Model testing

The current study employed SEM in AMOS to test the proposed model: whether consumers’ purchasing behaviour was influenced by their intention to buy, attitudinal

affections, attitudinal beliefs, perceived expectations from others, willingness to follow those expectations, perceived self-efficacy and controllability, perceived controllability of situations, perceived majority, tendency to fit in with the perceived majority, self- identity and past purchasing behaviour. Before assessing the relationships between the proposed constructs in this study (i.e. how one construct influences another and to what degree), it was important to confirm that the model was a good fit for the data (Tabachnick & Fidell, 2013).

SEM, also known as covariance structure analysis, path analysis and CFA (Kline, 2011; Tabachnick & Fidell, 2013), allows researchers to investigate the relationships between various independent variables (IVs) and dependent variables (DVs), as well as to assess parameters proposed in a model and evaluate hypotheses. It estimates the measurement errors in psychometric measures and provides fit indices for the model in question (i.e. whether the model is a good fit for the data, or whether the discrepancy between the proposed model and data is significant). SEM has been an important and widely used statistical technique for researchers in consumer research (Fabrigar, Porter, & Norris, 2010; Iacobucci, 2010). However, SEM is generally a large-sample technique, meaning estimations are less stable if the results are generated from small samples. As discussed earlier, the adequate sample size for the current study was around 300.

3.5.5.1 Estimation method and statistical assumptions

The statistical estimation method for the parameters of the proposed model in this study was ML. The main statistical assumption based on the ML estimation method is that the examined data is normally distributed, especially at the multivariate level (Kline, 2011).

ML is the default estimation method in most SEM computer programs and is a widely reported method in studies using SEM for data analysis (Kline, 2011). ML estimates and maximises the likelihood that the observed covariances (i.e. data collected from random samples) are drawn from the whole population. A chi-square value in conjunction with the p-value and the df are generated by the ML estimation to describe the model’s fit. The assessment of the model’s goodness-of-fit is discussed in Section 3.5.5.2.

One main assumption of ML estimation is that the data is normally distributed, especially at the multivariate level (Kline, 2011). If the requirement of multivariate normality cannot be met, the bootstrap technique can be used as a post hoc adjustment to assess model fit (Bollen & Stine, 1992; Byrne, 2010). By bootstrapping the data, a researcher can create various subsamples from an original dataset. Through repetitively estimating the parameter distributions from the subsamples, the bootstrap technique will generate a p-value of an adjusted chi-square distribution.

3.5.5.2 Assessment of model fit

The focus of this subsection is on the assessment of model fit. There are two common ways to assess model fit: through chi-square (X2) goodness-of-fit statistics and through fit indices (Hu & Bentler, 1999; Iacobucci, 2010). The assessments, generated by AMOS, are detailed below.

Chi-square (X2) and degree of freedom

The X2 goodness-of-fit statistics include the X2 value, df and p-value. The df refers to the model’s degrees of freedom (dfM), which is the difference between the

number of observations ( , where v refers to the observed variables in the model) and the number of parameters measured (q). Therefore, the dfM is calculated by the

following formula: dfM =

(Kline, 2011). The X2 value assesses the discrepancy between the model and the data, to the specified df, and the p-value suggests the significance of the discrepancy. A non-significant p-value (>.05) is desirable for a model fit, suggesting that the proposed model does not significantly deviate from the sample (Iacobucci, 2010; Kline, 2011; McDonald & Ho, 2002).

However, X2 is sensitive to sample size and multivariate normality (Tabachnick & Fidell, 2013). When the sample size is large, the X2 value tends to signal significant discrepancy for trivial differences. When the sample size is small and/or the multivariate distribution is not normal, the probability levels of the computed X2 will

not be accurate. A corrected chi-square value for sample size (i.e. CMIN/DF, ratio of the chi-square value to the df, where CMIN is the chi-square value and DF refers to the degree of freedom) can be used for inspecting the model fit; a value less than five is considered a reasonable fit (Marsh & Hocevar, 1985; West, Taylor, & Wu, 2012).

As well as indices relating to the chi-square, there are other fit indices used for supporting model fit. Commonly reported fit indices include the standardised root mean square residual (SRMR), the comparative fit index (CFI), the root mean square error of approximation (RMSEA) and bootstrap p-value (for indicating the significance level of an adjusted discrepancy between the proposed model and the data, as discussed earlier) (Bollen & Stine, 1992; Hu & Bentler, 1999; Iacobucci, 2010; Tabachnick & Fidell, 2013).

Standardised root mean square residual (SRMR)

SRMR estimates the differences between the sample’s and the estimated population’s variances and covariances. The SRMR value ranges from zero to one. Smaller SRMR values indicate a good-fitting model. A cut-off point suggested by Hu and Bentler (1999) is .08; i.e. the SRMR values that are less than .08 indicate a model that is a good fit.

Comparative fit index (CFI)

CFI is an incremental fit index, weighing the relative fit of the proposed model over the independence model (Bentler, 1990). An independence model refers to the model that only measures error variances and in which the variables in the model are unrelated to each other (Kline, 2011). The CFI value ranges from zero to one. Values greater than .95 indicate that the model is a good fit for the data (Hu & Bentler, 1999).

Root mean square error of approximation (RMSEA)

RMSEA measures a model’s poorness-of-fit by inspecting the error of approximation in the examined population. The greater the value, the larger the error in the examined population (Browne & Cudeck, 1993; Byrne, 2010). Values of .06 or less suggest that the model is a good fit. Values greater than .10 indicate that the model does not fit the data (Byrne, 2010; Hu & Bentler, 1999). This index favours larger models with more observed variables and is less useful for a dataset with a small sample size, as it tends to over-report model rejection (Kline, 2011). AMOS also examines the closeness of fit (PCLOSE), which indicates the significance level of the computed error

(Byrne, 2010). A non-significant result of the PCLOSE is desirable (i.e. PCLOSE >.05), suggesting that the error is not significant.

3.6 Summary

This study conducted an online survey to collect quantitative data for model testing. The questionnaire contained a total of 62 questions, of which 55 were designed to collect data to analyse the proposed constructs in the hypothesised model: attitudinal affections, attitudinal beliefs, injunctive norm (the perception of the injunctive norm and the willingness to comply with the perception), perceived self-efficacy and controllability, descriptive norm (the perception of the descriptive norm and the willingness to comply with the perception), self-identity, past behaviour, intention and behaviour.

Preliminary data analyses were conducted first to identify and resolve any issues relating to missing data and the data’s normality. Then the relationships between the variables and their related underlying concepts were assessed. The next inspection focused on the relationships between the constructs to assess the discriminant validity of the examined variables. Before testing the proposed model, CMV was inspected to determine the existence of common method bias. The final step was model testing (i.e. testing hypotheses). The results from the analyses are reported in Chapters 4 and 5.