# Chapter 2 Theory

A theory –including a necessity theory– consists of four parts: concepts, propositions, focal unit and theoretical domain. The concepts are the variable parts of a theory that can increase or decrease. In NCA the independent concepts are called conditions and the dependent concepts outcomes. A proposition describes the causal relationship between the concepts. In NCA the causal relationship is a necessity relationship: ‘$$X$$ is necessary for $$Y$$.’ The focal unit is the object to which the theory applies: country, person, firm, project. etc. The theoretical domain is the set of cases of the focal unit where the theory is supposed to hold. A case is one particular example of the focal unit: a specific country, a specific person, etc.

The four characteristics of theory on which the nca.example data set of the NCA software is based are:

• Focal unit: country.

• Concepts:

• Independent concept (condition): Individualism.

• Dependent concept (outcome): Innovation performance.

• Proposition: Individualism is necessary for Innovation performance.

• Theoretical domain: all countries of the world.

In theory testing research, empirical data are used to test the propositions. The theoretical concepts are operationalized into variables that can be measured, the propositions are operationalized into hypotheses consisting of variables with their expected relationship, the focal unit becomes the unit of analysis, and cases are selected from the theoretical domain. For the case selection usually a population of cases is identified in the theoretical domain and a sample is taken from this population. From the sample a dataset is obtained with variables scores of the cases.

## 2.1 Formulation of necessity hypotheses

The propositions (or the operationalized hypotheses) are the core elements of a theory. They describe the expected causal relationships between the concepts. NCA starts with formulating a hypothesis that a condition is a necessary cause for the outcome. In some fields the existence of a causal necessity relationship is widely known and accepted. An example is the psychological theory that intelligence is necessary for creativity. This hypothesis was proposed in the 1960’s and is still widely around. Until recently, this theory could not be tested with a specific necessity method. When NCA became available it was possible to ensure theory-method fit by testing the hypothesis with NCA, as was done by .

However, most research areas do not have widely accepted necessity theories. Although necessity causality exists in virtually all research areas, and necessity statements are commonly made, necessity statements are usually not part of the theories. NCA gives the researcher and opportunity to build and test necessity theories.

Three complementary approaches can be used for for formulating necessary condition hypotheses. First, existing necessity statements in the literature can be identified. Although several necessity statements may use the word ‘necessity’ rather loosely as synonym for ‘important,’ many necessity statements refer to necessity logic and causality.

Second, when ‘important’ contributing causal factors for a outcome of interest have been identified with conventional methods, several of them could also be necessary conditions. For example, when a researcher formulates an additive theory (to be analysed with regression analysis) arguments are provided why a concept is an important contributor to an outcome. As a standard, the arguments imply sufficiency logic (‘$$X$$ produces $$Y$$’), but as an alternative, the relationship could also be described with necessity logic: an important factor that cannot be compensated for. Not only independent concepts but also mediator and moderator concepts in additive theories could be candidate necessary conditions. In other words, when current additive theories state that concepts are ‘important’ contributing concepts they may or may not (also) be necessary. But also contributing concepts that are considered ‘unimportant’ according to additive theories could be necessary.

Third, ‘critical’ and ‘bottleneck’ factors in practice could be candidate necessary conditions to be included in the theory. Practitioners commonly act upon ‘critical success factors’ or ‘must have’ factors (versus ‘nice to have’ factors). When such factor does not have the required level it can become a bottleneck on which the practitioner must act to ensure a desired outcome. Practitioners often have a ‘theory in use’ in which they argue why a factor is related to an outcome. Often the arguments imply necessity logic.

When a potential necessary condition is selected the researcher can do a ‘thought-experiment’ to test if necessity is possible. She can ask the question “Can I imagine cases with outcome $$Y$$, but without condition $$X$$?” When such cases are relatively common, the conclusion is that the condition is not necessary. When cases with the outcome $$Y$$ and without the condition $$X$$ are impossible or rare, the hypothesis may generally hold. The rare cases can be used to define the context where the hypothesis holds and where not, and thus to define the theoretical domain of the theory. Defining the theoretical domain –where the theory is supposed to hold– is important for all theories, because theories do rarely hold universally.

To illustrate the thought-experiment and the process of defining the theoretical domain, assume that a researcher wants to test the hypothesis ‘understanding English is necessary for reading this book.’ This statement is generally correct, but it is possible to imagine cases (persons) with the outcome (reading the book) but without the condition (not mastering English). Such exception is possible when someone translates the book in the language other than English, such that a reader who does not master English can read the translated book. This exception helps to specify the theoretical domain of the hypothesis: ‘persons reading the original version of book.’ Further exploration of exceptions can help to specify the theoretical domain. This process continues until the theoretical domain is precisely specified where the hypotheses is expected to hold virtually always. For testing this hypothesis, cases are selected from this specified theoretical domain. This can help to avoid sampling error (see section 3.7).

