# Necessary Condition Analysis (NCA) using PLS-SEM in #SmartPLS4

## Introduction

Go beyond traditional SEM! Discover Necessary Condition Analysis (NCA) with PLS-SEM in SmartPLS4 and unlock deeper insights into your data. Learn how to identify variables essential for achieving desired outcomes, even if they’re not sufficient on their own. This tutorial covers:

- What is NCA, and how does it differ from SEM?
- When to use NCA in your research
- A step-by-step guide to conducting NCA in SmartPLS4
- Interpreting NCA results for actionable insights

### How to perform Necessary Condition Analysis using SmartPLS

The tutorial is a step by step guide on how use NCA with SmartPLS4

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Introduction

- This session introduces the combined use of partial least squares structural equation modelling (PLS-SEM) and necessary condition analysis (NCA).
- The use of PLS-SEM and NCA enables researchers to identify the must-have (necessary) factors required for an outcome in accordance with the necessity logic. At the same time, this approach shows the should-have (sufficient) factors that follows the additive sufficiency logic.

## Sufficient and Necessary

**Necessary Condition**: This is something that must be present for a particular outcome to occur. Without this condition, the outcome cannot happen.**Sufficient Condition**: This is something that, if present, guarantees the occurrence of a particular outcome. However, the outcome can still occur even if this condition is not present.- Consider passing a test:
**Necessary Condition**: Studying is a necessary condition for passing the test. If you don’t study, you won’t pass the test. However, just because you studied doesn’t guarantee you’ll pass; other factors like understanding the material also play a role.**Sufficient Condition**: Getting every question correct is a sufficient condition for passing the test. If you answer every question correctly, you’ll pass the test. However, you could still pass the test even if you don’t get every question correct, if you meet the passing threshold.- For Example: For information systems to be effective in organizations, they must be used; they cannot be effective if not used. Hence, usage is a necessary condition for systems to contribute to success.
- However, usage alone may not be sufficient, since other requirements, such as the correct use and organizational workflows, could also play a role in information system effectiveness.
- Hence, there are must-have and should-have factors. The existence of both – necessary conditions or must-have factors and sufficient conditions or should-have factors – is common in many fields of research.

## PLS-SEM and NCA

- In several fields of management research, partial least squares structural equation modeling (PLS-SEM) has become a standard multivariate analysis technique to investigate causal-predictive relationships.
- This method empirically substantiates the determinants (X) that lead to an outcome (Y). Authors who interpret their PLS-SEM findings normally use expressions such as “X increases Y” or “a higher X leads to a higher Y”.
- The interpretation of relationships between the determinants and the outcome therefore follows a sufficiency logic.
- While, according to a sufficiency logic, a determinant (e.g. enjoyment) may be sufficient to produce the outcome (e.g. the use of a technology), it may not be necessary. The absence of enjoyment could be compensated by other determinants, for example, role of technology in career growth.
- By contrast, necessity logic implies that an outcome – or a certain level of an outcome – can only be achieved if the necessary cause is in place or is at a certain level.
- To express necessity, researchers refer to expressions such as “X is needed for Y,” “X is a precondition for Y” or “Y requires X”. Accordingly, the necessary condition – being a constraint, a bottleneck or a critical factor – must be satisfied to achieve a certain outcome.
- Other factors cannot compensate in a situation where a necessary condition is not satisfied; that is, if determinant X is a necessary condition for outcome Y, Y will not be achieved if X is not in place.

## Fundamentals of Necessity Logic and NCA

- NCA does not impose specific requirements on the data or measurement other than the standard requirements in empirical studies.
- To test necessities in the SEM context, an NCA needs to be done on the scores (e.g., as obtained by PLS-SEM) of the involved constructs.
- NCA’s focus is—other than in the typical PLS-SEM estimation—on single conditions that are necessary for an outcome.
- Thus, NCA is a bivariate technique—if more than one necessary condition is analyzed, this is called a
*multiple NCA*or a*multiple bivariate NCA*. - The necessity association found between a condition X1 and an outcome Y in a multiple bivariate NCA does not depend on other conditions in the estimation. That is, adding a further condition X2 to the model does not change the estimated association between X1 and Y.

