Structural equation modelling (SEM) is a tool widely used in quantitative IS research to analyse data and confirm theoretical propositions (Gefen et al., 2000). Software, such as LISREL, Stata (StataCorp, 2015), and SPSS Amos (Arbuckle, 2012), provides functions to support SEM analysis. In addition to evaluating hypothesis, and confirming theoretical models, SEM also guides researchers towards detecting hidden relationships (Bagozzi & Yi, 2012). SEM also provides greater advantages when compared to other statistical methods, such as ANOVA or multiple regression. If the analysis needs to identify causal relations, SEM can be used to identify complex structures i.e. more than two layers of mediation (Hoyle, 1995).
Hair et al. (2009) proposes the process for structural equation modelling, consisting of six steps.
These steps are explained in detail below.
Step 1 - Define Individual Constructs
This step involves the approach of defining the theoretical constructs that will be used in the study. Theoretical constructs can be adapted from seminal research and / or developed from literature in cases where there is no prior work. The defined constructs will then be operationalised into measurable items through the use of the Likert scale.
Step 2 - Specify Measurement Model
SEM measurement model is based on the factor analysis approach. Three factor models (principal components analysis, exploratory factor analysis and confirmatory factor analysis) are often used to develop SEM measurement models (Blunch, 2013). The Factor analysis groups, operationalises items into specific constructs derived from theory, this analysis confirms the reliability of each constructs and helps researchers to decide, which variables should be included for further analysis (Blunch, 2013).
This section applied the steps for the development of a path diagram, that represented the context of the research. The diagram consisted of relevant elements drawn in the form of SEM notation. The SEM notation consists of indicator, relationship and error terms, there are two
types of SEM indicator: Exogenous (X ⎯ influencing variable); Endogenous (Y ⎯ influenced factor) (Hair et al., 2009).
The SEM relationship, also consists of measurement, structural and correlational. The measurement (loading) relationship represents the relations between the operationalised items and the latent variables. The structural relationship represents the direction of path diagram.
The correlational relationship, is expressed using a two-way arrow, which shows that the two constructs are correlated.
There are error terms representing residual error value of each SEM indicator, figure 3.3 shows how SEM notation simply fit in SEM path diagram. Figure 3.3 presents three operationalised variables ⎯ i.e. x1, x2, x. X is an unobserved variable representing x1, x2, x3, and X has measurement relationships with x1, x2, x3. X is an exogenous variable influencing dependent variable y ⎯ i.e. endogenous.
Figure 3.3: SEM Notation adapted from StataCorp (2015, p. 9)
Step 3 - Design a Study to Produce Empirical Results
This step involved procedures to handle empirical data, such as missing data handling, sample size and model complexity, normality and estimation technique. Missing data handling is one of the key tasks when dealing with empirical data. Two approaches are considered at this point:
complete case approach (delete record if any missing value) and imputation techniques (replacing missing value with mean). Sample size and model complexity (number of constructs), are key factors towards indicating the reliability and validity of the study. Table 3.4, relating to sample size and model complexity, shows the recommended minimum sample size comparing with the number of constructs. For example, if the defined theoretical constructs
were less than or equal five, then the recommended sample size will be greater than 100 to make the analysis represent the population, and the item communalities (factor loading) for each measurable item (each question in the questionnaire) should be more than 0.6. Although there is a recommendation on sample size, impact by the number of constructs and item communalities, sample size larger than 200 is deemed universally acceptable for SEM analysis (Bagozzi & Yi, 2012).
Table 3.4: Sample Size and Model Complexity adapted from Hair et al. (2009) Minimum sample size Number of construct Item communalities
100 <=5 >.6
150 <=7 .5
300 <=7 <.45
500 > 7 -
The Maximum Likelihood Estimation (MLE) method uses the most likely approach to perform estimation of the model; yet also makes the assumption of data normality (Gefen et al., 2000).
Generalised Least Square (GLS) is an alternative method of estimation for cases where the empirical data is not in the normal distribution (Hair et al., 2009). Bagozzi and Yi (2012), however, argued that MLE is reliable in the satisfactory level of estimation, independent of the normality of the data.
Step 4 - Assess Measurement Model Validity
This step concerns the validity of the measurement. Different types of validity check are involved at this point. The basic goodness of fit test, using chi-square (χ2), tests the hypothesis, i.e. that the model fits with the empirical data. There are other indices that can be used to assess the validity, the most common are: root mean square error approximation (RMSEA);
standardised root mean square residual (SRMR); comparative fit index (CFI) and the goodness of fit index (GFI). Table 3.5 shows the recommended value of each index.
Table 3.5: SEM FIT Index
Indicators Hair et al. (2009) Bagozzi and Yi (2012) χ2
Step 5 - Specify Structural Model
All the confirmed theoretical constructs, from the measurement model defined within section step 2, were included in this step. Moreover, all relationships between constructs are identified when using structural equation modelling (Hair et al., 2009). The structural model should be drawn according to the hypotheses and/or theoretical propositions based on the literature theory (Hair et al., 2009).
Step 6 - Assess Structural Model Validity
This step, assessed the structural model validity according to defined structures presented within the previous step, which concerned the statistical significance and the direction of the relationship; also including model fitness (as defined in step 4). However, there are existing approaches in SEM to improve model validity, using modification indices that specify additional correlational relationships (Arbuckle, 2012). Altering the direction of the relation, and adding new or remove existing structural relationships, can be done to improve the model validity (Hair et al., 2009).