Review of A Primer on Partial Least Squares Structural Equaltion Modeling (PLS-SEM)
Hair, Jr., Hult, Ringle, Sarstedt

* with additional sources

Chapter 1: An Introduction to Structural Equation Modeling

Summary

Multivariate Analysis

Multivariate analysis (MVA) is classified a second generation statistical technique\(^*\) which extends from first generation statistical techniques\(^*\).
  • first generation statistical techniques: analyzes only one layer of linkages; identify patterns and relationships between outcome and predictor; do not adjust for measurement error - difference between measured value and true value; systematic (mis-calibration) or random

  • second generation statistical techniques: simultaneously estimate relationships within factors and between factors and outcome and adjust for measurement error; “answer interrelated questions in a single, systematic, comprehensive analysis”
  • measurement error

Its objective is simultaneous analysis of the many factors that affect the variability of a singular outcome. These factors may have dependencies on other factors. MVA seek to understand how variability of one factor will affect the variability in a different factor and how the simultaneous variability of factors affect an outcome. There are several different methods of MVA with different objectives, including data reduction or structural simplification, sorting and grouping, investigation of dependence among variables, prediction relationships between variables, hypothesis construction and testing.

Structural Equation Modeling (SEM)

  • SEM is a MVA method that models causal complex structures. The causal structure represents and investigate how multiple, observable, and measurable factors of a latent theoretical phenomenon are related to each other and their connection to the underlying theoretical phenomenon.

  • The objectives of causal analysis is (1) provide guidance on actions and treatment on causes (“variables that can be changed or manipulated”) and (2) provide “scientific explanation”.

  • With these objectives, SEM is a method that can be used to understand how to engage and intervene on complex mechanisms like social determinant of health (SDOH).

About SEM method:

  • gives simple statistics to describe “the scientific explanation of phenomena”
  • SEM translates theory\(^*\)
    • theory- scientific explanation of interrelated hypothesis; used to predict outcomes
    that is consistent with observable experience, reality
  • SEM growing in use because of its objective and its applicable use in many different fields for a wide variety of purpose;
  • although growing in use, it is not widely used despite its capability to precisely and appropriately handle measurement errors\(^*\)
    • measurement error - difference between variable measuring the true indicator
    (which other methods ignore which affect estimation)
  • Advantages of SEM
    • modeling the “complex, multidimensional” structure of abstract social phenomena by “precise analysis of empirical data” within the context of the observed occasions of the phenomena which is abstract and latent that is explained and outlined in theory
    • second generation statistical technique still models the same parameters of first generation techniques like GLM while adjusting measuring error, mediation\(^*\)
      • mediation - indirect effect on outcome to explain direct effect to outcome

      , and moderation\(^*\)
      • moderation - directly affects relationship between predictor and outcome
  • models relationships that are hierarchical or non-hierarchical and recursive or non-recursive
  • To use SEM, research problem must be clearly defined with clearly defined variables that will estimate phenomena through examined variables and their relationships. Requires clearly defined context and definition of theory used to develop research problem and model. Requires latent variables to be fully defined with defined context of the latent variables which will guide its explaination and application.

    • SEM model:

    • the construction of the model is based on theory - drives model, provides context of explanation
    • the model’s results are reflective of the data, answering Does the data reflect or fit the theory?
      • model represents theory which manifest/ causes given data - not that theory mimics observed data
      • theory supports model not just that model supports theory
    • the model is not determined by data
      • estimation are objective need to state why; what about algorithm and estimation makes this objective
    • “What one virtually does with the SEM as an analytical strategy is to test if these assumptions are in agreement with the obtained empirical data.”
      • Because model estimate if theory agrees with observed data and NOT the validity of sample to population, global goodness of fit (gof) is important and unsolved
        • gof - test if sample data estimates are representative of the expected population estimates
      • Unsolved because many SEM methods require large sample size and the SEM models have that lead to tendency to reject gof null hypothesis (\(H_O:\) perfect as well as approxmite fit) define overidentifying restrictions