- NCA reveals areas in scatter plots of dependent and independent variables that denote the presence of a necessary condition.
- While PLS-SEM establishes a linear function, NCA uncovers a ceiling line on top of the data.
- The ceiling line separates the area with observations from the area without observations (C; also called the ceiling zone). The larger the empty area is relative to the total area (S; also called the scope), the larger the constraint that X puts on Y (Dul et al., 2020).
- There are commonly two default ceiling lines. One is the ceiling envelopment—free disposal hull (CE-FDH) line, which is a nondecreasing, stepwise linear line (step function). Another is the ceiling regression—free disposal hull (CR-FDH) line, which is a simple linear regression line through the data points of the CE-FDH line.
- The CE-FDH ceiling line is recommended for discrete data. The CR-FDH line is recommended for continuous data.

- The ceiling line specifies the minimum level of X that is necessary to achieve a certain level of Y.
- To grasp this concept, consider Fig, which shows an example of an NCA ceiling line chart from a SmartPLS output.
- The independent variable X must have at least a level of 3.0 to achieve a level of 4.0 for the dependent variable Y.

- A bottleneck table is another way to illustrate the NCA results. In such a table, the first column shows the outcome, while the next column represents (and any additional columns represent) the condition(s) that must be satisfied to achieve the outcome.
- The conditions represent the necessary levels of the independent variables for the outcome.
- Table is an illustrative bottleneck table. Table shows that, to achieve a level of 4.0 for the dependent variable Y (second column), the independent variable X must achieve a level of 3.0 (third column).
- Furthermore, NN indicates that the independent variable is not necessary for this level of the dependent variable. For instance, there is no necessary level of X to accomplish a Y outcome level of 2.8 (or lower) in this example.
The first column lists the percentage ranges for the outcome. It expresses the values of Y in percentages of their ranges (in which 0 corresponds to the lowest observed value, and 100 to the highest observed value). For instance, to achieve an outcome level of 50% (first column), which is indicated by an actual value of 4.0 on our 7-point scale (second column), X needs to be at a level of 3.0 (third column).

- In addition, Table presents X in counts (fourth column) and in percentiles (fifth column). Displaying X in the bottleneck table in terms of counts focuses on the number of cases (i.e., the observations) that do not meet the necessary level of X to accomplish a certain level of Y.
- For instance, when considering an outcome level of 5.2 for the dependent variable Y, we find that 20 cases do not achieve the necessary level of X (i.e., a level for X of at least 4.5) to accomplish Y’s desired outcome level of 5.2.
- Similarly, the percentile option displays the percentage of cases that do not meet the necessary level of X to accomplish a certain level of Y.
- We see for instance that the 20 cases that did not achieve a level of 4.5 correspond to 33.3% of all cases. In a multiple NCA, this result is helpful to select important necessary conditions where many cases do not achieve certain levels.

## Effect Size

- The key NCA parameters are the necessity effect size (d) and its significance, which indicate whether a variable or construct is a necessary condition.
- The value d is calculated by dividing the area without observations (the ceiling zone C) by the total area that contains or could contain observations (the scope S) as per the boundaries outlined by the minimum and maximum theoretical or empirical values of X and Y.
- Thus, by definition, d ranges between 0 ≤ d ≤ 1. Dul (2016) suggested that
- 0 < d < 0.1 can be characterized as a small effect,
- 0.1 ≤ d < 0.3 as a medium effect,
- 0.3 ≤ d < 0.5 as a large effect, and
- d ≥ 0.5 as a very large effect.

- Previous studies have used the threshold of d = 0.1 to accept necessity hypotheses. Thus, an effect size of 0.1 and higher is required to consider a variable a necessary condition.
- However, the absolute magnitude of d only indicates the meaningfulness of the effect size from a practical perspective.
- Accordingly, researchers should also evaluate the statistical significance of the necessity effect size using NCA’s (approximate) permutation test. If the
*p*-value is low enough (e.g.,*p*< 0.05), the result can be considered statistically significant and a necessity hypothesis can be appraised. - Two key NCA parameters are the ceiling accuracy and necessity effect size d. The ceiling accuracy represents the number of observations that are on or below the ceiling line divided by the total number of observations, multiplied by 100.
- While the accuracy of the CE-FDH ceiling line is per definition 100%, the accuracy of the other lines, for instance, the CR-FDH, can be less than 100%. There is no specific rule regarding the acceptable level of accuracy.
- However, a comparison of the estimated accuracy with a benchmark value (e.g. 95%) can assist to assess the quality of the solution generated (Dul, 2016a).