PLS-SEM Glossary

Adopted from the primer book on PLS-SEM by Hair, Hult, Ringle, and Sarstedt and the book on advanced PLS-SEM issues by Hair, Sarstedt, Ringle, and Gudergan.

10 times rule: one way to determine the minimum sample size specific to the PLS path model that one needs for model estimation (i.e., 10 times the number of independent variables of the most complex ordinary least squares regression in the structural model or any formative measurement model). The 10 times rule is not a reliable indication of sample size requirements in PLS-SEM and should at best be seen as a rough estimate. While statistical power analyses provide more reliable minimum sample size estimates, researchers should primarily draw on the inverse square root method, which stands out in terms of precision and ease of use.

Absolute contribution: the information an indicator variable provides about the formatively measured item, ignoring all other indicators. The absolute contribution is provided by the loading of the indicator (i.e., its bivariate correlation with the formatively measured construct).

Absolute importance: see Absolute contribution.

AIC: see Akaike's information criterion.

AIC₃: see Modified AIC with factor 3.

AIC₄: see Modified AIC with factor 4.

Akaike weights: the weight of evidence in favor of a certain model being the best model for the situation at hand given a set of alternative models.

Akaike's information criterion: an information criterion that allows assessing the relative goodness-of-fit of a segmentation solution produced by FIMIX-PLS. A smaller AIC value for a certain number of segments indicates a better fit. The AIC has a strong tendency to overestimate the correct number of segments.

Algorithmic options: offer different ways to run the PLS-SEM algorithm by, for example, selecting between alternative starting values, stop values, weighting schemes, and maximum number of iterations.

All antecedents: uses data from all antecedent constructs and their indicators to generate predictions when using PLS_predict and CVPAT.

Alpha inflation: refers to the fact that the more tests you conduct at a certain significance level, the more likely you are to claim a significant result when this is not so (i.e., a Type I error).

Alternating extreme pole responses: a suspicious survey response pattern where a respondent uses only the extreme poles of the scale (e.g., a 7-point scale) in an alternating order to answer the questions.

Artifacts: are human-made concepts, which are typically measured with formative indicators.

Attribute: an element of the construct definition. It defines the general type of property to which the focal construct refers, such as an attitude.

AVE: see Average variance extracted.

Average loss: the mean prediction error of a model across all cross-validation folds obtained when using CVPAT. It reflects the model’s overall out-of-sample predictive accuracy based on a chosen loss function (e.g., MAE or RMSE). A lower average loss indicates better predictive performance.

Average variance extracted (AVE): a measure of convergent validity. It is the degree to which a latent construct explains the variance of its indicators; see Communality (construct).

Bandwidth-fidelity dilemma: a practical dilemma resulting from the trade-off between using measures that will cover most of the variation in a trait or measures that will assess a few specific traits more precisely.

Bayesian information criterion (BIC): a criterion for model selection among an alternative set of models. The model with the lowest BIC is preferred.

Bias-corrected and accelerated (BCa) bootstrap confidence intervals: a method for constructing confidence intervals that adjusts for biases and skewness in the bootstrap distribution. The method yields very low type I errors but is limited in terms of statistical power.

Bias-corrected and Bonferroni-adjusted confidence intervals: a confidence interval type used for testing the significance of multiple tetrads considered per measurement model.

BIC: see Bayesian information criterion.

Blindfolding: a sample reuse technique that omits singular elements of the data matrix and uses the model estimates to predict the omitted part. It is used to compute the Q² statistic.

Bonferroni correction: a method used to counteract the increase in the familywise error rate when performing multiple comparisons across several groups of data.

Bootstrap cases: these make up the number of observations drawn in every bootstrap run. The number is set equal to the number of valid observations in the original data set.

Bootstrap confidence interval: provides an estimated range of values that is likely to include an unknown population parameter. It is determined by its lower and upper bounds, which depend on a predefined probability of error and the standard error of the estimation for a given set of sample data. When zero does not fall into the confidence interval, an estimated parameter can be assumed to be significantly different from zero for the prespecified probability of error (e.g., 5%).

Bootstrap MGA: compares the bootstrap estimates of a parameter across two groups. By counting the number of occurrences where the bootstrap estimate of the first group is larger than those of the second group, the approach derives a p value for a one-tailed test.

Bootstrap samples: the number of samples drawn in the bootstrapping procedure. Generally, 10,000 or more samples are recommended.

Bootstrapping: a resampling technique that draws many subsamples from the original data (with replacement) and estimates models for each subsample. It is used to determine standard errors of coefficients to assess their statistical significance without relying on distributional assumptions.

Bottleneck table: a tabular representation of the ceiling lines (typically the CR-FDH ceiling line). It shows, row by row, how a certain outcome level of the dependent construct and the corresponding necessary minimum condition level of an independent construct have been achieved.

Bottom-up approach: a way to establish an HCM in which several latent variables (the LOCs) are combined into a single, more abstract construct (the HOC).

CAIC: see Consistent AIC.

Cascaded moderator analysis: a type of moderator analysis in which the strength of a moderating effect is influenced by another variable (i.e., the moderating effect is again moderated).

Casewise deletion: a missing value treatment option, where an entire observation (i.e., a case or respondent) is removed from the data set.

Categorical moderator variable: see Multigroup analysis.

Categorical scale: see Nominal scale.

Causal indicators: a type of indicator used in formative measurement models. Latent variables measured with causal indicators have an error term, which captures major elements of the concept that are not covered by the indicator set. Causal indicators must correspond to a theoretical definition of the concept under investigation.

Causal links: are directed relationships between constructs, which can be interpreted as causal if supported by strong theory.

CB-SEM: see Covariance-based structural equation modeling.

CCA: see Confirmatory composite analysis.

Ceiling envelopment free disposal hull (CE-FDH) line: given by the scatterplot of the values of the independent (x-axis) and dependent construct (y-axis). The outermost values of this relationship (lowest x-value and highest y-value) are associated with a step function that represents the CE-FDH line.

Ceiling regression free disposal hull (CR-FDH) line: given by the scatterplot of the values of the independent (x-axis) and dependent construct (y-axis). The outermost values of this relationship (lowest x-value and highest y-value) are associated with a linear regression function. The CR-FDH line is given by a simple linear regression line through the data points that constitute the ceiling regression free disposal hull (CE-FDH) line.

Centroid weighting scheme: uses in the first stage of the PLS-SEM algorithm a value of +1 or -1 for relationships between the constructs in the structural model depending on the sign of their correlations; see Weighting scheme.

cIPMA: see Combined IPMA (cIPMA).

Cluster analysis: see Clustering.

Clustering: a class of methods that partition a set of objects with the goal of obtaining high similarity within the formed groups and high dissimilarity across groups.

Coding: the assignment of numbers to scales in a manner that facilitates measurement.

Coefficient of determination (R²): a measure of the proportion of an endogenous construct’s variance that is explained by its predictor constructs. It indicates a model’s explanatory power regarding a specific endogenous construct.

Collect model: an HCM type in which the HOC is a combination of several specific LOCs representing more concrete components that form the general concept. The relationship between HOC and LOCs is formative.

Collinearity: arises when two variables are highly correlated.