It is also possible that the necessary condition is rejected in the thought experiment because the condition is formulated too narrow. For example, ‘green apple’ is not necessary for an apple pie, and also red apple is not necessary for an apple pie. However, the higher-order construct (apple) is necessary. Then it would make sense to formulate the necessary condition hypothesis with the higher order concept. In general, attractive theories are supposed to be valid in a broad set of contexts, not only in very specific situations.

A hypothesis is usually only generally and semantically described as a theoretical statement. In NCA the common hypothesis is a qualitative theoretical statement like “X is necessary for Y” (in kind). A hypothesis usually is not described as a quantitative statement like “a specific level of X is necessary for a specific level of Y” (in degree). A hypothesis usually includes or implies a ‘direction’ of the causal relationship. In NCA four ‘directions’ are possible: the presence/high value of $$X$$ is necessary for the presence/high value of $$Y$$ (+ +), the absence/low value of $$X$$ is necessary for the presence/high value of $$Y$$ (- +), the presence/high value of $$X$$ is necessary for the absence/low value of $$Y$$ (+ -), and the absence/low value of $$X$$ is necessary for the absence/low value of $$Y$$ (- -). This is shown in figure 2.1, where the empty space is in different corners.

If the direction is not specified, the + + direction is implied. Note that in NCA the hypothesis is not described by a verb like in ‘$$X$$ increases $$Y$$’ or ‘$$X$$ has a positive effect on $$Y$$,’ which are common formulations to express sufficiency relationships. In NCA a noun or adverb is used to describe levels of $$X$$ and $$Y$$ as for example in ‘the absence of $$X$$ is necessary for the presence of $$Y$$’ or ‘low $$X$$ is necessary for high $$Y$$.’

## 2.2 Justification of necessity hypotheses

A theory is more than a set of hypotheses. It is also important to describe the mechanism why $$X$$ is necessary for $$Y$$. A first requirement for claiming causality is that condition occurs before the outcome: first the condition, then the outcome. Furthermore, the necessity relationship can be argued by answering three why questions:

• Why if $$Y$$ is present also $$X$$ is present?
• Why if $$X$$ is absent also $$Y$$ is absent?
• Why the absence of $$X$$ cannot be compensated by another concept?

Figure 2.2 shows that these questions relate to three cells of the 2x2 contingency table that are compatible with the necessary condition hypothesis: where cases are possible or impossible when the necessary condition ‘the presence of $$X$$ is necessary for the presence of $$Y$$’ holds. Note that the lower right cell is not informative about necessity.

Describing the causal mechanism is often difficult. It is a creative process inspired by the three questions. The answers can be based on exploring and combining knowledge from the literature, from practice and from the researcher’s own experience. In the literature, researchers may partly use necessity arguments when describing the causal mechanism why an ‘important’ factor produces an outcome. Practitioners may tell stories why a ‘must have’ factor is ‘critical’ or a ‘bottleneck’ for the outcome and why he acts upon them for getting the outcome.

## 2.3 Types of necessity theories

Two types of necessity theories can be distinguished. First, Pure necessity theories are theories that consist only of necessary condition relationships between $$X$$’s and $$Y$$’s. Because necessary conditions operate in isolation from the rest of the causal structure, such theories can be parsimonious with only one or a few necessary conditions. An example of a pure necessity theory with one condition and one outcome is the early theory of that intelligence is ‘necessary-but-not-sufficient’ for creativity. Shortly after NCA was introduced , this theory was empirically tested with NCA by . Other examples of pure necessity theories that have been proposed and tested with NCA and that are described in well-cited articles are theories about necessary conditions for lean manufacturing , for workplace spirituality , and for innovation in buyer-supply relationships . One theory about the necessary conditions for success of start-up firms was developed based on literature and common beliefs but was rejected after empirical testing .

Second, Embedded necessity theories are theories that consist of a mix of necessity relations and common additive relations where all factors are supposed to contribute to producing the outcome, but some factors (additionally) may also be necessary. These theories are usually complex as their main goal is to describe how the outcome is produced (sufficiency). One of the first embedded necessity theories is an extension of the Technology Acceptance Model (TAM). first described TAM as a structural (sufficiency) model including the classical antecedents ‘perceived usefulness’ and ‘perceived ease of use’ and analysed this model with Partial Least Squares Structural Equation Modeling (PLS-SEM). Subsequently, the relations were described as necessity conditions, and analysed with NCA. The results show that, for example the two classical antecedents not only help to produce technology acceptance on average, but they are also necessary.

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