Qualitative comparative analysis

In statistics, qualitative comparative analysis (QCA) is a data analysis technique for determining which logical conclusions a data set supports. The analysis begins with listing and counting all the combinations of variables observed in the data set, followed by applying the rules of logical inference to determine which descriptive inferences or implications the data supports. The technique was originally developed by Charles Ragin in 1987.

Summary of technique

In the case of categorical variables, QCA begins by listing and counting all types of cases which occur, where each type of case is defined by its unique combination of values of its independent and dependent variables. For instance, if there were four categorical variables of interest, {A,B,C,D}, and A and B were dichotomous, C could take on five values, and D could take on three, then there would be 60 possible types of observations determined by the possible combinations of variables, not all of which would necessarily occur in real life. By counting the number of observations that exist for each of the 60 unique combination of variables, QCA can determine which descriptive inferences or implications are empirically supported by a data set. Thus, the input to QCA is a data set of any size, from small-N to large-N, and the output of QCA is a set of descriptive inferences or implications the data supports.

In QCA's next step, inferential logic or boolean algebra is used to simplify or reduce the number of inferences to the minimum set of inferences supported by the data. This reduced set of inferences is termed the "prime implicants" by QCA adherents. For instance, if the presence of conditions A and B is always associated with the presence of a particular value of D, regardless of the observed value of C, then the value that C takes is irrelevant. Thus, all five inferences involving A and B and any of the five values of C may be replaced by the single descriptive inference "(A and B) implies the particular value of D".

To establish that the prime implicants or descriptive inferences derived from the data by the QCA method are causal requires establishing the existence of causal mechanism using another method such as process tracing, formal logic, intervening variables, or established multidisciplinary knowledge.[1] The method is used in social science and is based on the binary logic of Boolean algebra, and attempts to ensure that all possible combinations of variables that can be made across the cases under investigation are considered.

Motivation

The technique of listing case types by potential variable combinations assists with case selection by making investigators aware of all possible case types that would need to be investigated, at a minimum, if they exist, in order to test a certain hypothesis or to derive new inferences from an existing data set. In situations where the available observations constitute the entire population of cases, this method alleviates the small N problem by allowing inferences to be drawn by evaluating and comparing the number of cases exhibiting each combination of variables. The small N problem arises when the number of units of analysis (e.g. countries) available is inherently limited. For example: a study where countries are the unit of analysis is limited in the fact that are only a limited number of countries in the world (less than 200), less than necessary for some (probabilistic) statistical techniques. By maximizing the number of comparisons that can be made across the cases under investigation, causal inferences are according to Ragin possible.[2] This technique allows the identification of multiple causal pathways and interaction effects that may not be detectable via statistical analysis that typically requires its data set to conform to one model. Thus, it is the first step to identifying subsets of a data set conforming to particular causal pathway based on the combinations of covariates prior to quantitative statistical analyses testing conformance to a model; and helps qualitative researchers to correctly limit the scope of claimed findings to the type of observations they analyze.

Criticism

As this is a logical (deterministic) and not a statistical (probabilistic) technique, with "crisp-set" QCA (csQCA), the original application of QCA, variables can only have two values, which is problematic as the researcher has to determine the values of each variable. For example: GDP per capita has to be divided by the researcher in two categories (e.g. low = 0 and high = 1). But as this variable is essentially a continuous variable, the division will always be arbitrary. A second, related problem is the fact that the technique does not allow an assessment of the effect of the relative strengths of the independent variables (as they can only have two values).[2] Ragin, and other scholars such as Lasse Cronqvist, have tried to deal with these issues by developing new tools that extend QCA, such as multi-value QCA (mvQCA) and fuzzy set QCA (fsQCA). Note: Multi-value QCA is simply QCA applied to observations having categorical variables with more than two values. Crisp-Set QCA can be considered a special case of Multi-value QCA.[3]

Statistical methodologists have argued that QCA's strong assumptions render its findings both fragile and prone to type I error. Simon Hug argues that deterministic hypotheses and error-free measures are exceedingly rare in social science and uses Monte Carlo simulations to demonstrate the fragility of QCA results if either assumption is violated.[4] Chris Krogslund, Donghyun Danny Choi, and Mathias Poertner further demonstrate that QCA results are highly sensitive to minor parametric and model-susceptibility changes and are vulnerable to type I error.[5] Bear F. Braumoeller further explores the vulnerability of the QCA family of techniques to both type I error and multiple inference.[6] Braumoeller also offers a formal test of the null hypothesis and demonstrates that even very convincing QCA findings may be the result of chance.[7]