Combined IPMA (cIPMA): uses the results of necessary condition analysis (NCA) to extend the outcomes of importance–performance map analysis (IPMA). The combined IPMA (cIPMA) highlights the performance and relative importance of constructs for a target construct and identifies those that serve as bottlenecks to achieving desired outcome levels.

Common factor model: assumes that only the variance shared by the indicators used to measure a construct (i.e., the common variance) should be used to estimate the construct and its relationship with other constructs in a model. Exploratory factor analysis (EFA), confirmatory factor analysis (CFA), and CB-SEM (also referred to as common factor-based SEM) are the three main types of analyses based on common factor models.

Common factor-based SEM: a type of SEM method that considers constructs as common factors that explain the covariation among their associated indicators.

Common variance: the variance that an indicator shares with other indicators in the measurement model of a construct.

Communality (construct): see Average variance extracted (AVE).

Communality (item): see Indicator reliability.

Competitive mediation: a situation in mediation analysis that occurs when the indirect effect and the direct effect are both significant and point in opposite directions.

Complementary mediation: a situation in mediation analysis that occurs when the indirect effect and the direct effect are both significant and point in the same direction.

Composite indicators: a type of indicator used in formative measurement models. Composite indicators form the construct (or composite) fully by means of linear combinations.

Composite model approach: an approach to estimating construct proxies. Its objective is to account for the total variance in the observed indicators rather than to explain the correlations between the indicators.

Composite reliability (ρ_A): a measure of internal consistency reliability that uses indicator weights as input. The ρ_A reliability metric usually lies between Cronbach’s alpha and composite reliability ρ_C and is therefore considered a good compromise between these two measures. It should be above 0.70 (in exploratory research, 0.60 to 0.70 is considered acceptable). Reliability values higher than 0.95 are not desirable.

Composite reliability (ρ_C): a measure of internal consistency reliability that, unlike Cronbach’s alpha, does not assume equal indicator loadings. It should be above 0.70 (in exploratory research, 0.60 to 0.70 is considered acceptable). Reliability values higher than 0.95 are not desirable.

Composite scores: see Construct scores.

Composite variable: a linear combination of several variables.

Composite-based SEM: a type of SEM method that represents the constructs as composites, formed by linear combinations of sets of indicator variables.

Compositional invariance: exists when the composite scores across the groups are perfectly correlated.

Conceptual variables: broad ideas or thoughts about abstract concepts that researchers establish and propose to measure in their research.

Conditional indirect effect: see Moderated mediation.

Conditional process models: combine mediation and moderation analysis. See Mediated moderation and Moderated mediation.

Confidence interval: see Bootstrap confidence interval.

Configural invariance: exists when constructs are equally parameterized and estimated across groups.

Confirmatory: describes applications that aim at empirically testing theoretically developed models.

Confirmatory composite analysis (CCA): a set of analyses used to verify the quality of a composite measurement of a theoretical concept of interest.

Confirmatory factor analysis (CFA): a set of analyses used to verify the quality of a common factor measurement of a theoretical concept of interest.

Confirmatory tetrad analysis in PLS-SEM (CTA-PLS): a statistical procedure that allows for empirically testing the measurement model setup (i.e., whether the measures should be specified reflectively or formatively).

Consistency at large: describes an improvement in the precision of PLS-SEM results when both the number of indicators per measurement model and the number of observations increase, provided that the data stem from a common factor model.

Consistent AIC: an information criterion that allows assessing the relative goodness-of-fit of a segmentation solution produced by FIMIX-PLS. A smaller CAIC value for a certain number of segments indicates a better fit. The criterion should be used in conjunction with AIC3 to determine the number of segments in FIMIX-PLS.

Consistent PLS-SEM (PLSc-SEM): a variant of the standard PLS-SEM algorithm that provides consistent model estimates in common factor models by disattenuating the correlations between pairs of latent variables, thereby mimicking CB-SEM results.

Construct definition: the specific way in which a conceptual variable is measured in a particular study, and could differ from one study to another.

Construct scores: columns of data (vectors) for each latent variable that represent a key result of the PLS-SEM algorithm. The length of every vector equals the number of observations in the data set used.

Constructs: measure theoretical concepts that are abstract, complex, and cannot be directly observed by means of (multiple) items. Constructs are represented in path models as circles or ovals and are also referred to as latent variables.

Content specification: the specification of the scope of the latent variable; that is, the domain of content the indicators are intended to capture.

Content validity: a subjective but systematic evaluation of how well the domain content of a construct is captured by its indicators.

Continuous moderator variable: a variable that affects the direction and/or strength of the relation between an exogenous latent variable and an endogenous latent variable. Continuous moderator variables can also be used to generate categories, which serve as basis for a subsequent multigroup analysis.

Control variables: the variables that researchers seek to keep constant when conducting research.

Convergence: is reached when the results of the PLS-SEM algorithm do not change much. In that case, the PLS-SEM algorithm stops when a prespecified stop criterion (i.e., a small number such as 0.00001) that indicates the minimal changes of PLS-SEM computations has been reached. Thus, convergence has been accomplished when the PLS-SEM algorithm stops because the prespecified stop criterion has been reached and not the maximum number of iterations.

Convergent validity: the degree to which a reflectively specified construct explains the variance of its indicators (see Average variance extracted). In formative measurement model evaluation, convergent validity refers to the degree to which the formatively measured construct correlates positively with an alternative (reflective or single-item) measure of the same concept (see Redundancy analysis).

Correlation weights: see Mode A.

Covariance-based structural equation modeling (CB-SEM): an approach for estimating structural equation models that assumes that the concepts of interest are represented by common factors. It can be used for theory testing but has clear limitations in terms of testing a model’s predictive power.

Coverage error: occurs when the bootstrapping confidence interval of a parameter does not correspond to its empirical confidence interval.

Cramér-von Mises test: allows the test for the normality of a variable’s data distribution.

Critical t value: the cutoff or criterion on which the significance of a coefficient is determined. If the empirical t value is larger than the critical t value, the null hypothesis of no effect is rejected. Typical critical t values are 2.57, 1.96, and 1.65 for significance levels of 1%, 5%, and 10%, respectively (two-tailed tests).

Critical value: see Significance testing.

Cronbach’s alpha: a measure of internal consistency reliability that assumes equal indicator loadings. Cronbach’s alpha represents a conservative measure of internal consistency reliability. It should be above 0.70 (in exploratory research, 0.60 to 0.70 is considered acceptable). Reliability values higher than 0.95 are not desirable.

Cross-loadings: an indicator’s correlation with other constructs in the model.

Cross-validated communality: is used to obtain the Q² value based on the prediction of the omitted data points by means of the underlying measurement model (see Blindfolding).

Cross-validated redundancy: is used to obtain the Q² value based on the prediction of the omitted data points by means of the underlying structural model and measurement model (see Blindfolding).

CTA-PLS: see Confirmatory tetrad analysis in PLS-SEM (CTA-PLS).

Cubic effect: a nonlinear relationship represented by a polynomial of the degree 3; see also Nonlinear effect and Polynomial.

Data matrix: includes the empirical data that are needed to estimate the PLS path model. The data matrix must have one column for every indicator in the PLS path model. The rows represent the observations with their responses to every indicator on the PLS path model.

Degrees of freedom (df): the number of values in the final calculation of the test statistic that are free to vary.