    Considerations of SEM:

    what is involved to build appropriate model:

    define covariation, correlation, collinearity

    • composite variable (linear combination of weighted variables)
    • measurements need to be of accurate representation of variables interest
      • latent variables (construct)\(^*\)
        • latent variables (constructs) - cannot be directly measured
        are measured through indicators which are observable
    • measure of latent variables include composite score that combine several indicator which reduces measurement error
  • measurement scales (PLS SEM)
    • 4 type (least to most informative): nominal, ordinal, interval (zero does not represent absence), and ratio (zero represents absence)
    • equidistant interval and ratio required for MVA
  • coding: assigning numbers that facilitates measurement
    • precoding vs postcoding
  • data distributions: test for distinction between normality and non-normality

    • Principles of SEM:

    • the components of model
      • path models - visualization of the phenomena
        • structural (inner) model: contain the relationships between constructs,
        • measurement (outer) model: contain indicators specified to measure phenomena,
        • latent constructs,
        • the measured indicators,
        • the relationships,
        • error terms
      • what path models do:
        • specify theory and apply to empirical data to test theoretical relationships
          • testing the structural model (answers what) and measurement model (are the indicators accurately measuring the phenomena)
        • specify relationships between constructs, based on ______
        • specify how constructs are being measured

    Criticisms of SEM methodology

    • difficulties in applications and model specification
    • vulnerability to multicollinearity
    • model fit correspondence to strength of correlation between observed factors
      • weak correlations increases probability of good model fit; need to be caution in conclusion
    • simplified mathematical model of complex latent phenomenon that do not represent causal process in individuals
    • non-experimental data give illusion of causal process

    Piotr Tarka’s response to criticisms “if the hypothesized model is only empirically determined, at minimal theory input, then such a model is simply a convenient summary of a covariance matrix. The interpretation of this model’s equations express only the statistical relationships between variables in reference to the analyzed set of data. If, however, the tested SEM model is theoretically determined by a strong theory, then it receives the status of representing stable causal relationships in the empirical process of data processing”

    Developments of SEM

    • With the development of SEM, there are variation of the method.

    Considerations of PLS-SEM:

    • overview of statistical properties of algorithm which need to be assessed for application
    Data Characteristics Model Characteristics Model Estimation Model Evaluation
    sample size number of construct measures
    higher order construct estimation allowed    		 objective of estimates overall model
    distribution
    non-normal    		 relationships between constructs and measures algorithm efficiency structural model
    scale of measurements Model complexity and setup definition of constructs measurement model
    missing values parameter estimates construct scores calculation and use
    • PLS SEM extends into advanced modeling, assesssment, and analysis procedures
    • follows Gregor’s causal - predictive paradigm GIVE OVERVIEW
    • Criticisms of PLS SEM are based on CB SEM
      • when comparing CB SEM outputs to PLS SEM the estimates for measurement model are higher and estimates for structural model are lower
    • the methods are objectives are different with different algorithms and respective performance cannot be compared

    Data Characteristics

    • minimum sample size requirements
      • sample size depends on population (more heterogeneous, larger sample to reduce sampling error)
      • calculate sample size:
        • 10 times rule: sample size 10 times the number of independent variables in the most complex regression in path model
        • power analysis using G*Power: using most complex path model to achieve specified power level
        • inverse square root method: Pr(path coefficient/standard error(path coefficient)) > critical value
    • complexity of structural model has little influence on sample size
    • measurement scales allowed: metric (ratio and interval), ordinal (equidistant), binary (control variable and moderators)
    • secondary data: use for exploratory research to investigate causally relationships; purpose to examine relationships rather than model fit

    Model Characteristics

    • no circular or loop relationships in structural model
    • multi-sage estimation: separates estimation of measurement and structural models
    • caution with high collinearity among formative measures

