Dimension reduction using exploratory factor analysis (EFA)

Factor analysis is used to simplify large sets of data in order to reduce the number of variables and to explore in further detail any structures in the relationships between the variables, establishing those that are independent and those that are not independent.

Variables highly correlated are collected together into a new variable called a factor (Costello and Osborne, 2005). So factor analysis is more “model based”. PCA can be seen as a first step in factor analysis. There is no rotation in PCA but rotation is used in factor analysis (Fabrigar et al., 1999). There are four requirements or assumptions for a dataset to be suitable for factor analysis which are normality, linear relations, factorability, and sample size.

Two factor analysis methods were considered for use in this research, namely Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA). EFA and CFA techniques are similar, but their purposes are different. EFA is used to provide a number of factors with specified variables that are assimilated into factors, whilst CFA is used to examine whether expectations concerning the factor structure are indeed present. EFA is briefly described in this section as it is more applicable to the objectives of this study. This is because EFA is data focussed, whereas CFA is based on theory or empirical research. In the initial steps of scale development, EFA is suitable since items loading on the non-hypothesised factors did not show in CFA.The origins of factor analysis can be traced back to Pearson (1901) and Spearman (1904), and the term was first introduced by Thurstone (1931). A review of the subject can be found in Gorsuch (1983).

The seven steps involved in EFA, suggested by Yong and Pearce (2013) have been used to create a conceptual diagram for the approach adopted in this research as shown in Figure 3.1.

SETTING UP

MODEL DEVELOPMENT

INVESTIGATION

Figure 3.1: Steps involved in factor analysis

EFA is conducted using the correlation coefficients between variables and factors referred to as factor loading (Field, 2009). The squared factor loading represents the percentage of variance explained by a factor. If the observed variables are the common factors are and the unique factors are where the variables may be expressed as linear functions of the factors:

Clarification of the objectives

Selection of variables and sample

Specification of assumptions of FA e.g.

normality, homoscedasticity and linearity among variables

Extraction of factors and decisions concerning number of

factors

Rotation of factors and interpretation

Validation of factor analysis solutions

Further analysis such as creating scales, or

computing factor scores

Each of these equations is a regression equation; EFA is used to find the coefficients which best reproduce the observed variables from the factors. The coefficients are weights in the same way as regression coefficients.

In EFA, the coefficients are called factor loadings and when the factors are not correlated, they also show the correlation between each variable and a given factor. In the model above, is the loading for variable on , is the loading for variable on and so on.

The sum of the squares of the loadings for variable , labelled as

, shows the proportion of the variance of variable which is accounted for by the common factors. This is called communality. EFA solutions are more successful if larger values of communality are obtained for each variable.

There are various measures used to identify the inter-correlation among variables. The Kaiser Meyer Olkin (KMO) measure is used to assess the degree of correlation among variables (Field, 2009). Hair et al. (2006) recommended this measure as being appropriate to deliver a specific level of confidence of the prediction value ranging from 0.9 – 1.00 to be perfectly predicted down to a value less than 0.50 for unacceptable results. The minimum sample required for PAF is 50 (Hair et al., 2006).

Costello and Osborne (2005) argued that principal component analysis is one of the factor analysis techniques used for data reduction which produces “components” while principal axis factoring produces “factors”. However, both are acceptable and used depending on the research questions and ease of interpretation of the results (Yong and Pearce, 2013). Also, they pointed out that maximum likelihood extraction method is more suitable for CFA and is used to estimate the factor loading for a population.

There are two rotation methods in factor analysis, orthogonal rotation and oblique rotation. In orthogonal rotation, factors are assumed not to be correlated and are rotated 90⁰ from each other. Quartimax and Varimax are commonly selected in

In oblique rotation technique, factors are assumed to be correlated and are not rotated 90⁰ from each other. Oblimin and Promax are two common oblique rotation methods.

Oblimin attempts to simplify the structure of the output. However, Promax is advantageous because of its speediness in raising the loading in a larger dataset to reach a simple structure (Gorsuch, 1983).

In transportation studies, factor analysis has been widely applied to analyse categorical data, for example Anable (2005); Steg (2005); Van et al. (2014); Kamruzzaman et al.

(2016); Molin et al. (2016); and Batool and Carsten (2017). Table 3.1 presents the differences in choice of extraction and rotation methods that have been applied in previous studies to conduct EFA.

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dyTopics Details of the research Extraction method Rotation method PCAPAF VarimaxPromaxOblimin Car use; Motives; Symbolic function.

Examined important factors that influence the level of car use and found three main attributes: symbolic and affective, instrumental, and independence. √√ Attitudes; Cluster analysis; Market segmentation; Mode choice; Theory of planned behavior.