Diagonal lining: a suspicious survey response pattern in which a respondent uses the available points on a scale (e.g., a 7-point scale) to place the answers to the different questions on a diagonal line.

Direct antecedents: uses data from the exogenous constructs and their indicators to generate predictions when using PLS_predict and CVPAT.

Direct effect: a relationship linking two constructs with a single arrow between the two.

Direct-only nonmediation: a situation in mediation analysis that occurs when the direct effect is significant but not the indirect effect.

Disattenuated correlation: the correlation between two constructs, if they were perfectly measured (i.e., if they were perfectly reliable).

Discriminant validity: the extent to which a construct is empirically distinct from other conceptually distinct constructs in the model.

Disjoint two-stage approach: uses only the lower-order components of a higher-order construct in its first stage to compute the construct scores, which serve as indicators of the higher-order component in the second stage.

Earliest antecedents: uses data from the earliest antecedent constructs and their indicators to generate predictions when using PLS_predict and CVPAT.

Effect indicators: see Reflective measurement.

Embedded two-stage approach: uses the entire higher-order construct in its first stage to compute the construct scores, which serve as indicators of the higher-order component in the second stage.

Empirical t value: the test statistic value obtained from the data set at hand (here: the bootstrapping results). See Significance testing.

EN: see Normed entropy statistic.

Endogeneity: occurs when a predictor construct is correlated with the error term of the dependent construct to which it is related. Endogeneity violates one of the key assumptions of regression analysis, which PLS-SEM uses to estimate the model relations—that predictors must be uncorrelated with the disturbance term.

Endogenous constructs: see Endogenous latent variables.

Endogenous latent variables: serve only as dependent variables or as both independent and dependent variables in a structural model.

Equality of composite mean values and variances: the final requirement to establish full measurement invariance.

Equidistance: when the distance between data points of a scale is identical.

Equidistant scale: a scale in which the intervals are distributed in equal units. For example, a 5-point Likert scale with two negative categories (completely disagree and disagree), a neutral option, and two positive categories (agree and completely agree) can be considered an equidistant scale.

Error terms: capture the unexplained variance in constructs and indicators when path models are estimated.

Evaluation criteria: used to evaluate the quality of the measurement models and the structural model results in PLS-SEM based on a set of nonparametric evaluation criteria and procedures such as bootstrapping.

Ex post analysis: aims at identifying one or more explanatory variable(s) that match the latent class segmentation results in the best possible way to facilitate a multigroup analysis.

Exact fit test: a model fit test that applies bootstrapping to derive p values of the Euclidean distance (d_L) or geodesic distance (d_G) between the observed correlations and the model-implied correlations. Research has shown that these measures are largely unsuitable for detecting model misspecification in situations commonly encountered in applied research.

Exogenous constructs: see Exogenous latent variables.

Exogenous latent variables: latent variables that serve only as independent variables in a structural model.

Expectation-maximization (EM) algorithm: an iterative algorithm for finding maximum likelihood estimates of parameters in a statistical model. The algorithm alternates between performing an expectation (E) step and a maximization (M) step. The E step creates a function for the expectation of the log-likelihood, which is evaluated using the current estimate of the parameters. The M step computes parameters by maximizing the expected log-likelihood found in the E step. The E and M steps are successively applied until the results stabilize.

Explained variance: see Coefficient of determination (R²).

Explaining and predicting (EP) theories: a theory type that implies both understanding of underlying causes and prediction, as well as description of theoretical constructs and the relationships among them.

Explanatory power: provides information about the strength of the assumed causal relationships in a PLS path model. The primary measure for assessing a PLS path model’s explanatory power is the coefficient of determination (R²).

Exploratory: describes applications that focus on exploring data patterns and identifying relationships.

Extended repeated indicators approach: a method for estimating a formatively specified higher-order construct whose higher-order component serves as an endogenous construct in the PLS path model. Also see Repeated indicators approach.

f² effect size: a measure used to assess the relative impact of a predictor construct on an endogenous construct in terms of its explanatory power.

Factor (score) indeterminacy: means that one can compute an infinite number of sets of factor scores matching the specific requirements of a certain common factor model. In contrast to their explicit estimation in PLS-SEM, the scores of common factors as assumed in CB-SEM are indeterminate.

Factor weighting scheme: uses the correlations between constructs in the structural model to determine their relationships in the first stage of the PLS-SEM algorithm; see Weighting scheme.

Factor-based SEM: see Covariance-based structural equation modeling.

Familywise error rate: the probability of making one or more Type I errors when performing multiple comparisons across several groups of data.

FIMIX-PLS: see Finite mixture partial least squares.

Finite mixture partial least squares (FIMIX-PLS): a latent class approach that allows for identifying and treating unobserved heterogeneity in PLS path models. The approach applies mixture regressions to simultaneously estimate group-specific parameters and observations’ probabilities of segment membership.

First-generation techniques: statistical methods traditionally used by researchers, such as regression and analysis of variance.

Fixed seed: is a number used to initialize a (pseudo-)random number generator in bootstrapping. If the seed is fixed, the same sequence of random numbers is generated every time bootstrap is run, leading to reproducible results.

Focal object: an element of the construct definition. It refers to the entity to which an attribute is applied.

Forced-choice scale: a scale without a neutral category.

Formative measurement: see Formative measurement model.

Formative measurement model: a type of measurement model setup in which the indicators form the construct, and arrows point from the indicators to the construct. The outer weights estimation of formative measurement models usually uses Mode B in PLS-SEM.

Formative measures: see Formative measurement model.

Formative–formative higher-order construct: has formatively measured lower-order components and relationships from the lower-order components to the higher-order component.

Formative–reflective higher-order construct: has formatively measured lower-order components and relationships from the higher-order component to the lower-order components.

Fornell-Larcker criterion: a measure of discriminant validity that compares the square root of each construct’s average variance extracted with its correlations with all other constructs in the model. The Fornell-Larcker criterion is largely unsuitable for detecting discriminant validity problems.

fsQCA: see Fuzzy-set qualitative comparative analysis.

Full measurement invariance: this is confirmed when (1) configural invariance, (2) compositional invariance, and (3) equality of composite mean values and variances are demonstrated.

Full mediation: a situation in mediation analysis that occurs when the mediated effect is significant but not the direct effect. Hence, the mediator variable fully explains the relationship between an exogenous and an endogenous latent variable. Full mediation is also referred to as indirect-only mediation.

Fuzzy-set qualitative comparative analysis (fsQCA): is a method used to search for model configurations by identifying specific combinations of conditions that are either necessary or sufficient for producing a particular outcome. It systematically analyzes how different causal factors interact within cases, enabling researchers to uncover multiple pathways or configurations that lead to the same result.

Gaussian copula approach: is an instrumental variable-free method for diagnosing and treating endogeneity, which directly models the correlation of an antecedent construct with its endogenous construct’s error term.

Genetic algorithm segmentation in PLS-SEM (PLS-GAS): a distance-based segmentation method in PLS-SEM that builds on genetic algorithms, a search heuristic, which aims to find a good (not necessarily the best) solution for the classification problem.

Geweke and Meese criterion (GM): a criterion for model selection among a set of alternative models. The model with the lowest GM is preferred.

GM: see Geweke and Meese criterion.

GoF: see Goodness-of-fit index.