    Comparing Methods

    • partial least square structural equation modeling (PLS SEM) vs covariance based structural equation modeling (CB SEM)
      • difference is in how estimate of measurements are calculated
      • results are used differently

    create sidenote definingt composite based and common factor

    PLS SEM CB SEM
    composite based common factor
    combines indicators based on linear method total variance divided into common shared part, unique variance of individual indicator, and error
    forms composite variables only uses common shared variance to estimate construct
    accounts for measurement errors estimates the commonality of sets indicators and its covariations
    using ordinary least squares to minimize error of constructs states that indicators and covariations are manifestation of underlying construct
    composite variable is a valid proxie of constructs explains covariations between associated indicators
    comprehensive representation of constructs direct and precise measurement of constructs
    best for predicting and explaining target constructs best for confirming theory manifestation
    • CB SEM assumes model theory is correct
    • PLS SEM relaxes strong CB SEM assumptions that all covariation between sets of indicators are explained by a common factor
    • Alternatives: more restrictive method of measuring latent variables
    PLS SEM Sum scores PLS regression
    composite variables give individual weights to indicators form composite variable but all indicators are weighted equally linear relationships between multiple independent variables and dependent variable(s)
    weights inform importance of indicator in composite equalize differences in indicator no structural model
    must have structural and measurement models simplification of PLS SEM

    Chapter 2: Specifying the Path Model and Examining Data

    Summary

    PLS-SEM application procedures

    • Specifying the path model
      • Structural model
      • Measurement model
    • Data Exploration - collection, examining

    Path Models

    • developed by Sewall Wright in 1920s
    • as known as path diagrams
    • depiction of theory that visualize relationships and dependency within a set of variables
    • developed based on directed acyclic graphs
      • vertices (variables) are ordered (directed)
      • recursive - unidirectional and does not contain feedback loops or reciprocals
      • consist of paths (the relationships between two variables is unique)
      • causality application of directed acyclic graph follows intuition that prior events influence following event and following evens cannot influence prior events
    • path model is developed from theory, therefore, arrangement and inclusions of variables are not singular and definite
    • path model for SEM contains: structural model and measurement model

    NEED TO ADD VISUAL OF PATH MODEL

    Structural Model

    • inner model
    • depicts how latent variables are related
    • types of latent variables and relationships:
      • exogenous variables - strictly independent,
        • variance does not depend on any other variables in the model
      • endogenous variables - can be solely dependent or both dependent and independent; there is at least one variable identified in the model that affects its value, its value can but not always affect another variable’s value
        • variance dependent on other prior variables and can affect following variables variances
        • SEM adjust for error term that are variables or factors outside the model that influence endogenous variables
      • relationships: indicted by arrows implying predictive
        • double headed (curved) arrows represent correlations of constructs
        • direct relationship
        • indirect relationship - relate to another variable through connection of another
      • mediators - indirect effect; explains why direct relationship exist
        • general mediation analysis:
          1. test if mediator significantly relates to predictor
          2. test if mediator significantly relates to response
          3. test if mediator significantly relates to response controlling for predictor
          4. test if inverse relationship of response predicting predictor are non-significant
          • use of bootstrap to achieve higher statistical power
      • moderators - changes the strength and direction of relationship;
        • general moderation analysis: test if the moderator interacts with the predictor in predicting response
        • categorically effects explored through multi-group analysis testing the significance of group path coefficients
      • control variables - independent variables that are not of interest but has influences

    Measurement Model

    • describes relationships between latent variables and its measures
    • includes measurable indicators of latent variables in structural model
      • structural model reliability depends on measurement models
    • types of measures (indicators):
      • reflective measures: represents the effects of the underlying construct
        • implied causality; construct caused reflective measure
        • the items\(^*\)
          • item - an indicator in a set measuring a given construct
          in a set should be highly correlated
        • maximize the overlap
    • formative measures:each indicator of a construct measures a specific aspect of the construct’s domain
      • set of items should have little overlap, are not interchangeable
      • omitting item can change nature (meaning) of the construct
      • PLS SEM:
        • combined items linearly to form composite variable
        • there is no specific pattern among items
        • no common cause
        • not required to be correlated, can be completely independent
        • indicator approximate the theoretical concept of the construct
        • collinearity of indicators can cause problem of unstable and nonsignificant weights
      • CB SEM
        • use causal indicator that uses error terms
        • indicators are treated as common factor
    • single items: individual indicator of a construct
      • should be interchangeable with construct without loss of meaning
      • promotes higher response rate
      • less informative about construct
      • fewer options to partion data
      • special attention and consideration with use:
        • small sample size
        • expected weak effect
        • multi-items in set are highly correlated - items are redundant
    • PLS SEM allows for modeling of higher order constructs
      • higher order constructs - models latent variable on a more abstract dimension
      • simultaneously models lower order components that are more concrete
      • higher order constructs summarize the lower order components
      • higher order constructs allow for a more parsimonious model

