3.2.2. Variable Preparation
The FsQCA 3.0 (Fuzzy set Qualitative Comparative Analysis) software was used to apply the fuzzy methodology since it uses (fuzzy) set theory and Boolean algebra to analyze the extent to which certain factors or combinations of factors are present or absent when a phenomenon of interest occurs or not [
25]. This methodology performs a systematic cross-search analysis that models a relationship between variables related to the membership of a set and configuration of identities that reflect a sufficient condition for an outcome of interest. The factors that are considered to be causes of a phenomenon are called “conditions”, while the phenomenon itself is called “outcome”; thus, once the sample of 48 people (or cases) is available, with the 12 input variables (the characteristics of the profile that professionals from consulting firms or the IDB should have) and the 4 output variables (the factors that influence the success of development cooperation projects), they are calibrated to analyze the data in the fsQCA 3.0 program. The calibration allows to evaluate the established scores in relation to external norms and existing theory. Boolean algebra facilitates the transformation of the original scale values into values of the fuzzy sets for the antecedent (independent variable) and outcome (dependent variable) conditions. Calibration makes fuzzy sets superior to conventional measures, as they offer a middle way between quantitative and qualitative measures [
26].
Direct calibration was used for the investigation, as it uses the full membership threshold, the not full membership threshold, and the crossover point, which is the value of the interval scale variable at which there is maximum ambiguity about whether a case is more inside or more outside the target set. These three crossover points are used to transform the original ratio or interval scale values into fuzzy membership scores using transformations based on the logarithmic probabilities of full membership. Calibration determines the degree of membership of the cases in each of the sets, with scores ranging from 0 to 1. In the program the operation is performed through the calibrate function (x1, n1, n2, n3), where x1 represents the name of a ratio or interval scale variable already existing in the file, n1 corresponds to the threshold of full membership in the target set (0.95), n2 corresponds to the crossover point (0.5) in the target set and n3 corresponds to the threshold of non-membership in the target set (0.05) [
23]. For these reasons, it was decided to work with the maximum, minimum and mean of the scores obtained. Thus, in
Appendix C it can be seen what the interpretation of these calibrations would be.
3.2.3. Analysis of the Necessary Conditions
As explained in the fsQCA software User’s Guide, the main difference between a necessary and sufficient condition is that a necessary condition must be present for an outcome to occur, whereas a sufficient condition by itself can produce a given outcome [
23]; however, neither necessity nor sufficiency exists independently of the theories proposing the conditions; rather, they are often considered together because all combinations of the two are meaningful. There are four categories of conditions formed from the cross-tabulation of presence or absence of sufficiency versus presence or absence of necessity.
A condition is necessary and sufficient if it is the only condition that produces an outcome, and it occurs because of a combination of causes.
A condition is necessary, but not sufficient, if it can produce a result in combination with other causes and appears in all those combinations. Finally, a condition is neither necessary nor sufficient if it appears in only a subset of the combinations of conditions that produce an outcome.
For the research, since the fuzzy methodology results in a logical statement describing combinations of conditions that are sufficient for the outcome, the listed combinations may not explain all cases of the outcome. Next, both the necessity and sufficiency of individual conditions were examined before analyzing sufficient combinations of conditions.
That said, the values obtained for the outcome SUCCESS and its negated version (~SUCCESS) are analyzed, while the conditions were the factors (EFT, PTN, SGR) and their negated versions (~EFT, ~PTN, ~SGR), which represent the absence of the conditions or the outcome. According to Ragin [
26], a condition is necessary when it has a consistency index value greater than 0.9. From
Table 8, which shows the summary of the results obtained for the necessary conditions, it can be seen that for a development cooperation project to be very successful, according to the Necessary conditions, it needs to consider mainly the effectiveness and sustainability factors. This can be interpreted that as long as the objectives are met with those foreseen, making good use of the resources, meeting the expectations of the population, presenting a good technical and operational feasibility that is controlled with adequate risk management, and is sustainable over time, generating a positive impact on the population in the short, medium, and long term, contributing to society, the environment, and the economy of the region, the project can be considered successful. Similar results were obtained in previous studies such as Rodríguez-Rivero et al. 2020, analyzing development projects in Colombia [
27].
On the other hand, when success is absent (~Success), the most influential condition is the absence of effectiveness. This is interpreted as meaning that a project will not be successful if there is no good control of this factor in the management of cooperation projects. Similarly, the factors of relevance and sustainability must be considered since their absence would cause the failure of the project.
3.2.4. Analysis of the Necessary Conditions
To continue with the data processing, the data matrix was transformed into a truth table. The truth table algorithm asks to indicate the result through the settings option and the conditions through the add option to add the conditions. These conditions will be used to analyze the conditions leading to the presence of the result and to analyze the absence of the result. To do this, the negation of the result must also be set with the “Set negated” option. The program allowed to show the cases of each row that represent the scores of the participants in the truth table, so the option to activate the cases in the output was activated through the option “Show solution cases” in the output. As mentioned, the purpose of the methodology is to identify the sufficient configuration for the truth table algorithm to identify enough cases to achieve the result. The first outcome defined is SUCCESS and the causal conditions EFT, PTN, and SGR.
Once the result has been archived, the conditions and cases of the model and the truth table of the Efficiency factor, have been indicated. The conditions in the truth table are described in terms of zeros, which indicate absence, and ones, which indicate presence. Therefore, although the data matrix contains fuzzy data, the truth table shows only zeros and ones.