Goodness-of-fit index (GoF): has been developed as an overall measure of model fit for PLS-SEM. However, as the GoF cannot reliably distinguish valid from invalid models and since its applicability is limited to certain model setups, researchers should avoid its use.

Heterogeneity: occurs when the data underlie groups of data characterized by significant differences in terms of model parameters. Heterogeneity can be either observed or unobserved, depending on whether its source can be traced back to observable characteristics (e.g., demographic variables) or whether the sources of heterogeneity are not fully known.

Heterotrait-heteromethod correlations: the correlations of the indicators across constructs measuring different constructs.

Heterotrait-monotrait ratio (HTMT): a measure of discriminant validity. The HTMT is the mean of all correlations of indicators across constructs measuring different constructs (i.e., the heterotrait-heteromethod correlations) relative to the (geometric) mean of the average correlations of indicators measuring the same construct (i.e., the monotrait-heteromethod correlations). Different variants of the HTMT criterion exist.

Hierarchical common factor model: see Reflective-reflective HCM.

Hierarchical component models: see Higher-order constructs.

Higher-order component: represents a more abstract dimension of a concept in a higher-order construct.

Higher-order constructs: represent a higher-order structure (usually second-order) that contains several layers of constructs and involves a higher level of abstraction. Higher-order constructs involve a more abstract higher-order component related to two or more lower-order components in a reflective or formative way.

Higher-order models: see Higher-order constructs.

Hill climbing: a heuristic optimization method that belongs to the family of local search procedures. The method starts with a random partition into a prespecified number of segments and iteratively improves this solution one element at a time until it arrives at a (locally) optimized solution.

HOC: see Higher-order construct.

Holdout sample: a subset of a larger data set or a separate data set not used in model estimation.

HTMT: see Heterotrait-monotrait ratio.

HTMT2: is a variant of the HTMT criterion, which considers the geometric mean instead of the arithmetic mean for calculating the average indicator correlations.

Hypothesized relationships: proposed explanations for constructs that define the path relationships in the structural model. The PLS-SEM results enable researchers to statistically test these hypotheses and thereby empirically substantiate the existence of the proposed path relationships.

Importance: a term used in the context of IPMA. It is equivalent to the unstandardized total effect of some latent variable on the target variable.

Importance–performance map: a graphical representation of the importance–performance map analysis.

Importance–performance map analysis (IPMA): extends the standard PLS-SEM reporting of path coefficient estimates by adding a dimension that considers the average values of the latent variable scores. More precisely, the IPMA contrasts the structural model’s total effects on a specific target construct with the average latent variable scores of this construct’s predecessors.

Importance-performance matrix: see Importance-performance map analysis (IPMA).

In-sample predictive power: see Coefficient of determination.

Inconsistent mediation: see Competitive mediation.

Index: a set of formative indicators used to measure a construct.

Index of moderated mediation: quantifies the effect of a moderator on the indirect effect of an exogenous construct on an endogenous construct through a mediator.

Indicator average (IA): predicts each indicator’s value using the mean of the corresponding training sample. Thereby, the IA serves as a naïve prediction benchmark employed in the context of PLS_predict and CVPAT.

Indicator reliability: the square of a standardized indicator’s outer loading. It represents how much of the variation in an item is explained by the construct and is referred to as the variance extracted from the item.

Indicators: these are directly measured observations (raw data), also referred to as either items or manifest variables, which are represented in path models as rectangles. They are also available data (e.g., responses to survey questions or collected from company databases) used in measurement models to measure the latent variables.

Indirect effect: represents a relationship between two latent variables via a third (e.g., mediator) construct in the PLS path model. If p₁ is the relationship between the exogenous latent variable and the mediator variable, and p₂ is the relationship between the mediator variable and the endogenous latent variable, the indirect effect is the product of path p₁ and path p₂.

Indirect-only mediation: a situation in mediation analysis that occurs when the indirect effect is significant but not the direct effect. Hence, the mediator variable fully explains the relationship between an exogenous and an endogenous latent variable. Indirect-only mediation is also referred to as full mediation.

Individual mediating effect: a type of mediating effect in a multiple mediation model which only considers one mediator.

Information criteria: statistical measures of the relative quality of a certain segment solution that contrast the fit (i.e., the likelihood) of a solution and the number of parameters used to achieve that fit, which increase with the number of segments. The smaller the value of a certain information criterion, the better the segmentation solution.

Initial values: the values for the relationships between the latent variables and the indicators in the first iteration of the PLS-SEM algorithm. Since the user typically has no information about which indicators are more or less important in each measurement model, an equal weight for every indicator in the PLS path model serves well for initialization. Accordingly, all relationships in the measurement models have an initial value of +1.

Inner model: see Structural model.

Interaction effect: see Moderating effect.

Interaction term: an auxiliary variable included in the path model to account for the interaction of a moderator variable and the antecedent construct.

Internal consistency reliability: a form of reliability used to judge the consistency of results across items on the same test. It determines whether the items measuring a construct are similar in their scores (i.e., if the correlations between the items are strong).

Interpretational confounding: a situation in which the empirical meaning of a construct departs from the theoretically implied meaning.

Interval scale: can be used to provide a rating of objects and has a constant unit of measurement so the distance between the scale points is equal.

Inverse square root method: a method for determining the minimum sample size requirement, which uses the value of the path coefficient with the minimum magnitude in the PLS path model as input.

IPMA: see Importance–performance map analysis.

Items: see Indicators.

Iterative reweighted regressions segmentation (PLS-IRRS): a particularly fast and high-performing distance-based segmentation method for PLS-SEM.

Jangle fallacy: describes the inference that two measures (e.g., scales) with different names measure different constructs.

Joint mediating effect: see Parallel mediating effect.

k-fold cross-validation: a model validation technique for assessing how the results of a PLS-SEM analysis will generalize to an independent data set. The technique combines k-1 subsets into a single training sample that is used to predict the remaining subset.

k-means clustering: a group of nonhierarchical clustering algorithms that work by partitioning observations into a predefined number of groups and then iteratively reassigning observations until some numeric goal related to cluster distinctiveness is met.

Kurtosis: is a measure of whether the distribution is too peaked (a very narrow distribution with most of the responses in the center).

Label switching: occurs when the label of a specific segment changes from one FIMIX-PLS run to the next.

Latent class techniques: a set of statistical methods that facilitate uncovering and treating unobserved heterogeneity. Various approaches have been proposed, which generalize, for example, finite mixture, genetic algorithm, or hill-climbing approaches to PLS-SEM.

Latent variable scores: see Construct scores.

Latent variables: elements of a structural model that are used to represent theoretical concepts in statistical models. A latent variable that only explains other latent variables (only outgoing relationships in the structural model) is called exogenous, while latent variables with at least one incoming relationship in the structural model are called endogenous. Also see Constructs.

Linear effect: represented by a straight line when plotted as a graph.

Linear regression model (LM) benchmark: a benchmark used in PLS_predict and CVPAT, derived from regressing an endogenous construct’s indicators on the indicators of all exogenous constructs. The LM benchmark thereby neglects the measurement model and structural configurations. PLS-SEM results are assumed to outperform the LM benchmark.

Linear relationship: see Linear effect.

Listwise deletion: see Casewise deletion.

LOC: see Lower-order components.