    Data Exploration

    • data
      • quantitative
      • primary or secondary
    • examine data:
      • missingness: survey non-response and item non-response
        • depends of length of survey, subject matter, employment of survey
        • Hair & Hult if 15% missingness from
          • survey remove
          • indicator remove
        • missing value treatment in SMARTPLS3
          • mean value replacement - reduces variability and possibilty of finding meaningful relationships, use with less than 5% missing in indicator
          • easewise (listwise) deletion - removes all cases that contain missing values estimates stable at 9% missing; mindful of systemic deletion
          • pairwise deletion - use only complete observation in estimates; bias reults because different calculations on different samples; advised use only with many missing observations
        • base approach on demographic of missingness
          • apply missing balue treatment to subgroups
          • minimzes decrease in variability
      • suspicious response patterns
        • straight lining
        • diagonal lining
        • alternating extreme responses
        • inconsistency
        • met requirements
      • outliers
        • rarity of single answers or combination
        • analysis impact to result
        • can represent subgroup
      • data distribution: although non-parametric, extreme non-normality problematic in parameter significance
        • cause type II error with inflate errors after applying bootstrapping
        • test for normality:
          • Shapiro-Wilks for normality
          • Skewness for symmetry: beyond \(\pm2\) extreme non-normality
          • Kurtosis for peakness: beyond \(\pm3\) extreme curve height

    Code

    Partial Least Squares Structural Equation Modeling

    INSERT NOTES FROM COMMON BELIEFS AND REALITY ABOUT PLS, PARTIAL LEAST SQUARES STRUCTURAUAL EQUALTION MODELING WITH R, REFELCATIONS ON PARTIAL LEAST SQUARES PATH MODELING

    Chapter 3: Path Model Estimation

    Summary

    PLS-SEM objective

    • developed by Wold (1975, 1982)
      • extended by Lohmoller (1989), Bentler & Huong (2014), Dijkstra (2014)
    • model’s objective: maximize the explained variance in dependent variables by using partial regression
      • for latent variable estimation residual variance is minimized and theorized causation is explained
      • PLS-SEM estimating parameters that describe how latent variable cause other latent variables and indicators
      • goal is PLS-SEM predicting the covariance in indicator set in forming the latent variable
    • algorithmic process: theoretical (inner) model and measurement (outer) model used to obtain estimations
      • assumes a recursive inner model that is subject to predictor specification
      • casual chain system - uncorrelated residuals, without correlations between the residual term of a certain endogenous latent variable and its explanatory latent variables; residual are random and cannot be explain by any predictors identified; no significance/ interpretation value of residual

    • Stage 1: Iterative estimation of inner and outer model weights (combined as composite)
      • weights represents variable importance in forming the construct, and therefore, weights represent how much the construct effects respective variable
      for latent variable score (LVS)
    • latent variable score assumed to be comprehensive representation of construct; proxies of latent variable
    • iterative procedure uses outer and inner approximation of LVS
      • outer approximation - weights of indicators are combined as estimation of LVS
      • inner approximation - other related (adjacent, neighboring) LVS are weighted and combined as the estimation of focal LVS
        • weights reflect how strong other latent variables are connected to it
        • weights of zero assigned to nonadjacent latent variables
      • inner model LVS estimation used to obtain outside approximate weights
      • outer model LVS estimation used to obtain inner approximate weights
    • iteration stops at convergence - when the changes in all outer weights is less than specified amount (typically 0.001 percentage change)
  • Stage 2: Estimation of path coefficients
    • path coefficients - estimates of the relationship between latent variables
  • Stage 3: Estimation of mean and location parameters

