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).
Guidelines for the Combined Use of PLS-SEM and NCA
Extraction of Scores (Step 5)
- To test necessities, the use of the latent variable scores is recommended in PLS-SEM. For this purpose, we use the PLS-SEM algorithm.
- In our example, all indicators used for the antecedent constructs in the model have unitary interval scales (ranging from 1 to 7 (with 1 = low ratings for all indicators).
- In this case, as all indicators of a construct are measured on the same scale, the interpretation of the unstandardized latent variable scores is straightforward, which would not be the case if differently scaled indicators were used to measure a construct.
- Both the standardized and unstandardized latent variables scores will produce the same NCA parameters. However, the bottleneck levels will differ owing to the different scales that are involved.
- In this example, we therefore will draw on the unstandardized latent variable scores.
- The NCAs are performed individually for different outcome variables; for instance, if there are two outcome variables, run two NCAs, one for each DV.
Run the Necessary Condition Analysis (Step 6)
- Per default, the tables always present both the effect sizes based on the CE-FDH and the CR-FDH ceiling lines. To support the decision on the ceiling line to choose, we can evaluate the ceiling accuracy.
- 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.
- A higher accuracy indicates that a lower number of observations is above the CR-FDH ceiling line. While the accuracy of the CE-FDH ceiling line is per definition 100%, the accuracy of 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 help assess the quality of the generated solution.
- Thus, the 100% coverage accuracy of the CE-FDH is not a meaningful selection criterion, since this value is met by definition. In contrast, a low ceiling accuracy for a CR-FDH line indicates that the data pattern is not linear, and researchers are advised to select a nonlinear ceiling line, such as the CE-FDH.
- The decision to use CE-FDH or CR-FDH can be based on the Continuous vs. discrete data. In the example the original data collected was on a 5-point likert scale.
- We find information on the ceiling accuracy in the results report under ‘Final results’ →‘Ceiling lines – details’ → ‘CE-FDH’ respectively ‘CR-FDH.’
- The report indicates the lowest ceiling accuracy for the CR-FDH ceiling line in our example at 98.240 for Reliability. It has 6 observations on or above the ceiling line, meaning that the remaining 335 of the total 341 observations are within the ceiling line, resulting in an accuracy of 98.240% (335 divided by 341).
- Even the accuracy is above 95%, we still use CE-FDH as the data is discrete. Since Likert scale is based on discrete values the transformation to LV does not change the characteristic of the input scale. We use CE-FDH.
- The magnitudes of the effect sizes indicate the effects’ relevance, we will need the statistical significance of the effect sizes for a full interpretation later.
- For this purpose, a permutation test is used. To initiate the permutation test, click on the arrow symbol with the label ‘Edit’ in the menu bar to return to the modeling window, which shows the model for the NCA.
- Then select ‘Calculate’ → ‘NCA permutation’ in the menu and run the analysis. Ensure that the permutations are set to 10,000 and that a 0.05 significance level is applied. Before initiating the analysis by clicking on ‘Start calculation,’ check the box next to ‘Open report.’
- In the results report that opens, go to ‘Final results’ → ‘Ceiling line effect size overview’ to see the effect sizes already reported (in the column ‘Original effect size’) and the p-values (in the column ‘Permutation p-value’).
- With these outputs, we have generated the core parameters. For the later interpretation, the bottleneck tables are useful. To access the bottleneck tables, we return to the NCA results or re-run the NCA.
- The bottleneck table for the CE-FDH ceiling line is found under ‘Final results’ → ‘Bottleneck tables—CE-FDH’.
- Each row of the table represents a particular level of Loyalty that can be achieved if the necessary threshold level of each antecedent construct is met.
- By clicking on ‘Counts’ or ‘Percentiles’ the bottleneck table shows the number or percentage of cases that do not meet the necessary levels of the antecedents to accomplish a certain level of Organizational Performance.
Evaluate the Structural Model Relationships (Step 7)
- We can now start evaluating the relationships in the structural model.
- First, we check the inner model for collinearity issues using the Variance Inflation Factor (VIF).