Log transformation: a type of data transformation to account for nonlinear relationships, which applies a base 10 logarithm to every observation.

Loss: a metric used in CVPAT that corresponds to a model’s average squared prediction error for one or more target constructs.

Lower-order components: represent more concrete subdimensions of a concept in a higher-order construct.

MAE: see Mean absolute error (MAE).

Main effect: refers to the direct effect between an exogenous and an endogenous construct in the path model without the presence of a moderating effect. After inclusion of the moderator variable, the main effect typically changes in magnitude. Therefore, it is commonly referred to as simple effect in the context of a moderator model.

Manifest variables: see Indicators.

Maximum number of iterations: is needed to ensure that the PLS-SEM algorithm stops. The goal is to reach convergence. But if convergence cannot be reached, the algorithm should stop after a certain number of iterations. This maximum number of iterations (e.g., 300) should be sufficiently high to allow the PLS-SEM algorithm to converge based on the stop criterion. Also see Convergence.

Mean absolute error (MAE): a metric used in PLS_predict and CVPAT, defined as the average absolute differences between the predictions and the actual observations, with all the individual differences having equal weight.

Mean value replacement: inserts the sample mean for missing data. It should only be used when indicators have less than 15% missing values.

Mean-centered data: subtracts the mean value of a variable from every data point. As a result, the newly obtained mean-centered data has a mean value of zero.

Measurement: the process of assigning numbers to a variable based on a set of rules.

Measurement equivalence: see Measurement invariance.

Measurement error: the difference between the true value of a variable and the value obtained by a measurement.

Measurement invariance: refers to whether, under different conditions of observing and studying phenomena (e.g., across different groups of respondents), measurement operations yield measures of the same attribute.

Measurement invariance of composite models (MICOM) procedure: a series of tests to assess the invariance of measures (constructs) across multiple groups of data. The procedure comprises three steps that test different aspects of measurement invariance: (1) configural invariance (i.e., equal parameterization and way of estimation), (2) compositional invariance (i.e., similar composite scores), and (3) equality of composite mean values and variances.

Measurement model: an element of a path model that contains the indicators and their relationships with the constructs and is also called the outer model in PLS-SEM.

Measurement model misspecification: describes the use of a reflective measurement model when it is formative or the use of a formative measurement model when it is reflective. Measurement model misspecification may yield invalid results and misleading conclusions.

Measurement scale: a tool with a predetermined number of closed-ended responses that can be used to obtain an answer to a question.

Measurement theory: specifies how constructs should be measured with (a set of) indicators. It determines which indicators to use for construct measurement and the directional relationship between construct and indicators.

Mediated moderation: combines a moderator model with a mediation model where the continuous moderating effect is mediated.

Mediating effect: occurs when a third construct intervenes between two other related constructs.

Mediation: represents a situation in which one or more mediator construct(s) explain the processes through which an exogenous construct influences an endogenous construct.

Mediation effect size ω: a metric used to quantify the strength of a mediating effect in a simple mediation model.

Mediation model: see Mediation.

Mediator construct: a construct that intervenes between two other directly related constructs.

Mediator model: see Mediation.

Metric scale: represents data on a ratio scale and interval scale; see Ratio scale, Interval scale.

Metrological uncertainty: the dispersion of the measurement values that can be attributed to the concept being measured.

MICOM: see Measurement invariance of composite models (MICOM) procedure.

MIMIC model: see Multiple indicators and multiple causes model.

Minimum Description Length 5 (MDL₅): an information criterion that allows assessing the relative goodness-of-fit of a segmentation solution produced by FIMIX-PLS. A smaller MDL₅ value for a certain number of segments indicates a better fit. The MDL₅ has a strong tendency to underestimate the correct number of segments.

Minimum sample size requirements: the number of observations needed to represent the underlying population and to meet the technical requirements of the multivariate analysis method used or to achieve a sufficient level of statistical power. See Inverse square root method.

Missing value treatment: can employ different methods such as mean replacement, EM (expectation-maximization algorithm), and regression imputation to obtain values for missing data points in the data set used for the analysis.

Mode A: uses correlation weights to compute composite scores from sets of indicators. More specifically, the outer weights are the correlation (or single regression) between the construct and each of its indicators. See Reflective measurement.

Mode B: uses regression weights to compute composite scores from sets of indicators. To obtain the weights, the construct is regressed on its indicators. Hence, the outer weights in Mode B are the coefficients of a multiple regression model. See Formative measurement.

Model comparisons: involve establishing and empirically comparing a set of theoretically justified competing models that represent alternative explanations of the phenomenon under research.

Model complexity: indicates how many latent variables, structural model relationships, and indicators exist in a PLS path model.

Model overfit: occurs when the model estimates fit the data set used for model estimation but do not generalize well to other data sets.

Model parsimony: see Parsimonious models.

Model selection criteria: see Information criteria.

Model-implied nonredundant vanishing tetrads: tetrads considered for significance testing in CTA-PLS.

Moderated mediation: combines a mediation model with a moderator model where the mediator relationship is moderated by a moderator construct.

Moderating effect: see Moderation.

Moderation: occurs when the effect of an antecedent construct on a target construct depends on the values of a third variable, referred to as a moderator variable.

Moderator effect: see Moderation.

Moderator variable: see Moderation.

Modified AIC with factor 3 (AIC₃): an information criterion that allows assessing the relative goodness-of-fit of a segmentation solution produced by FIMIX-PLS. A smaller AIC₃ value for a certain number of segments indicates a better fit. The criterion should be used in conjunction with CAIC to determine the number of segments in FIMIX-PLS.

Modified AIC with factor 4 (AIC₄): an information criterion that allows assessing the relative goodness-of-fit of a segmentation solution produced by FIMIX-PLS. A smaller AIC₄ value for a certain number of segments indicates a better fit. The criterion generally performs well for identifying the number of segments in FIMIX-PLS.

Monotrait-heteromethod correlations: the correlations of indicators measuring the same construct.

Multicollinearity: see Collinearity.

Multigroup analysis: a type of moderator analysis where the moderator variable is categorical (usually with two categories) and is assumed to potentially affect all relationships in the structural model; it tests whether parameters (mostly path coefficients) differ significantly between two or more groups. Research has proposed a range of approaches to multigroup analysis, which rely on the bootstrapping and permutation procedures.

Multimethod MGA approach: involves applying different MGA.

Multiple battery model: an HCM type in which the LOCs measure the same construct at different points of time using data from the same set of respondents.

Multiple indicators and multiple causes (MIMIC) model: a type of structural equation model that incorporates both formative and reflective indicators to measure latent constructs.

Multiple mediation analysis: describes a mediation analysis in which multiple mediator variables are included in the model.

Multiple testing problem: occurs when the Type I error of a series of tests increases exponentially.

Multiple-moderator model: describes a moderation analysis in which multiple moderators are included in the model.

Multivariate analysis: a statistical method that simultaneously analyzes multiple variables.

NCA: see Necessary condition analysis.

Necessary condition analysis (NCA): a statistical method that facilitates analyzing whether 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.

Necessity effect size d: indicates whether a construct is necessary for achieving a certain outcome. A necessary condition should have at least a small effect size d (i.e., ≥ 0.1), which is significant.