    • PLS-SEM algorithm

    • must standardized data
      • using z-standardization where all indicators are transformed to have (\(\bar x = 0\), \(\sigma^{2} = 1\))
      • result in estimates values between \(\pm 1\), values close to 0 usually have little signficance and values closer to extreme have stronger directional relationships
      • similarly when estimating construct relationship, estimates are standardized regression coefficients

    Algorithmic Process:

    Stage 1:

    • during each iteration, weights are scaled to obtain unit variance for the LVS over the N cases in the sample size

    • initial:

      • outside approximation of LVS is sum of equally weighted indicators in the LV block
      • must have all indicator response oriented the same
      • if not in same orientation, rescale remembering to change labeling accordingly also

    • inner approximation of weights: choice between 3 primary weighting schemes

      • weighting schemes specify how focal LV’s neighboring LVs are combined in order to estimate focal LVS

      • centroid weighting scheme:

        • weight of relationship between neighboring LV and focal LV is assigned the sign of their correlation (\(\pm 1\))
        • strength and direction not included
        • estimation of focal LV is the sum of correlation signs of its neighboring LV
        • estimation similar to centroid factor (side note explanation)
        • advantage: simple and effective if all correlation are the same sign
        • disadvantage: if correlation is close to 0, weight can change from \(\pm 1\) between iterations; the importance and influence of these relationship is exaggerated

      • factor weighting scheme:

        • weight of relationship is correlation between neighboring LV and focal LV
        • focal LV “becomes ‘principal component’ of its neighboring LVs”
        • LVS estimate explains maximum variance between all neighboring LVs, singular representation of all neighbors

      • path weighting scheme:

        • calculation of weight depends if neighbor proceeds or follows focal LV
        • the weight reflects both the magnitude and direction of neighboring and focal LV relationship
        • LVS estimation contains properties for independence and dependence
        • proceeding (independent) neighbor LVs: weight is multiple regression coefficient used when combining neighbors
          • multiple regression - focal LV is regressed on all predictor (proceeding, independent) LVs
        • following (dependent) neighbor LVs: weight is correlation coefficient
        • focal LVS serves as a mediator
        • path weighting scheme used when causal relation is hypothesized

    • outside approximation - using inside estimation of LVS, outside weights are calculated for the LVS estimation

      • weight calculation dependent on indicator type (reflective or formative)

      • Mode A: reflective indicator weights

        • weights are simple regression coefficients
          • each indicators (dependent) regressed on its block’s LVS estimation (independent)

      • Mode B: formative indicator weights

        • weights are indicator’s multiple regression coefficient
        • formative indicators are predictors for LVS (dependent)

    Stage 2:

    • Estimation of path coefficients
      • after convergence of weights, path coefficients are estimated by ordinary least squares regression
        • dependent variables are regressed on independent predictors
        • regression performed on outer and inner model

    Stage 3:

    • Mean and location estimation: optional
      • mean for indicators: original data to compute
      • mean for LVs: using derived weights
      • location for dependent LVs: using mean of LVs and path estimates as difference between mean and systemic influence of independent LVs
      • location for reflective indicator: difference from its mean and its estimate based on underlying LV and path loading

    Algorithmic Process Equations:

    Inner model:

    \(\eta = \beta_{0} + \beta\eta + \Gamma\xi+\zeta\)

    • \(\eta\) - endogenous, dependent LV vector
    • \(\xi\) - exogenous, independent LV vector
    • \(\zeta\) - residual variance vector
    • \(\beta\) & \(\Gamma\) - path coefficeint matrices

    \(\eta_{j} = \displaystyle\sum_{i}\beta_{ji}eta_{i} + \displaystyle\sum_{h} \gamma_{jh}\xi_{h} + \zeta_{j}\)

