Model Specification: Two step Procedure Application

The two step procedure, sometimes called the “two step rule” (Blunch, 2008, p.159), was then applied to the model. The two step procedure flows from the recommendation of Anderson and Gerbing (1988) that structural models should first be separately estimated, identified and re-specified before simultaneous estimation of the measurement and structural model. It is usual in Commitment Trust Theory research (and Structural Equation Modelling in general) to apply the “two step rule” to confirm the proposed pathways of models.

7.7.5.1 Step 1: Covariance/Correlation Matrix The first stage of the two step rule is to look at all of the latent variables as covariates of each other. This step presumes no causal linkage between the variables (that can only come from theoretical propositioning), and the results of this analysis are shown in Table 19 below.

Table 19: Covariance/Correlation Matrix of Latent Variables

As expected Trust as a latent variable displayed statistically significant correlations with availability of in-game information, in-game customer service interactions, knowledge of alternatives, opportunistic behaviours, perceptions of game developers communications, shared values with games company, shared values with rules and current satisfaction.

Similarly, Commitment as a latent variable displayed statistically significant correlations with game capital, group social benefits, metagame benefits, past satisfaction and current satisfaction. Trust and Commitment were also found to have a significant correlation with each other and Satisfaction.

In common with previous Commitment Trust Theory empirical work the antecedents displayed strong correlations with both Commitment and Trust.

In most cases, the stronger correlation of the two was seen to follow the theoretically expected pathway (as discussed in the previous chapter). For example in Table 19, availability of in-game information has a 0.577 correlation with Trust and a 0.311 correlation with Commitment. In a few cases though, like the knowledge of alternatives latent variable, while it displays statistically significant relationships with both Commitment (0.071, significant at the 5% level) and Trust (0.17, significant at the 0.01% level), the stronger relationship is with Trust and not Commitment as the theoretical model proposes. This is both common and expected in Commitment Trust Theory empirical work. The Relationship Benefits latent variable in Morgan and Hunt’s (1994a, p.26) paper for example was theoretically purported to be a determinant of Commitment, however it had a stronger correlation with Trust (0.425 vs 0.312). This is due to the covariance/correlation matrix displaying the measurement of strength and direction between two variables, but not a theoretical basis for causality. Thus while it is possible to infer that relationships exist between variables from the matrix, interpreting the causal nature of these relationships comes from a theoretical basis, not a statistical matrix.

Additionally, as is common in Structural Equation Modelling (Blunch, 2008), and as displayed in both the seminal Morgan and Hunt study (1994a, p.29)

and in subsequent Commitment Trust studies, many of the variables displayed significant co-variances. As such, the model was re-specified to have the antecedents as co-variants of each other for modelling purposes, which would normally be displayed as double headed arrows on the model.

As Blunch (2008, p.85) discusses however “…complicated models will give rise to a large number of such two headed arrows, which will contribute to the messiness of the drawing”. Structural equation diagrammatic models are to inform the reader, in an easy to understand format, as to the structure of the relationships and their direction of paths, not to confuse the reader with a messy diagram covered in covariance double headed arrows. In keeping with Blunch’s (2008) recommendations this study notes that on the structural diagrams presented in this thesis that the antecedent variables are co-variants, but does not display them on diagrams as such, for readability purposes.

7.7.5.2 Step 2: Modification Index Application In keeping with the structured two step approach to applying structural equation modelling (Arbuckle, 2009, p.107) the covariance sample matrix of the variables and error functions in the model was analysed by using the Modification Index application of AMOS. This index function identifies potential model modifications which could increase the reliability and goodness of fit of the model. Though (mis)-application of this technique, or

“slavish reliance” (Arbuckle, 2009, p.112) has its dangers in that inappropriate models can be identified, this study’s use of the Modification Index flows from the conceptual basis, “a modification should be considered only if it makes theoretical or common sense.” (Arbuckle, 2009, p.112)

From the output of the Modification Index analysis it was apparent from the data that a number of significant covariances existed in some of the error measurements (variances) of a number of observed variables. These variances related to concepts which would conceptually be expected to be interlinked measures, for example the variance (measurement error) of participants answering the fourth question on their Future Intentions to

re-subscribe is logically going to be similar to a related and subsequent fifth question regarding their Future Intentions to re-subscribe. Thus from a construct validity perspective, the addition of identified covariances of measurement error to the model makes “common sense” (Arbuckle, 2009, p.112) between the underlying variables singular latent variables. The model was consequentially re-specified on this basis with the errors allowed to co-vary in the model.

A structured approach was applied by this study in analysing and adapting the model to take into account the findings of the modification index (Appendix H). As conceptually it was logical that only covariances existed between the measurement errors (variances) of the items that constituted latent variables, only these where examined at the recommended threshold of 4 (Kline, 2007). This approach eliminated a number of spurious links identified by the modification index which did not logically fit with either the underlying literature or Commitment Trust Theory. Next, non-reciprocal links were eliminated from the analysis. By definition for there to be a covariance there must be a reciprocal connection between both items, thus while non-reciprocal indications from the Modification Index may indicate a possible connection between the variables (as may be expected in variables measuring the same latent construct), they do not fit within the logic being applied to examine covariance in the measurement errors.

Finally, with the model re-specified according to the two-step procedure, to check the internal validity of the additional measurement error covariance, significance tests were conducted. The significance tests concluded that of the covariances added to the amended model, two of the proposed covariances where not sufficiently statistically significant to indicate a robust and internally valid addition. These two non-significant amendments were eliminated from the model. Of the other measurement error covariances, all were found to be significant at either the 0.001 and 0.05 level. As such these amendments were incorporated into the re-specified model as they are internally valid.

As a final consideration for Construct Validity, and to add rigour to the re-specification, the questions the measurement error covariances related to were then re-examined to see if the logical basis of the argument for the amendments was compelling. This process is recommended by Arbuckle (2009) as a final “common sense” (p.112) check. After examination of the questions it was judged that there was sufficient logical rationale to conclude that the variance (measurement error) in the specified questions, all measuring the same latent variable, would be expected to be covariates. In other words, if a respondent is answering related questions regarding the same concept, it is logical to presume his answers would vary in the same direction.

7.7.6 Model Validation: Discrepancy Function, Missing