- Second, we shift our focus on the R2-values of the dependent constructs. Complement this evaluation by assessing the model’s predictive power by running the PLSPredict procedure.
- Third, we evaluated the significance and size of the structural model relationships.
- To evaluate the structural model relationships from a necessity perspective.
- we continue with an evaluation of whether the necessity effect size d is equal to or higher than 0.1 and is statistically significant with an alpha level of 0.05 to indicate whether a construct is a necessary condition.
- The bottleneck tables generated provide relevant levels of these antecedent constructs that are necessary to achieve specific outcome levels of interest.
Interpret the Findings (Step 8)
- Following from the above, we identified both must-have and should-have factors for Organizational Performance. We can use an interpretation grid that has been proposed in previous guidelines to aid our interpretation.
Interpret the Findings (Step 8)
- Following from the bottleneck table created for Performance, we can conclude that, to achieve a 80% level of OP (i.e., a value of 5.2 on a scale of 1–7), the Vision value must have at least a value of 2.150, the Development value must have at least a value of 2.529, and so on.
- If a respondent exhibits a condition (i.e., Vision, Development, Rewards, Reliability, Assurance, Empathy, and Responsiveness) at a value lower than the specified threshold, this respondent cannot achieve the corresponding level of Performance.
- Interpreting the percentiles offers further insights. We see for instance that 4.399% (i.e., 15 cases) did not achieve the required understanding of Vision for a 80% Performance.
Finally, the PLS-SEM and NCA results can be presented based as follows. The table presents different scenarios based on the significance of exogenous constructs and whether the conditions are necessary or not.
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What if the condition is not necessary?
- Currently, the SmartPLS software only tests whether the presence of an antecedent construct is necessary for the presence of Y.
- Theoretically, there may be other forms of necessity that can be formulated, such as that the absence of the antecedent construct is necessary for the presence of the outcome.
- NCA is not limited to situations where the presence of a condition is necessary for the presence of an outcome but can also be applied to different combinations of the presence and absence of the condition and the outcome.
- However, to test for other combinations, you will need to flip the coding of your scales. Thus, researchers need to ensure that the coding of their variables corresponds to the analytical procedure that was implemented.
- For instance, if the antecedent constructs were Role Ambiguity or Role Conflict measured with indicators from 1 = Low to 7 = High, you would most likely test for the necessity of the absence of the antecedent constructs for the presence of the outcome.
- You would test whether the absence of Role Ambiguity or Role Conflict is necessary for (the presence of/attainment of) Organizational Performance.
- To enable this, you would need to flip the scale to 1 = High to 7 = Low.
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NCA with Formative (Higher Order) Construct using #SmartPLS4
- For a PLS path model’s reflective constructs, we recommend focusing on the latent variable scores for both the exogenous and endogenous constructs in the NCA.
- For formative constructs, we recommend focusing on the latent variable scores in the case of endogenous constructs, as the objective is usually to explain or understand the relation to the construct.
- For the exogenous constructs, it is recommended to include the latent variable scores and the individual indicators, as we may want to complement the analysis on the construct level with analyses for the individual indicators.
- If one or more of the exogenous constructs are a formative construct, we recommend running additional analyses using the single indicator(s) of the formative construct(s).
- Therewith, we can test whether the individual indicators forming the construct are necessary conditions to be satisfied so that a certain outcome can occur.
- This will complement the findings that we automatically generate in the PLS-SEM context via the formative indicators’ weights and significance.
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References
- Richter, N. F., Schubring, S., Hauff, S., Ringle, C. M., & Sarstedt, M. (2020). When predictors of outcomes are necessary: Guidelines for the combined use of PLS-SEM and NCA. Industrial management & data systems, 120(12), 2243-2267.
- Richter, N. F., Hauff, S., Ringle, C. M., Sarstedt, M., Kolev, A. E., & Schubring, S. (2023). How to apply necessary condition analysis in PLS-SEM. In Partial least squares path modeling: Basic concepts, methodological issues and applications (pp. 267-297). Cham: Springer International Publishing.