Generated 19 factors out of 105 attitudinal statements and they included: moral norms, general attitudes towards the car, environmental beliefs, social and behavioural norms, and perceived behavioural control. The results demonstrate that different reasons could influence the same behaviour, however different behaviours could lead to the same attitudes.

√√ 9)Land use; Seemingly unrelated regression; Self-selection; Smart growth; Travel behavior; Urban design.

Collected 32 attitudinal variables concerning travel in Northern California using Likert scale options from “strongly agree” to “strongly disagree” and performed factor analysis. Generated six attitudinal factors: pro-bike or walk, pro-transit, pro-travel, travel minimizing, car dependent and safety of car. They discovered that the car dependent factor is positively associated with higher frequency of car trips and lower frequency of transit trips.

√√ 016)Attitude; Factor analysis; Latent class cluster analysis; Mode choice; Mode frequency; Multimodality.

Identified travellers’ attitudes using 19 statements mostly about public transport (PT) and acknowledged seven perception factors, namely; PT transfer acceptability, PT waiting acceptability, car inexpensive, PT timeliness, PT seat availability, PT planning ease and PT inexpensive. They concluded that changes to the built environment influence walking using the cross-sectional analysis, where there were significant relationships between environment factors with travel attitudes and perceptions and socio-demographics.

√√ e next page

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3.1 (continued) ple of studyTopics Details of the research Extraction method Rotation method PCAPAF VarimaxPromaxOblimin zzaman et 16) Residential self- selection; Travel attitudes; Urban form; Walking as a mode of transport.

Conducted factor analysis by using 16 questions of a 5-point Likert scale survey data regarding travel attitudes and perceptions. Four factors were identified and they were: respondents’ perceptions about PT, sensitivity to environmental externalities, car dependency and safety of car travel. They concluded that changes to the built environment influence walking using the cross-sectional analysis, where there was a significant relationship between environment factors with travel attitudes and perceptions and socio-demographics.

√√ and Carsten 7)Driving behaviour; Extended violations scale; Developing countries; Road safety.

Investigated drivers’ unusual actions in Pakistan and found that personal characteristics resulted in four behavioural factors which are aggressive driving, unlawful driving, risky driving and egoistic driving.

√√ i and Habib 7)Attitude; Changes in household state; Mode switch; Past travel behaviour; Random parameters logit model; Residential relocation.

Explored the long-term choices of commuters in terms of travel modes shift when relocating to another residential area. Factor analysis was used to produce 6 attitudinal factors based on 295 samples from the Household Mobility and Travel Survey (HMTS). The model results suggest that mode shift decisions are significantly influenced by previous travel experiences. Moreover, larger household size, closer location to transit stops and driver’s licence ownership also influence travel mode switch decisions.

√√ : *PCA: Principal component analysis **PAF: Principal axis factoring Table 3.1: Previous studies using different extraction and rotation methods in dimension reduction technique.

Along the lines of the discussions from previous studies, it is clear from Table 3.1 that EFA is used in a wide range of areas that embrace, for example, attitudes, travel choices, driving behaviour and land use. All seek to reduce the number of variables measured in qualitative surveys such as questionnaires and interviews, to remove commonality and any inherent correlation. Interestingly the sample size and number of variables vary widely from 105 to 19 and 295 to 6 respectively.

Based on previous research, PCA and PAF are among the popular dimension reduction techniques chosen by researchers. Steg (2005), Anable (2005), and Van et al. (2014) used PCA with Varimax rotation method. Whilst, Molin et al. (2016) and Kamruzzaman et al. (2016) selected PAF extraction method with Oblimin rotation method to conduct EFA in their studies. Whereas, recently, Batool and Carsten (2017) and Fatmi and Habib (2017) applied PCA with Promax to find factors involving driving behaviour and attitudes towards switching travel modes, respectively.

Several attempts have been made, using PCA and PAF, to investigate attitudinal variables to obtain important factors regarding car use (Steg, 2005; Batool and Carsten, 2017), public transport (Molin et al., 2016), travel attitudes and behaviour (Anable, 2005; Kamruzzaman et al., 2016) and travel mode shift (Fatmi and Habib, 2017). Based on previous research, this method demonstrated its suitability for the analysis of Likert scale survey data regarding travel attitudes and perceptions in order to investigate behavioural and attitudinal related factors (Kamruzzaman et al., 2016) and, more specifically, to investigate travel mode choice decisions (Fatmi and Habib, 2017).

3.3.2 Exploring the data structures with socio-demographic and travel behaviour