Assumptions of multiple regression

191 Multiple regression techniques make a number of assumptions about the data that is being analysed, and therefore these assumptions need to be

accounted for. Prior to the multiple regression analysis, a number of tests were carried out to ensure that there had been no violation of the

assumptions, as outlined below.

Sample size – ‘The size of the sample has a direct impact on the

appropriateness and statistical power of the multiple regression’ (Hair et al., 2010 p174). Small samples, usually fewer than 30 responses, only allow simple regression with a singular independent variable. At the other end of the scale, large samples (greater than 1000) can make the data highly sensitive so that almost any relationship can be statistically significant (Hair et al., 2010). The base of 403 used in this study is well above the minimum to be considered small and well below the larger sample sizes that can generate sensitivity issues.

Multicollinearity – This occurs when the correlation among the independent variables is high – generally accepted as 0.90 or higher (Hair et al., 2010).

Such an occurrence creates problems as a high correlation between two independent variables can result in more than one variable explaining the same degree of variance in the dependent variable.

As the final scale correlation matrix shown in Table 4.44 (Chapter 4) demonstrates, none of the variables used in this study are too highly correlated, as no correlation scores are greater than 0.6.

To further ensure a lack of collinearity, the two most common diagnostics of tolerance and its inverse, the variance inflation factor (VIF) (Hair et al., 2010), were substantiated. The tolerance level is a direct measure that indicates how much of the variability of the specified independent variable is not explained by other independent variables, and should not be less than 0.10 (Tabachnick and Fidell, 2007). A low or small tolerance level indicates that there is a

degree of collinearity between variables. To ascertain the appropriate level of

192 tolerance, VIF is a secondary measure of multicollinearity, and should not be greater than 10.00 (Tabachnick and Fidell, 2007). All the observed variables were examined and were found to be within an acceptable range.

5.2.2 Partial least squares structural equation modelling (PLS-SEM)

SEM is important in enabling a comprehensive examination of the hypotheses presented in the conceptual model in this study. The analysis of the results is built from the technique of multiple and hierarchical regression in order to establish the direct relationships between the interdependent and dependent variables. However, regression analysis can only be applied to one dependent variable at a time. SEM examines the interrelationships expressed similarly in a series of multiple regression equations and estimates the dependence among all of the variables in the model (Hair et al., 2010). SEM is often considered as a covariance structure analysis, latent variable analysis or by the names of the software programs used to operate it, such as Linear Structural Relations (LISREL) or SPSS AMOS (Hair et al., 2010). There are two types of SEM methodology: covariance-based techniques (CB-SEM) and partial least squares (PLS-SEM).

More recently, PLS-SEM has become a common method of choice for

academics publishing in many of the leading marketing journals (Lacroix and Jolibert, 2015, Psychology and Marketing). Hair et al. (2012) have also identified well in excess of 200 PLS-SEM application studies published since 1981 in journals such as the Journal of Consumer Research and Journal of Product Innovation Management.

SEM analysis was undertaken in association to the regression analysis of this study for the following reasons. It is a standard model in marketing academic research, such as the Journal of Consumer Research. It also best suits the model and type of data characteristics examined in this study, and it has the ability to test interaction effects or moderating effects (Ringle, Wende and Will, 2005). However, a limitation of SEM is that parameter estimates are not

193 optimal with small sample sizes or a small number of indicators per latent variable. A rule of thumb calculation of 10 times the number of incoming paths on a construct is suggested by Chin, Marcolin and Newsted, (2003). The sample size for this study (n=403) is well in excess of the lower limit of 150 and hence is considered acceptable for this method.

The next section presents the results and a discussion of the regression analysis. The common abbreviations used are presented in Table 5.1.

Table 5.1 Legend:

PPRU = a consumer’s psychological predisposition to rapidly upgrade DE = Domain expertise

UM = Unique materialism BL = Brand loyalty

PF = Product factors PP = Perceived price

PEOU = Perceived ease of use VI = Vicarious innovativeness AD = Advertising

PLAY = Played with it

MOD/OSV = Modelled/observed people using the product VA = Vicarious adoption

DO = Disposal orientation DO_speed = Disposal speed DO_ethics = Disposal ethics SOU = Speed of upgrade

FIU = Future intent to quickly upgrade

194 5.3 Main study – regression analysis

The psychological propensity for a consumer to make a quick product upgrade decision is based on a number of existing constructs such as: DSI, DUCP, MAT, MM and BL. Figure 4.13 in Chapter 4 showed how these constructs could be combined to form subcategories after EFA. Hence, the PPRU measure is presented as a combination of:

 DE – DSI, MM and DUCP

 UM – MAT, DUCP and DSI

 BL.

These revised factors are now used in the hierarchical regression analysis, which is also used to screen for the influence of the key demographic factors of age, gender and household income.