.

1. Automobile 2. Public transport 3. Non-motorised

1. Life situation 2. Travel-related utility ued on the next page

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inued) dyTopicDetails of the research Dependent variableIndependent variable l. Highway development; Perception; Residential satisfaction; Residential self- selection; Residents.

Studied the perceptions of residents regarding the impact of new highway development. MLR was used to explore the comparison between before and after a highway development among the original population with those who have moved into the area. The results indicated that residents who had moved into the area after the highway improvement had a slightly more ‘highway-oriented’ profile than the original residents.

1. Environmental quality 2. Car accessibility 3. Highway proximity

1. Age 2. Number of children 3. Income 4. House ownership 8)Attitude; Future cycling and car purchasing; Mobility policy; Perceived cycling environment.

Analysed the perception of cycling environment, current travel behaviour, urban form and socio-demographic variables to forecast attitudes towards future cycling and car purchasing by using MLR. The results of surveyed data (n=1427) collected in 8 Beijing neighborhoods suggested that respondents have a greater tendency towards cycling rather than buying a car. However, travel distance was more likely to affect respondents' attitudes towards future cycling. Also, the results showed that respondents with low levels of education and income were less likely to buy a car in the future.

1. Cyclists 2. Non-cyclists 3. Non-car owners

1. Perceived cycling environment 2. Current travel behaviour 3. Urban form 4. Socio-demographics l. Mode; Preference; Public transport; Tourists.

Investigated public transport mode preferences of international tourists in Ghana using data collected from 479 out-bound international tourists at the departure hall of the Kotoka International Airport in Ghana. MLR was used to examine the relationships between tourists’ socio-demographic characteristics and their mode preference. The results showed that they have strong relationships.

Travel mode preference Socio-demographics Table 3.5: Examples of study using MLR

It can be seen from the table that MLR has been applied across the world in countries as diverse as Ghana, China, South Korea, Netherlands, Ireland and USA. They conducted investigations involving a wide range of modes for instance car, cycling, public transport and air travel. MLR was applied for impact assessments, highways, noise and other areas.

Data for this research were collected by means of attitudinal surveys, questionnaires and direct measurement.

MLR has been widely used in transport research: to analyse the combined effect of personal and household characteristics of car users (Zandvliet et al., 2006); to investigate impacts of traffic noise levels (Geraghty and O’Mahony, 2015); to examine demographic and personal characteristics together with distance travelled by cycle (Wuerzer and Mason, 2015); to study mode choice and more specifically the frequency of use of the automobile, public transit, and non-motorised on the year to year basis (Gim, 2017); to explore the comparison between before and after highway development (Hamersma et al., 2017); to observe the effects of different incentives, government measures, and demographic characteristics on residents’ travel mode choice behaviours (Geng et al., 2017); to analyse the perception of cycling environment, current travel behaviour, urban form and socio-demographic variables to forecast attitudes towards future cycling and car purchasing (Zhao et al., 2018) and to examine the relationships between tourists’ socio-demographic characteristics and their mode preference (Nutsugbodo et al., 2018).

Previous research has demonstrated the value and appropriateness of this method to investigate the relationships between socio-demographic and travel related variables (Geng et al., 2017; Nutsugbodo et al., 2018; Zhao et al., 2018) and also to understand the association of socio-demographic with the environmental variables (Zandvliet et al., 2006; Hamersma et al., 2017). In addition, among all the studies mentioned above, none have used clustered groups as dependent variables and factors as independent variables to investigate relationships between them. Given the above evidence and underlying benefits, MLR was chosen to study the relationships between factors obtained in EFA and the clusters obtained in HCA, as illustrated in Figure 3.3. Hence, this is a novel area pursued in the research reported in this thesis.

Figure 3.3: MLR approach in this study

The practical advantages of using multinomial logistic regression, as claimed by Tabachnick and Fidell (2013), are as follows:

i. more robust to violations of assumptions of multivariate normality and equal variance-covariance matrices across groups,

ii. similar to linear regression, but gives more easily interpretable diagnostic statistics.

Furthermore, advantages of this analysis that have increased its reputation come from the following assumptions:

i. a linear relationship between the dependent and independent variables is not assumed;

ii. independent variables need not be interval;

iii. no requirement that the independent variables to unbounded, and finally;

iv. normally distributed error terms are not assumed.