Configurational fuzzy-set analysis method

Research on firm performance (or basically any other output variable) often assumes that causal and linear relationships exist between firm performance and its causes. In reality, these relationships are much more complex and tenuous. In order to take this complexity into account, I employ fuzzy-set qualitative comparative analysis as complementary analysis method in sub-study 2, focusing on the effectiveness of the configurations of marketing investments and other strategic factors in terms of sales and

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profitability growth. FSQCA allows me to examine how complex combinations of variables (beyond two-way interactions) interact to produce outcome variable (i.e., high effectiveness in sub-study 2).

Traditional methods such as regression analysis and FSQCA differ in their view of cases with extreme values: they are frequently seen as atypical outliers in regression studies, whereas they are often seen as crucial and highly representative instances of a phenomenon in fuzzy-set studies (Katz, Vom Hau and Mahoney 2005). Additionally, unlike regression, fuzzy-set analysis requires researchers to measure causal factors and outcomes on a scale of 0 to 1 according to their degree of membership in a given qualitative state (Katz, Vom Hau and Mahoney 2005; Kent and Argouslidis 2005; Viswanathan and Childers 1999). Furthermore, in regression research, analysts frequently assume linear causation and attempt to estimate the average effect of a given variable net of all other variables (Katz, Vom Hau and Mahoney 2005). In fuzzy-set research, in contrast, analysts assume necessary and sufficient causation, including combinations of jointly sufficient causes (Katz, Vom Hau and Mahoney 2005).

To empirically accomplish the identification of causal processes, FSQCA proceeds in three steps. After the independent and dependent measures have been transformed into sets, the first step is using these set measures to construct a data matrix known as a truth table with 2ހ rows, where h is the number of causal conditions (i.e., independent variables) used in the analysis. In a second step, the number of rows is reduced in line with two conditions: (1) the minimum number of cases required for a solution to be considered and (2) the minimum consistency level of a solution. In a third

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step, an algorithm based on Boolean algebra is used to logically reduce the truth table rows to simplified combinations (Fiss 2011).

Consistency refers to the degree to which cases correspond to the set-theoretic relationships expressed in a solution (Järvinen et al. 2009). In other words, consistency measures how often the solution terms and solution as a whole are subsets of the outcome, and they reflect the frequency with which solutions can be considered sufficient conditions for the outcome (Ordanini and Maglio 2009). The value of the consistency score ranges from zero to one. The value of one indicates full consistency, that is, all cases are subsets of the outcome. In general, consistency scores between 0 and .75 indicate the existence of substantial inconsistency (Järvinen et al. 2009). To simplify, in the context of this thesis, consistency of .80, for example, means that 80 per cent of firms with a given combination exhibit high business growth.

In the third step, when the truth table algorithm of FSQCA (in the program) is employed to obtain the final solution, two solutions of interest can be obtained. These are called the complex solution and the parsimonious solution. The parsimonious solution is generated by re-analyzing the truth table with the “remainder” rows (configurations lacking adequate empirical instances) set to “don’t care” (i.e., configurations with cases less than the frequency threshold [see below] are considered to be associated with the outcome of interest) (Rihoux and Ragin 2007). I interpret the complex solutions in my analysis24_{. Some researchers argue that many of the parsimonious solutions can be}

24 In the present study, there are only very few configurations that fulfill the criteria (frequency threshold 3 for B2B firms and 2 for B2C firms). Thus, the parsimonious solutions can be considered to be “too parsimonious” (cf. Ragin and Sonnett 2004). Consider as an example the FSQCA analysis of B2B firms with outcomes sales growth after one year, sales growth after two years and profitability growth after one year. In the analyses of B2B firms with these outcomes, parsimonious solutions consist of every potential configuration of variables (that is, independent of investment selection, business model, assets and funding source configurations are associated with high effectiveness in parsimonious solutions). With the

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considered to be “too parsimonious” (i.e., when assumptions oversimplify) (cf. Ragin and Sonnett 2004) because the simplifying assumptions that are incorporated via counterfactual analysis are untenable (i.e., the rows in the truth table that have no empirical evidence) (Järvinen et al. 2009).

“The fuzzy-set analysis can be done veristically with no tolerance for contradictory outcomes, or probabilistically with the researcher defining the level of probability to be tolerated (e.g., 0.80 for “almost always” necessary)” (Kent and Argouslidis 2005: 651). In this dissertation, I will complete my analysis probabilistically and, following Fiss (2011), the level of probability to be tolerated is .80. Hence, sets with levels above the consistency threshold (i.e. .80) will be identified as consistent sufficient conditions for the outcome (1), and the remaining sets will be codified accordingly (0). Following Fiss (2011), the minimum number of cases required for a solution to be considered in my empirical analysis (i.e., frequency threshold) was 3 for B2B firms. Due to smaller sample size, the frequency threshold was relaxed to 2 for my analysis with B2C firms. To simplify, these selected figures mean that for a certain configuration of factors (i.e., investment, market-based assets, source of capital etc.) to qualify as a solution leading to a “high” outcome (of sales or profitability growth), 80% of firms exhibiting that configuration are needed to exhibit the high (sales/profitability growth)

aforementioned frequency threshold 3 after “delete and code” command of FSQCA program (the command removes paths without adequate empirical evidence and sorts the remaining paths in order of the consistency) only 2 paths (3 for sales growth after two years) remain in the truth table. Both these paths (or all 3 paths for sales growth after two years) are associated with the favorable outcome, that is high effectiveness. Thus, when there are no paths in the truth table that are not associated with high effectiveness, parsimonious solution results table would be empty (see reporting of Fiss 2011), with all conditions “don’t care”. For the aforementioned analyses of B2B firms, the FSQCA program does not show any parsimonious solution, instead it returns an error message “Error (Quine-McCluskey): The 1 Matrix Contains All Configurations”. Due to the above reasoning, parsimonious solutions have been left out from reporting of the present dissertation.

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outcomeʊand additionally, there needs to be two firms in the sample that exhibited that configuration of factors (three in the case of B2B firms).

FSQCA, thus, enables us to study the influence of configurations of several contingent variables on the marketing investment effectiveness. Essentially, the configurational approach rests on the assumption that organizational phenomena can be best understood by identifying distinct, internally consistent sets of firms rather than universal relationships that hold across all firms (Ketchen et al. 1997). Organizational configurations can be defined as any multidimensional constellations of conceptually distinct but interdependent characteristics that commonly occur together, falling into coherent patterns (Meyer et al. 1993). In the context of this dissertation, these configurations consist of source of capital, market-based asset structure, and product profile, as well as investment selection, that occur together.

The configurational approach acknowledges that there are usually more than one configuration associated with the outcome of interest (Meyer et al. 1993): so called equifinality. Thus, in the context of this analysis, it is possible that there are various combinations of contingent variables that explain a specific performance outcome (i.e., sales/profitability growth).

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