**3. Methodological Background**

According to the literature review above, the main aim of the article is to identify brand value sources of loyalty which are relevant to sustainable brand managemen<sup>t</sup> of alimentary goods. To achieve this aim, we have used the data from our own research provided on the socio-demographically representative sample of 2000 respondents (sample without outliers and incompatible units was 697) during the first half of 2019. We conducted this research via a questionnaire survey in the form of computer-assisted web interviewing respecting the ICC/ESOMAR (International code on Market, Opinion and Social Research and Data Analytics). The questionnaire was administered in Slovak Republic among its inhabitants over 15 years of age who were asked to complete the questionnaire because of their legal working subjectivity. Thus, the main presumption of autonomous buying decision-making has been fulfilled. On the other hand, one of the limitations of general applicability of the research outcomes has been caused by this fact—that is, territorial applicability of the recommendations done on the basis of research outcomes only in scope of Slovak consumer´s preferences. Thus, possible implementations of statements which result from research itself are applicable only in case of alimentary goods brands addressed to Slovak consumer (domestic or foreign). The questionnaire consisted of three parts with the following reasoning: (1) the first part covered the general socio-demographic profile of respondents; (2) the second part covered questions about perception of brand value sources generally, and (3) the third part covered questions about perception of brand value sources in details across the traditional typology of buying behavior and representative product categories.

To provide research of brand value sources in scope of buying behavior typology, the traditional quadratic typology of buying behavior has been used, where on the basis of the degree of engagemen<sup>t</sup> and differentiation, we can identify the following categories: (1) complex buying behavior (high involvement/significant differences between brands); (2) variety seeking behavior (low involvement/significant differences between brands); (3) dissonance-reducing buying behavior (high involvement/few differences between brands), and (4) habitual buying behavior (low involvement/few differences between brands) [53]. The last mentioned category is the category which is relevant for purposes of research of sustainable brand managemen<sup>t</sup> of alimentary goods. Brand value sources are analyzed in their traditional structure defined by Aaker—that is, (1) imageries; (2) attitudes; (3) attributes, and (4) benefits. The components of brand value sources are set in accordance with provided literature review and with relevance to so far identified specifics of psychographic profile of Slovak consumers [54].

The model of brand value sources identified by Aaker was used in accordance with the provided literature review due to its general applicability regardless specifics of product categories formulated on the principle of typology of buying behavior. The reason is that the presented article is only a partial outcome of complex research aimed to verify the internal diversification in brand value sources, ranking in case of brand value presence vs. absence across four basic product categories. Brand value sources and their relevant components which have been, through the realized questionnaire survey, tested in scope of their importance across product categories relevant for the types of buying behavior are summarized in the Table 1 below.


**Table 1.** Coding of brand value sources and their components relevant to further research evaluation.

> Source: Authors' own research, 2019.

Factor analysis has been chosen as the main statistical tool for evaluation of the consumer's perception of brand value sources in case of brand loyalty absence vs. brand loyalty presence. This analysis is one of the group of multidimensional statistical methods which are used to create so-called factors (previously unobservable variables) to reduce the amount of originally set attributes without losing the relevant information obtained inside the data set [55,56]. Recently, this statistical tool has been used with higher frequency in the social sciences due to the boom in information technology development and the need of reducing subjectivity. The definition of the relevant statistical model as well as the identification of rational assumptions is the base of this analysis. In the process of identification of relevant factors, it is primarily important to identify and test the dependence between originally defined variables through the correlation matrix. The basic presumption for the data reduction is the correlation of these variables verified by the correlation matrix creation as well as the fulfilment of the assumption that identified correlation exists as a consequence of less undetected hidden variables (factors). Based on this, it is possible to diversify originally defined variables into partial groups. In these groups, there are unified factors which internally correlate more inside the group than in comparison with other groups.

We assume that x is a p-dimensional random vector of the considered variables with a vector of mean values μ, a covariance matrix C (X) = Σ, and a correlation matrix of simple correlation coe fficients P (X) = P. One of the basic assumptions of factor analysis is the existence of R common background

factors *F*1, *F*2, ... , *FR*; trying to have them as little as possible, preferably less than *p*. The P-dimensional random vector consists of the *j*-observable random variables *xj*, *j* = 1, 2, ... , *p*; which can be expressed by Equation (1) as

$$X\_{\!\!\!\/} = \mu\_{\!\!\/} + \gamma\_{\!\!\/\/1}F\_1 + \gamma\_{\!\!\/12}F\_2 + \dots \, + \, \gamma\_{\!\!\/R}F\_R + \varepsilon\_{\!\!\/ \/1} \tag{1}$$

where ε1, ε2, ... , ε*p* are p stochastic error terms referred to as specific factors. If we write this in matrix, we ge<sup>t</sup> the Equation (2):

$$
\lambda \mathbf{x} = \mu + \Gamma f + \kappa,\tag{2}
$$

where Γ is a matrix of factors loadings type p R; *ƒ* is R-member vector of common factors, and ε is p-member vector of specific factors. Factors loadings can be considered as regression coe fficients p of observed variables on R nonobservable factors, and when certain conditions of solution are met, they are also covariance between the original and the new variables. Factors loadings can be interpreted as the contribution of the r-factor of the j-specified variable, when the same units of measurement are used. To determine the adequacy of the statistical sample, we use the KMO (Kaiser–Meyer–Olkin) Test Equation (3):

$$\text{KMO} = \frac{\sum\_{j \neq j'}^{p} \sum\_{j \neq j'}^{p} r^2(\mathbf{x}\_{j'}, \mathbf{x}\_{j'})}{\sum\_{j \neq j'}^{p} \sum\_{j \neq j'}^{p} r^2(\mathbf{x}\_{j'}, \mathbf{x}\_{j'}) + \sum\_{j \neq j'}^{p} \sum\_{j \neq j'}^{p} r^2(\mathbf{x}\_{j}, \mathbf{x}\_{j'}, \text{other } \mathbf{x})} \tag{3}$$

where *r*2 (*xj*, *xj'*) are simple correlation coe fficients and *r*2 (*xj*, *xj'* · other *x*) are partial correlation coe fficients under the condition of statically constant remaining p-2 variables. (*<sup>x</sup>*1, *x*2, ... , *xj* − 1, *xj* + 1, ... , *xj'* − 1, *xj'* + 1, *xp*).

Required value of KMO test should be higher than 0.6. By acquiring it, the adequacy of statistical sample is proved [57]. Required value of Barlett's test of sphericity should be lower than 0.05. By acquiring it, the dependence between variables is proved [58]. Required value of Cronbach's Alpha should be higher than 0.8. By acquiring it, the intrinsic consistency of the factors is proved [59]. Detection of the optimal values of these tests forms appropriate basis to the identification of the order of brand value sources in case of loyalty absence vs. loyalty presence. Thus, a set of advices formulated on the basis of factors identification and comparison of obtained results can be submitted to the practice of sustainable brand value building and managing of alimentary goods.