Necessity logic: implies that an outcome - or a certain level of an outcome - can only be achieved if the necessary condition (e.g., a certain indicator or construct) is in place or has reached a certain level. If the necessary condition is not in place, the outcome will not materialize (i.e., the condition is necessary, but not sufficient for an outcome).

No-effect nonmediation: a situation in mediation analysis that occurs when neither the direct nor the indirect effect is significant.

Nominal scale: a measurement scale in which numbers are assigned that can be used to identify and classify objects (e.g., people, companies, products, etc.).

Nomological validity: the degree to which a construct behaves as it should in a system of related constructs.

Nonlinear effect: is not represented by a straight line when plotted on a graph but by a curve.

Nonlinear relationship: see Nonlinear effect.

Nonparametric distance-based test: allows testing whether the complete model is different across two (or more) groups. The test applies the permutation procedure to compare the average (squared Euclidean or geodesic) distance of the model-implied indicator correlation matrix across the groups.

Nonredundant tetrads: tetrads considered for significance testing in CTA-PLS.

Normed entropy statistic (EN): a statistical measure that uses the observations' probabilities of segment membership as an indication of how well segments are separated. Values above 0.50 permit a clear-cut classification of data into the segments.

Observed heterogeneity: occurs when the sources of heterogeneity are known and can be traced back to observable characteristics such as demographics (e.g., gender, age, income).

Omission distance D: determines which data points are deleted when applying the blindfolding (see Blindfolding) procedure.

One-tailed test: see Significance testing.

Optimization criterion: a certain measure whose value defines the quality of a tested set of parameters.

Ordinal scale: a measurement scale in which numbers are assigned that indicate relative positions of objects in an ordered series.

Orthogonalizing approach: an approach to model the interaction term when including a moderator variable in the model. It creates an interaction term with orthogonal indicators, which are uncorrelated with the indicators of the independent variable and the moderator variable in the moderator model.

Out-of-sample predictive power: see Predictive power.

Outer loadings: the bivariate correlations between a construct and the indicators. They determine an item’s absolute contribution to its assigned construct. Loadings are of primary interest in the evaluation of reflective measurement models but are also interpreted when formative measures are involved.

Outer model: see Measurement model.

Outer weights: these are the results of a multiple regression of a construct on its set of indicators. Weights are the primary criterion to assess each indicator’s relative importance in formative measurement models.

Outlier: an extreme response to a particular question or extreme responses to all questions.

p value: in the context of structural model assessment, it is the probability of error for assuming that a path coefficient is significantly different from zero. In applications, researchers compare the p value of a coefficient with a significance level selected prior to the analysis to decide whether the path coefficient is statistically significant.

Pairwise deletion: uses all observations with complete responses in the calculation of the model parameters. As a result, different calculations in the analysis may be based on different sample sizes, which can bias the results. The use of pairwise deletion should generally be avoided.

Parallel mediating effect: a type of mediating effect in a multiple mediation model that considers the total indirect effect of an antecedent construct on a target construct via all mediators.

Parameter settings: see Algorithmic options.

Parametric approach: a type of multigroup analysis representing a modified version of a two-independent-samples t test.

Parametric MGA: a multigroup variant, representing a modified version of a two-independent-samples t test. The test comes in two forms - parametric MGA (equal) or parametric MGA (unequal) - depending on whether the population variances of the groups are considered to be equal.

Parametric MGA (equal): see Parametric MGA.

Parametric MGA (unequal): see Parametric MGA.

Parsimonious models: models with as few parameters as possible for a given quality of model estimation results.

Partial least squares algorithm: allows estimating path models with latent variables.

Partial least squares k-means (PLS-SEM-KM): a clustering method that maximizes group-specific latent variable score differences, while at the same time accounting for heterogeneity in the structural and measurement model relations.

Partial least squares path modeling: see Partial least squares structural equation modeling.

Partial least squares regression: an approach designed to reduce the problem of multicollinearity in regression models. It uses a principal components analysis that extracts linear composites of the independent variables and their respective scores, taking into consideration the relationship between the independent and dependent variables, and maximizing the explanation of the dependent variable.

Partial least squares structural equation modeling (PLS-SEM): a composite-based method to estimate structural equation models. The goal is to maximize the explained variance of the endogenous latent variables.

Partial measurement invariance: is confirmed when only (1) configural invariance and (2) compositional invariance are demonstrated.

Partial mediation: occurs when a mediator variable partially explains the relationship between an exogenous and an endogenous construct. Partial mediation can come in the form of complementary and competitive mediation, depending on the relationship between the direct and indirect effects.

Path analysis: an extension of multiple regression analysis (i.e., using observed variables) that considers more than one dependent variable and allows researchers, for instance, to assess direct and indirect effects, including mediation, moderation, and moderated mediation.

Path coefficients: estimated path relationships in the structural model (i.e., between the constructs in the model). They correspond to standardized betas in a regression analysis.

Path model: a diagram that visually displays the hypotheses and variable relationships that are examined when structural equation modeling is applied.

Path weighting scheme: uses the results of partial regression models to determine the relationships between the constructs in the structural model in the first stage of the PLS-SEM algorithm; see Weighting scheme.

Percentile method: an approach for constructing bootstrap confidence intervals. Using the ordered set of parameter estimates obtained from bootstrapping, the lower and upper bounds are computed directly by excluding a certain percentage of the lowest and highest values (e.g., the 2.5% and 97.5% bounds for a 95% bootstrap confidence interval). The method can be extended by adding a bias correction. The bias-corrected percentile method is generally recommended.

Performance: a term used in the context of IPMA. It is the mean value of the unstandardized (and rescaled) scores of a latent variable or an indicator.

Permutation: generates a reference distribution of some set of parameters from the actual data by randomly exchanging observations between the groups multiple times.

Permutation MGA: randomly permutes observations between two groups and re-estimates the model to derive a test statistic for the group differences.

Permutation test: a type of multigroup analysis. The test randomly permutes observations between the groups and re-estimates the model to derive a test statistic for the group differences.

PLS algorithm: see Partial least squares algorithm.

PLS path modeling: see Partial least squares structural equation modeling.

PLS regression: an analysis technique that explores the linear relationships between multiple independent variables and a single or multiple dependent variable(s). In developing the regression model, it constructs composites from both the multiple independent variables and the dependent variable(s) by means of principal component analysis.

PLS typological path modeling (PLS-TPM): a distance-based segmentation method developed for PLS-SEM.

PLS-GAS: see Genetic algorithm segmentation in PLS-SEM.

PLS-IRRS: see Iterative reweighted regressions segmentation (PLS-IRRS).

PLS-MGA: a bootstrap-based multigroup analysis technique.

PLS-POS: see Prediction-oriented segmentation in PLS-SEM (PLS-POS).

PLS-R: see Partial least squares regression.

PLS-SEM: see Partial least squares structural equation modeling.

PLS-SEM algorithm: the heart of the method. Based on the PLS path model and the indicator data available, the algorithm estimates the scores of all latent variables in the model, which in turn serve for estimating all path model relationships.

PLS-SEM bias: refers to PLS-SEM’s property that structural model relationships are slightly underestimated and relationships in the measurement models are slightly overestimated compared to CB-SEM when using the method on common factor model data. This difference can be attributed to the methods’ different handling of the latent variables in the model estimation but is negligible in most settings typically encountered in empirical research.