In addition, one can see that the program has distinguished between all possible configurations in the rows, which is the first step in obtaining the truth table. The column “Cases” shows the number of cases in each row of the truth table and in brackets the cumulative percentage of each row. By pressing the buttons, it was possible to observe the cases that were assigned to the rows, representing the participants. Then, the value of the result of each row was determined according to its gross consistency in order to finish with the last part of the elaboration of the truth table and perform the logical minimization process. To determine which configurations or rows of the truth table are sufficient for the result, the column with the results in the table was defined. It is worth noting that the consistencies must be at least 0.75 for crisp sets and at least 0.8 for fuzzy sets to be considered a consistent and sufficient configuration for the result.
From the truth table, which presents 2k rows, with k being the number of causal conditions or independent variables, all possible combinations of causal conditions were reflected by presenting ones and zeros. These numbers represent the total membership and the null membership of each condition, respectively. For each row of the Truth Table, a value is created for each of the following variables: cases, raw consist, PRI consist, and SYM consist.
Cases indicates the number of cases that show the combination of conditions;
Raw consist presents the consistency or proportion of cases in each row of the truth table that show the result;
PRI consist is an alternative measure of consistency developed for fuzzy sets based on a quasi-proportional reduction of the error estimate;
SYM consist is an alternative measure of consistency for fuzzy sets based on a symmetric version of PRI consistency.
In the research, tests were carried out until the conditions of the sufficiency of coverage and consistency of the solution were at least 0.8. This means a good representativeness according to Ragin (2008); however, there were also cases in which it was decided to accept a solution with average representativeness so that the values of own and unique coverage were acceptable, since their combinations would represent the best option within the valid working margins to obtain a reliable solution. This was the case for the efficacy, ~effectiveness, and relevance factors. On the other hand, since the research does not have many cases, the frequency threshold equivalent to 1, which represents the minimum number of times a configuration must occur before including it in the minimization process, was kept at one. To start the logical minimization process, the Standard Analysis option was used, which automatically performs the minimization, unlike the Specific Analysis. The research analyzed how the conditions should contribute to the occurrence of the result when they are present or absent. The Standard Analysis produced three different results: complex solutions; simplified solutions; and intermediate solutions:
Complex solutions, although the most complete and detailed solution, are the most difficult to interpret and is not recommended, as they provides very little insight into the causal conditions [
28];
Simplified solutions opt for maximization. In the program, they are those assumptions whose combination of conditions is false, id est., there are no cases present in the result. The main conditions can be found in this solution;
There are also intermediate solutions, which are solutions that combine the logic of the two previous ones, and it is specified that certain causal configurations not included in real cases determine the success of the project. In this solution, main and contributing conditions can be found.
The Quine–McCluskey algorithm is the one applied in the software. Given that the most recommended solution for research projects for presenting better consistency than the simplified and complex solutions, the intermediate solutions were used [
29]; likewise, it was also chosen to use the simplified solutions because it corroborated the presence of the main conditions since the intermediate ones presented these and the contributory ones. The intermediate solution is constituted by the effective thresholds of frequency and consistency. In addition, the minimum formula is found with each term of the solution in a row of the table described with the Boolean operations of the asterisk; and the consistency and coverage specified for each term of the solution and the solution as a whole:
The analysis of the combination of sufficient conditions to identify the causes of the success factors was performed with the fsQCA software. In the research only the analysis of the factors effectiveness, relevance and sustainability, and risk management was performed since the other factors (motivation and additionality) were summarized as a single component in the questions of the form; however, the presence of these factors in a project is as relevant as the factors that were analyzed.
Combination of Sufficient Conditions for the SUCCESS Factor Result
Of all the combinations, the most representative is the one with the highest own coverage. This is because the own coverage considers its participation in other conditions, while the single coverage only takes into account the coverage of the own condition. It is due to the overlap of cases in the different combinations that the single coverage presents very small values [
32,
33].
Table 9 presents the results for the intermediate and simplified solutions. With a minimum consistency threshold of 0.90, it is observed that the intermediate solution has a coverage of 0.97 and a consistency of 0.82, indicating that it has good representativeness of the conditions in the outcome variable, i.e., in the Efficiency Factor. Of the possible combinations, the configuration with the highest eigen-coverage of the table in the intermediate solution equals 0.954 and presents a very high consistency of 0.88 is ~PTN*SGR; as well as the other eigen-coverage of EFT*~SGR and EFT*~PTN equals 0.494 and consistency of 0.92. It can be inferred that the efficacy factor is more representative than the sustainability factor, and in two of them there is absence of significance. This means that the absence of relevance can be compensated by the effectiveness and sustainability factors. In the simplified solution, the EFT and SGR components are reaffirmed as important for the success of a project, presenting a solution with an own coverage equivalent to 0.97 and a unique coverage of 0.82.
Thus, effectiveness and sustainability factors are considered as the main conditions; and absence of relevance (~PTN) as a contributing condition.
Combination of Sufficient Conditions for the ~SUCCESS Factor Result
Table 10 shows the possible combinations of the intermediate solution. For this case, the simplified solution is not shown because the software failed to detect any row in the truth table that is accepted as sufficient for the result. With a minimum consistency of 0.8, it was observed that the solution presents a high representativeness with a coverage of 0.95 and a consistency of 0.94. It can be observed that the most representative and successful unique combination is ~SGR, which has a coverage of 0.93 and 0.97, respectively. This means that, in the absence of good control over sustainability and risk management, the project will not be successful.
Thus, the absence of the sustainability and risk management (~SGR) factor can be considered as the main component. There are no contributing conditions.