The interpretation of an empirically complex construct like lifestyle builds on the understanding of the exact intercorrelations among all items. One possibility to the understanding of intercorrelations would be the application of bivariate correlation analysis, a method which allows to analyze pairs of variables. However, this approach becomes inappropriate when exceeding a certain number of variables (45 items of the activity scale, for example, result in a barely interpretable correlation matrix of 990 single values and 113 items of the media scale even in a matrix of 6328). Factor analysis (mainly developed by Hotelling 1933; Kelley 1935) expresses the intercorrelation structure by a limited number of variables (the factors), based on a simple principle: If several variables correlate with each other, they share common information. The idea is to create a new variable which captures this common information, i.e. which correlates as highly as possible with each of these variables. The new variable is called factor (which is not the same as ‘factor’ in analysis of variance or in varbrul). However, after having captured the common information by one factor, some residual intercorrelation remains which could not be captured. This residual variance is captured by a second factor. One continues this process until the intercorrelations among the variables are sufficiently explained. Therefore, the different factors maximally and successively explain the variance in a PCA. The method is based on an orthogonal rotation transformation. The different factors remain uncorrelated in the PCA (Principal Component Analysis, the type of factor analysis we used here) with so-called orthogonal rotation transformation and ensure a complementary, non-redundant assessment of the information. Factors are mutually independent, creating therefore an order structure with non-redundant information. A person is represented in the multidimensional space by one specific point and the whole sample by a scatterplot. This p-dimensional system of coordinates is then rotated such that the projections of all persons on one axis show maximal dispersion. This axis explains maximal variance and represents the first factor. Technically, this factor has been extracted and the whole technique is called extraction method. Then, another rotation of the p-1 axes is carried out such that one of the axes – the second factor – maximally explains the residual variance. This process continues in an iterative way. The rotations are orthogonal transformations: The axes are orthogonal to each other, in other words, the factors are independent. A rotation transformation of the whole system of coordinates maintains the total variance of the p variables. The transformation only distributes the total variances differently on the new axes. If the intercorrelations among the various variables are high, only a few factors are required until enough variance has been explained so that the residual is negligible. Table 1 shows the final factor-analytical solution, i.e. the rotation matrix, for the leisure dimension. The first column of the table shows the items (i.e. the original questions) regarding this lifestyle dimension.

The factor loading a_ij indicates the correlation between a variable i and a factor j. The variables with the highest loads (the cells in Table 1 are the factor loadings) are important for interpreting a factor. One aims at circumscribing the common information of all single variables included in a factor. +1 or -1 means perfect dependence, 0 means complete independence. In Table 1, loadings a_ij with |a_ij| < 0.3 are not shown since their impact on the factor can be considered as negligible.

The factor score f_mj shows how important factor j is for person m. Its mean value is always 0. If a person shows high values on the variables included in a factor, factor score f_mj will also be high. Each line in Figure 3 in the paper denotes the mean factor values of a lifestyle group. These mean values illustrate the sociocultural profile of the different lifestyle prototypes.

The result of this transformation does not necessarily provide for a comprehensible, i.e. well interpretable solution, because it produces much higher loadings on the first factor than on the q-1 following factors. Rather, one seeks a solution in which one can subsume a certain variable set under each factor and have a better balance between them with respect to the total variance explained. Therefore, a rotation technique is applied to the factors that have been extracted with the principal component analysis (this should not be confounded with the rotation explained above which is part of the PCA). After having decided the number of factors to be extracted, this rotation produces a redistribution of the total variance explained by the extraction solution among the different factors. As for the extraction technique, many possible methods exist for rotation. We apply the frequently used Varimax rotation method. Technically, the rotation results in a maximization of the variance of the squared loadings of each factor.

Factor and cluster analysis are heuristic methods and as such, they do not propose one single solution. Rather, there are many possible (in fact infinitely many) solutions of which a plausible one is chosen. This concerns primarily the number of factors and the number of clusters to be chosen. With regard to factor analysis, the solution has been retained based on (i) interpretability of the factors and (ii) a similar ratio of items to factors across the four factor analyses in order to maintain a similar degree of reduction (6.4 for activities, 7.1 for media, 9.3 for clothing, 6 for values). The eigenvalue λ_j, i.e. the amount of total variance explained by factor j, is also a useful information for determining the number of factors, but it will not be further discussed here (but see Adli 2004: 215-216). Interpretability is favored by solutions that correspond more to Thurstone’s (1947) criterion of simple structure: On each factor, loadings of some variables are as high as possible and the loadings of other variables are as low as possible, and across factors, one should have different sets of highly loading variables.

In the next step, the entire sample, consisting of 102 persons, each of them with an individual profile on 28 factors, has been divided into four groups by means of cluster analysis (Tryon 1939; Ward 1963). Homogeneity and heterogeneity within and between clusters are quantitatively measured by similarity or distance measures (here the Euclidian metric). The intricate aspect in cluster analysis is the fact that already at small sample sizes, the optimal solution cannot be found in a simple manner because of an excessive number of necessary computations. Our sample of 101 subjects leads, according to Bell number approximation, to as many as  possible groupings. Therefore, the algorithm has to get to a solution which is as close as possible to the (unknown) optimal solution, while considerably reducing the number of cluster solutions that are actually compared. We have used a two-step procedure (see Milligan & Sokol 1980): First, we applied a hierarchical method (Ward) which starts with the finest possible partitioning (i.e. each person is one cluster) and which successively reduces the number of clusters by merging some of them.

Then, we optimized the solution using the non-hierarchical k-means method (McQueen 1967) which starts at a given partitioning and tries to improve the initial solution by moving objects from one cluster to the other (i.e. not by changing the number of clusters). Each cluster has a center. Points that are close to the center are prototypical examples of the cluster, points at the margin are less prototypical but they still belong to the group.

In the final result of our study, each subject is characterized by one of four values, i.e. the cluster membership. We considered the 3-, 4-, and 5-cluster solution for our interpretation (less than three lifestyle groups would not allow sufficient social differentiation in Bourdieu’s framework, more than five clusters often lead to groups that are hard to interpret in a differential manner). The four-cluster solution has been retained: It is well interpretable and it also allows satisfactory grounding in the sociocultural theory of Bourdieu (at least one orthodoxy, one heterodoxy, and two doxa groups).