PLS-SEM kernel k-means clustering: is a latent class analysis procedure that applies kernel k-means clustering to residuals from the PLS-SEM analysis to separate non-linear data patterns.

PLS-SEM KKC:see PLS-SEM kernel k-means clustering.

PLS-SEM-KM: see Partial least squares k-means (PLS-SEM-KM).

PLS-TPM: see PLS typological path modeling (PLS-TPM).

PLSc: see Consistent PLS-SEM.

PLSc-SEM: see Consistent PLS-SEM.

PLSe2: a variant of the original PLS-SEM algorithm. Similar to PLSc-SEM, it makes the model estimates consistent in a common factor model sense.

PLS_predict procedure: a holdout-sample-based procedure that generates case-level predictions on an item or a construct level to facilitate the assessment of a PLS path model’s predictive power. The PLS_predict procedure relies on the concept of k-fold cross-validation.

Polynomial: is a mathematical expression consisting of a sum of terms, whereby each term includes a variable raised to a power and multiplied by a coefficient.

Polynomial degree: determines number of terms that are summed in a polynomial; see also Polynomial.

Prediction: see Predictive power.

Prediction error: the difference between a variable’s predicted and original value.

Prediction statistics: quantify the degree of prediction error.

Prediction-oriented segmentation in PLS-SEM (PLS-POS): a distance-based segmentation method for PLS-SEM.

Predictive power: indicates a model’s ability to predict new observations.

Presegmentation: an option for PLS-POS that, in the first round, assigns all observations at the same time to their closest segment. Then, in the subsequent iterations, PLS-POS reassigns only one observation per iteration.

Principal component analyses (PCA) weighting scheme: first estimates construct scores using separate PCAs for each measurement model, which are then used as input for regressions in the structural model to compute the path coefficients.

Principal components regression: performs a principal components analysis on the independent variables, and the principal components are used as predictive/explanatory variables for the dependent variable. It focuses on reducing the dimensionality of the independent variables without taking into account the relationship between the independent and dependent variables.

Priority map analysis: see Importance-performance map analysis (IPMA).

Product indicator approach: an approach to model the interaction term when including a moderator variable in the model. It involves multiplying the indicators of the moderator by the indicators of the exogenous latent variable to establish a measurement model of the interaction term. The approach is only applicable when both moderator and exogenous latent variables are measured reflectively.

Product indicators: indicators of an interaction term, generated by multiplication of each indicator of the exogenous construct with each indicator of the moderator variable. See Product indicator approach.

Q² statistic: a measure for evaluating structural models. The computation of Q² draws on the blindfolding technique, which uses a subset of the available data to estimate model parameters and then predicts the omitted data. Q² examines whether a model accurately predicts data points not used in the estimation of model parameters. As the measure blends in-sample and out-of-sample predictive power assessment, we advise against its use.

Q²_predict: a metric used in PLS_predict to assess the model’s predictive power. The metric represents a naïve benchmark for the PLS-SEM results. Values greater than zero indicate that the PLS-SEM estimation beats the naïve benchmark in terms of prediction.

Quadratic effect: represented by a curved nonlinear relationship characterized by a polynomial of the degree 2; see also Nonlinear effect and Polynomial.

R² value: see Coefficient of determination (R²).

Random seed: is a number used to initialize a (pseudo-)random number generator in bootstrapping. If the seed is random, bootstrap samples will differ across runs, leading to slightly different estimates.

Ratio scale: a measurement scale that has a constant unit of measurement and an absolute zero point; a ratio can be calculated using the scale points.

Raw data: the unstandardized observations in the data matrix that is used for the PLS path model estimation.

REBUS-PLS: see Response-based procedure for detecting unit segments in PLS path modeling.

Redundancy analysis: a method used to assess a formative construct’s convergent validity. It tests whether a formatively measured construct is highly correlated with a reflective or single-item measure of the same construct.

Reflective indicators: indicators of a reflective measurement model.

Reflective measure: see Reflective measurement.

Reflective measurement: a type of measurement model setup in which measures represent the effects (or manifestations) of an underlying construct. Causality is from the construct to its measures (indicators). The outer loadings estimation of reflective measurement models usually uses Mode A in PLS-SEM.

Reflective measurement model: see Reflective measurement.

Reflective–formative higher-order construct: has reflectively measured lower-order components and relationships from the lower-order components to the higher-order component.

Reflective–reflective higher-order construct: has reflectively measured lower-order components and relationships from the higher-order component to the lower-order component.

Regression weights: see Mode B.

Relative contribution: the unique importance of each indicator by partializing the variance of the formatively measured construct that is predicted by the other indicators. An item’s relative contribution is provided by its weight.

Relevance of significant relationships: compares the relative importance of predictor constructs to explain endogenous latent constructs in the structural model. Significance is a prerequisite for the relevance, but not all constructs and their significant path coefficients are highly relevant to explain a selected target construct.

Reliability: the consistency of a measure. A measure is reliable (in the sense of test-retest reliability) when it produces consistent outcomes under consistent conditions. The most commonly used measure of reliability is the internal consistency reliability.

Repeated indicators approach: a type of measurement model setup in higher-order constructs that reuses the indicators of the lower-order components as indicators of the higher-order component to identify the higher-order construct.

Rescaling: the act of changing the values of a variable’s scale to fit a predefined range (e.g., 0 to 100).

Response-based procedure for detecting unit segments in PLS path modeling (REBUS-PLS): a distance-based segmentation method for PLS-SEM that builds on the PLS-TPM method.

Response-based segmentation techniques: see Latent class techniques.

RMSE: see Root mean square error (RMSE).

RMS_theta: see Root mean square residual covariance.

Root mean square error (RMSE): a metric used in PLS_predict and CVPAT, defined as the square root of the average of the squared differences between the predictions and the actual observations.

Root mean square residual covariance (RMS_theta): a model fit measure that is based on the (root mean square) discrepancy between the observed covariance and the model-implied correlations. In CB-SEM, an SRMR value indicates good fit, but no threshold value has been introduced in a PLS-SEM context yet. Initial simulation results suggest a (conservative) threshold value for the root mean square residual covariance (RMS_theta) of 0.12. That is, RMS_theta values below 0.12 indicate a well-fitting model, whereas higher values indicate a lack of fit. However, model fit measures should generally be treated with extreme caution in PLS-SEM.

Sampling weights: assign the observations different importance in the parameter estimation in order to obtain unbiased estimates of the population effects.

Scale: a set of reflective indicators used to measure a construct.

Search depth: a parameter in PLS-POS that defines the maximum number of observations considered for reassignment to another segment.

Second-generation techniques: overcome the limitations of first-generation techniques, for example, in terms of accounting for measurement error. SEM is the most prominent second-generation data analysis technique.

Second-order constructs: a type of higher-order construct with two levels of abstraction.

Secondary data: data that have already been gathered, often for a different research purpose and some time ago.

Self-interaction: occurs when the effect of an exogenous latent variable on an endogenous latent variable depends on the values of the exogenous latent variable.

SEM: see Structural equation modeling.

Serial mediating effect: a type of mediating effect in a multiple mediation model that considers a sequence of effects via two or more mediators simultaneously.