Response to Criticisms

QCA can be performed probabilistically or deterministically with observations of categorical variables. For instance, the existence of a descriptive inference or implication is supported deterministically by the absence of any counter-example cases to the inference; i.e. if a researcher claims condition X implies condition Y, then, deterministically, there must not exist any counterexample cases having condition X, but not condition Y. However, if the researcher wants to claim condition X implies condition Y with at least 90% probability, then the proportion of counterexample cases to an inference to the proportion of cases having that same combination of independent variables must be less than 10%. For each prime implicant that QCA outputs via its logical inference reduction process, the "coverage"—percentage out of all observations that exhibit that implication or inference—and the "consistency"—the percentage of observations conforming to that combination of variables having that particular value of the dependent variable or outcome—are calculated and reported. Thus, one of the key benefits of the QCA method is its ability to identify subsets of the data conforming to implications or descriptive inferences that would be missed in typical statistical analyses that, of necessity, treat the entire dataset as being determined by one set of causal factors.

In real-life complex societal processes, QCA enables the identification of multiple sets of covariate combinations that consistently are associated with a particular output value.

Fuzzy set QCA aims to handle variables, such as GDP per capita, where the number of categories, decimal values of monetary units, becomes too large to use mvQCA.[8]

Fields of use

QCA has now become used in many more fields than political science which Ragin first developed the method for. Today the method has been used in:

References

  1. ↑ qualitative comparative analysis - History Of qualitative comparative analysis | Encyclopedia.com: Dictionary Of Sociology
  2. 1 2 J. Goldthorpe, "Current issues in comparative macrosociology" in Comparative social research, 16, 1997, pp. 1-26.
  3. ↑ Rihoux, Benoît (2006), "Qualitative Comparative Analysis (QCA) and Related Systematic Comparative Methods: Recent Advances and Remaining Challenges for Social Science Research", International Sociology 21 (5): 679, doi:10.1177/0268580906067836
  4. ↑ Hug, Simon (2013-04-01). "Qualitative Comparative Analysis: How Inductive Use and Measurement Error Lead to Problematic Inference". Political Analysis 21 (2): 252–265. doi:10.1093/pan/mps061. ISSN 1047-1987.
  5. ↑ Krogslund, Chris; Choi, Donghyun Danny; Poertner, Mathias (2015-01-01). "Fuzzy Sets on Shaky Ground: Parameter Sensitivity and Confirmation Bias in fsQCA". Political Analysis 23 (1): 21–41. doi:10.1093/pan/mpu016. ISSN 1047-1987.
  6. ↑ Braumoeller, Bear F. (2015-07-25). "Guarding Against False Positives in Qualitative Comparative Analysis". Political Analysis: mpv017. doi:10.1093/pan/mpv017. ISSN 1047-1987.
  7. ↑ Braumoeller, Bear (2015-05-19). "QCAfalsePositive: Tests for Type I Error in Qualitative Comparative Analysis (QCA)". Comprehensive R Archive Network. R Project. Retrieved 2015-08-26.
  8. ↑ Rihoux, Benoît (2013), "QCA, 25 Years after"The Comparative Method": Mapping, Challenges, and Innovations--Mini-Symposium", Political Research Quarterly 66: 167–235, doi:10.1177/1065912912468269
  9. ↑ Romme, A.G.L. (1995), Self-organizing Processes in Top Management Teams: A Boolean Comparative Approach. Journal of Business Research 34 (1): 11-34.
  10. ↑ Kask and Linton (2013) Business mating: when startups get it right http://www.tandfonline.com/doi/abs/10.1080/08276331.2013.876765#.U0UIwvl_t8E
  11. ↑ Stevenson 2013. "Does Technology have an Impact on Learning? A Fuzzy Set Analysis of&xnbsp;Historical Data on the Role of Digital Repertoires in Shaping the Outcomes of Classroom Pedagogy." Computers & Education 69 (0): 148-58.
  12. ↑ Basurto, X. (2013), "Linking Multi-Level Governance to Local Common-Pool Resource Theory using Fuzzy-Set Qualitative Comparative Analysis: Insights from Twenty Years of Biodiversity Conservation in Costa Rica." Global Environmental Change 23 (3): 573-87.
  13. ↑ Blackman, T. (2013), "Exploring Explanations for Local Reductions in Teenage Pregnancy Rates in England: An Approach Using Qualitative Comparative Analysis." Social Policy and Society 12 (1):61-72.
  14. ↑ Olya, Hossein G. T.; Altinay, Levent. "Asymmetric modeling of intention to purchase tourism weather insurance and loyalty". Journal of Business Research. doi:10.1016/j.jbusres.2015.11.015.

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