Method of Analysis

10.3.1 Structural Equation Modelling

Structural Equation Modelling (SEM) permits complicated variable relationships to be expressed through hierarchical or non-hierarchical, recursive or non-recursive structural equations, i.e. the representation and testing of entire theories. ([Ge 00]) For causal analysis the structural model introduced in section 6 containing latent variables (LVs) and the indicators (MVs) developed in section 7 were added together for empirical data analysis to form a structural equation model. ([Ge 00])

SEM enables researchers to answer a set of interrelated hypotheses in a single, systematic, and comprehensive analysis by modelling the relationships among multiple endogenous and exogenous constructs simultaneously. ([Ge 00])

In the same analysis SEM evaluates the structural model (the assumed causation among a set of dependent and independent constructs) but also the measurement models (the loadings of observed measurements on their expected LVs). Thus, in SEM, factor analysis and hypotheses are tested in the same analysis. ([Ge 00]) In SEM for hypotheses testing two main approaches should be considered – covariance-based SEM (CBSEM) and partial-least-squares-based SEM. For both approaches powerful analysis tools are available – f. e. LISREL for covariance-based SEM and f. e. SmartPLS ([Ri 05]) for partial-least-squares-based SEM.

Table 39 provides a comparison of a set of distinctive features between CBSEM and partial-least-squares (PLS) path modelling taken from [Ge 00].

For this research project PLS path modelling was deemed adequate:

1. due to the small sample size of 185 responses (according to a rule-of-thumb proposed in [Ch 98-2] the minimum sample size is ten times the maximum number of paths pointing to an endogenous LV in the model - in the initial models 11 paths point to the LV PU, leading to a minimum sample size of approx. 110 cases),

Data Analysis 144 2. because PLS path modelling is recommended for forecasting and variance explanation which fits the overall research goal of the project - explaining and forecasting behavioural determinants of participation behaviours in a blog community,

3. because PLS path modelling does not necessarily require a sound theory base and supports both exploratory and confirmatory research - this research project is the first research in the field of blogs about leisure time activities in a region and the hypothesized model elements and causal relationships among them rely on several theories set up in significantly different fields and considerably differing contexts,

4. because PLS path modelling is relatively robust to deviations from a multivariate normal distribution.

Table 39 Comparison: CBSEM - PLS path modelling

issue CBSEM PLS path modelling

objective of overall analysis show that the null hypothesis of the entire proposed model is plausible while rejecting path-specific null hypotheses of no effect

reject a set of path-specific null hypotheses of no effect

objective of variance analysis overall model fit, such as insignificant χ² or high AGFI

variance explanation (high R²)

required theory base requires sound theory base, supports confirmatory research

does not necessarily require sound theory base, supports both exploratory and confirmatory research

assumed distribution multivariate normal, if estimation is through ML; deviations from

minimum sample size at least 100-150 cases at least 10 times the number of items in the most complex construct

Data Analysis 145

10.3.2 PLS path modelling

As mentioned above a PLS path model consists of measurement models for each LV (the outer models) and a structural model (the inner model) specifying the hypothesized causal relationships between the endogenous and exogenous LVs.

Chin/Newsted [Ch 96] characterise and summarise the estimation performed in PLS path modelling as follows: ‘The PLS procedure is used to estimate the latent variables as an exact linear combination of its indicators with the goal of maximizing the explained variance for the indicators and latent variables. Following a series of ordinary least squares analyses, PLS optimally weights the indicators such that a resulting latent variable estimate can be obtained. The weights provide an exact linear combination of the indicators for forming the latent variable score which is not only maximally correlated with its own set of indicators (as in components analysis), but also correlated with other latent variables according to the structural (i.e.

theoretical) model.’

For this research project PLS path modelling was used for confirmatory and exploratory analyses. The pattern of loadings of the MVs on their LV was specified explicitly in the model. Then the fit of this pre-specified model was examined to determine its convergent and discriminant validities ([Ge 05]). The data analysis was based on reflective measurement assumptions, i.e. it was assumed that the MVs were reflections or ‘reflective’ of the LV they were assigned to.

For PLS path modelling SmartPLS ([Ri 05]) software was used. SmartPLS offers a graphical user interface for model specification and is executable on operating systems like Windows, Linux or Solaris requiring a Java 2 Standard-Edition Runtime Environment (J2SE JRE) of version 5.0 or higher. For the analyses of this research project SmartPLS was executed under the Windows Vista operating system.

10.3.3 Model validation

In science two central requirements in evaluating and safeguarding the quality of how LVs are captured by MVs and of overall models have evolved. These are reliability and validity ([Ho 96]). Reliability refers to the reliability of the measurement. The

Data Analysis 146 influence of random measurement error should be as low as possible to justify generalising results.

Validity refers to whether and in what quality a measurement actually reflects what it claims to measure. Reliability of the measurement is a non-sufficient prerequisite for validity.

Homburg and Giering ([Ho 96], [Ja 07]) subdivide construct validity in four aspects:

 content validity:

the indicators reflect the meaning of the construct (LV),

 convergent validity:

indicators assigned to the same LV should be correlated strongly to each other,

 discriminant validity:

indicators assigned to different LVs should not be correlated or only weakly correlated to each other.

 nomological validity:

the constructs (LVs) and results have to be integrated in a well-founded theoretical framework.

For the convergent and discriminant validity quality measures exist. Content validity and nomological validity have to be observed in the course of theory building, deduction of hypotheses and selection of indicators. For preventing misinterpretations of results knowledge of this latter aspect is important ([Ja 07]).

10.3.4 Validation criteria for PLS path models

In this section the validation criteria applied for analysing the hypothesized

relationships of this research project using the SmartPLS ([Ri 05]) software tool are introduced.

At present no systematic procedure for the assessment of PLS path models is recommended and agreed upon ([Ri 04]).

Data Analysis 147 Following steps were passed through in examining PLS path models:

1. Implementation of PLS path model and indicator data in SmartPLS ([Ri 05]).

2. Execution of the PLS algorithm (for program settings see Figure 5).

Assessment of the reflective measurement models 3. Indicator loadings (indicator reliability):

For the factor loadings of reflective indicators the requirement of a minimum value of 0.7 (0.707) as a rule of thumb is customary. The share of variance of an MV explained by its LV is the squared factor loading. This means that a factor loading of > 0.707 implies that more than 50% of the MV´s variance is explained by its LV and as explained variance and measurement error add up to 100% that the measurement error does not dominate ([Ja 07], [Jo 06]).

According to J. Hulland ([Hu 99]) researchers generally should have a strong theoretical rationale for including items with a loading below 0.7 and should drop items with loadings of less than 0.4 or 0.5.