Significance testing: the process of testing whether a certain result likely has occurred by chance (i.e., whether an effect can be assumed to truly exist in the population).

Simple effect: a cause–effect relationship in a moderator model. The parameter estimate represents the size of the relationship between the exogenous and endogenous latent variables when the moderator variable is included in the model. For this reason, the main effect and the simple effect usually have different sizes.

Single mediation analysis: describes a mediation analysis in which only one mediator variable is included in the model.

Single-item constructs: constructs that have only a single item measuring them. Since a single-item construct is equal to its measure, the indicator loading is 1.00, making conventional reliability and convergent validity assessments inappropriate.

Singular data matrix: occurs when a variable in a measurement model is a linear combination of another variable in the same measurement model or when a variable has identical values for all observations. In this case, the variable has no variance and the PLS-SEM approach cannot estimate the PLS path model.

Skewness: the extent to which a variable’s distribution is symmetrical around its mean value.

Slope plot: a type of line chart used to detect changes in linear slopes between groups.

Sobel test: a test that has been proposed to assess the significance of the indirect effect in a mediation model. However, research has dismissed the Sobel test for evaluating mediation analysis results of regression models and PLS-SEM.

Specific indirect effect: describes an indirect effect via one single mediator in a multiple mediation model.

Spread model: an HCM type in which the HOC is manifested in several more specific LOCs. The relationship between HOC and LOCs is reflective.

SRMR: see Standardized root mean square residual.

Stand-alone higher-order construct: a higher-order construct that is not embedded in a greater nomological net of constructs.

Standard error: the standard deviation of the sampling distribution of a given statistic. Standard errors are important to show how much sampling fluctuation a statistic has.

Standardized data: have a mean value of 0 and a standard deviation of 1 (z-standardization). The PLS-SEM method usually uses standardized raw data. Most software tools automatically standardize the raw data when running the PLS-SEM algorithm.

Standardized path coefficients: show how many standard deviations an endogenous construct changes per standard deviation increase in its antecedent construct.

Standardized root mean square residual (SRMR): a model fit measure, which is defined as the root mean square discrepancy between the observed correlations and the model-implied correlations. Research has shown that the SRMR is largely unsuitable for detecting model misspecification in situations commonly encountered in applied research.

Standardized values: indicate how many standard deviations an observation is above or below the mean.

Statistical power: the probability of detecting a significant relationship when the relationship is in fact present in the population.

Stop criterion: see Convergence.

Straight lining: describes a situation in which a respondent marks the same response for a high proportion of the questions.

Structural equation modeling (SEM): a set of statistical methods used to estimate relationships between constructs and indicators, while accounting for measurement error.

Structural model: includes the constructs and their relationships as derived from theory and logic.

Structural theory: specifies how the latent variables are related to each other. That is, it shows the constructs and the paths between them.

Studentized bootstrap method: computes confidence intervals similarly to a confidence interval based on the t distribution, except that the standard error is derived from the bootstrapping results.

Sufficiency logic: assumes that several factors contribute to the outcome and that one can compensate for another.

Sum scores: represent a naive way to determine latent variable scores. Instead of estimating the relationships in the measurement models, sum scores use the same weight for each indicator per measurement model (equal weights) to determine latent variable scores. As such, the sum scores approach does not account for measurement error.

Suppressor variable: describes the mediator variable in competitive mediation, which absorbs a significant share of or the entire direct effect, thereby substantially decreasing the magnitude of the total effect.

Tau equivalence: an assumption in a measurement model according to which all items measuring a construct have the same loading in the population.

Tetrad: the difference of the product of a pair of covariances and the product of another pair of covariances. In reflective measurement models, this difference is assumed to be zero or at least close to zero (i.e., they are expected to vanish). Nonvanishing tetrads in a latent variable’s measurement model cast doubt on its reflective specification, suggesting a formative specification.

Theoretical model: a set of equations with variables that formalize a theory.

Theoretical t value: see Critical t value.

Theory: a set of systematically related hypotheses developed following the scientific method that can be used to explain and predict outcomes and can be tested empirically.

Three-way interaction: an extension of two-way interaction, where the moderator effect is again moderated by another moderator variable.

TOL: see Variance inflation factor.

Tolerance (TOL): see Variance inflation factor.

Top-down approach: a way to establish an HCM in which a more abstract construct (the HOC) is defined that consists of several components (the LOCs).

Total effect: the sum of the direct effect and the indirect effect between an exogenous and an endogenous latent variable in the path model.

Total indirect effect: the sum of all specific indirect effects in a multiple mediation model.

Training sample: a subset of a larger data set used for model estimation.

Two-stage approach (higher-order constructs): an approach to modeling and estimating higher-order constructs in PLS-SEM, which is particularly useful when a reflective-formative or formative-formative higher-order construct serves as an endogenous construct in the PLS path model.

Two-stage approach (moderation analysis): an approach to model the interaction term when including a moderator variable in the model. The approach can also be used when the exogenous construct and/or the moderator variable are measured formatively.

Two-stage approach (nonlinear effects): an approach to model the nonlinear (e.g., quadratic) term. The approach can be used for any kind of exogenous construct no matter whether it is measured reflectively, formatively, or represents a single item construct.

Two-tailed test: see Significance testing.

Two-way interaction: the standard approach to moderator analysis where the moderator variable interacts with one other exogenous latent variable.

Type I higher-order construct: see Reflective-reflective higher-order construct.

Type II higher-order construct: see Reflective-formative higher-order construct.

Type III higher-order construct: see Formative-reflective higher-order construct.

Type IV higher-order construct: see Formative-formative higher-order construct.

Unidimensionality: the concept that all indicators in a measurement model are intended to reflect a single underlying construct.

Unobserved heterogeneity: occurs when the sources of heterogeneous data structures are not (fully) known.

Unstandardized data: are raw data that have not been transformed, for example, to have a mean of 0 and a standard deviation of 1 (z-standardization). Processing unstandardized data in PLS-SEM is only reasonable if all indicator variables are measured on the same scale level.

Unstandardized path coefficients: represent the expected change in the endogenous construct for a one-unit change in the antecedent construct, using the indicators’ original measurement scale. For this reason, unstandardized path coefficients should only be interpreted when all indicators have the same measurement scale.

Validity: the extent to which a construct’s indicators jointly measure what they are supposed to measure.

Vanishing tetrads: see Tetrad.

Variance inflation factor (VIF): quantifies the severity of collinearity among the indicators in a formative measurement model and among a set of constructs in the structural model. The VIF of indicator i in a formative measurement model is calculated as VIF_i = 1 / (1 − R_i²), where R_i² is the coefficient of determination obtained when indicator i is regressed on all other indicators in the same measurement model. The VIF calculation for constructs in the structural model is analogous.

Variance-based SEM: see Partial least squares structural equation modeling.

Variate: see Composite variable.

VIF: see Variance inflation factor.

Weighted PLS-SEM (WPLS): a modified version of the original PLS-SEM algorithm that allows the researcher to incorporate sampling weights.

Weighting scheme: describes a particular method to determine the relationships in the structural model when running the PLS-SEM algorithm. While the results of the weighting schemes don’t differ much, researchers should generally prefer the path weighting scheme.

Welch-Satterthwaite t test: see Parametric MGA.

WPLS: see Weighted PLS-SEM.