    • \(\beta_{ji}\) & \(\Gamma_{jh}\) - path coefficient the link predictors

    • inner model is subject to predictor specification \(E(\eta_{j}| \forall\eta_{i}, \xi_{h}) = \displaystyle\sum_{i}\beta_{ji}\eta_{i}+\displaystyle\sum_{h} \gamma_{jh}\xi_{h}\)

      • no linear relationship between predictors and residual
        \(E(\zeta_{j}|\forall\eta_{i}, \xi_{h}) = 0\) & \(Cov(\zeta_{j},\eta_{i})=Cov(\zeta_{j},\xi_{h})=0\)

    structural form

    need path model graphic to correspond with weighting schemes












    • factor weighting scheme: \(\xi_{1} = \rho_{110}\cdot\eta_{1,out} + \rho_{120}\cdot\eta_{2,out}\) \(\eta_{1} = \rho_{110}\cdot\xi_{1,out} + \rho_{210}\cdot\xi_{2,out}+\rho_{012}\cdot\eta_{2,out}\)

      • outside estimation of neighboring LVS used in estimation of weights and focal LV
      • \(\rho\) - correlation between neighboring and focal LV, weight

    • path weighting scheme: \(\xi_{1} = \rho_{110}\cdot\eta_{1,out}+\rho_{120}\cdot\eta_{2,out}\) \(\xi_{2} = \rho_{210}\cdot\eta_{1,out}+\rho_{220}\cdot\eta_{2,out}\) \(\eta_{1} = \beta_{1}\cdot\xi_{1,out}+\beta_{2}\cdot\xi_2,out+\rho_{012}\cdot\eta_{2,out}\) \(\eta_{2} = \beta_{1}\cdot\xi_{1,out}+\beta_{2}\cdot\xi_2,out+\beta_{3}\cdot\eta_{1,out}\)

      • \(\beta_{i}\) - multiple regression coefficient













    Outer model:

    • for each LV block, inside estimation of LVS used to calculate weights for indicators
      • indicators are assumed to generated by a linear function of its latent variable and the residual
      • formative indicators do not have residuals nor does exogenous variables
      • formative relationship better described as causal specification for (1) cases where latent variables are an exact linear combination of formative indicators and (2) cases where formative indicators do not completely determine latent variables

    Mode A - reflective indicators
    \(x = \Lambda_{x}\xi_+\varepsilon_{x}\) \(y = \Lambda_{y}\eta_+\varepsilon_{y}\)

    • \(x\) & \(y\) - indicators

    • \(\Lambda_{x}\) & \(\Lambda_{y}\) - simple regression coefficient (loading matrices)

    • \(\varepsilon_{x}\) & \(\varepsilon_{y}\) - residuals (measurement error/ noise)

    • predictor specification \(E(x|\xi) = \Lambda_{x}\xi\) \(E(y|\eta) = \Lambda_{y}\eta\)

    Mode B - formative indicators
    \(\xi = \Pi_{\xi}\cdot x + \delta_\xi\) \(\eta = \Pi_{\eta}\cdot y + \delta_\eta\)

    • \(x\) & \(y\) - indicators

    • \(\Pi_{\xi}\) & \(\Pi_{\eta}\) - multiple regression coefficients

    • \(\delta_{\xi}\) & \(\delta_{\eta}\) - residual from regression

    • predictor specification \(E(\xi|x)= \Pi_{\xi}\cdot x\) \(E(\eta|y)= \Pi_{\eta}\cdot y\)

    • formative specification - represent outer relationship between indicators and true LV


    Weights relation: how LV estimates are formed

    \(\hat\xi_{h}=\displaystyle\sum_{kh}w_{kh}x_{kh}\) \(\hat\eta_{i}=\displaystyle\sum_{ki}w_{ki}x_{ki}\)

    • \(w_{kh}\) & \(w_{ki}\) - \(k^{th}\) weight in LVS estimate
    • \(\hat\xi_{h}\) & \(\hat\eta_{i}\) - LVS estimates

    Statistical properties

    • Fit
      • assess model’s quality in predecitive capability; ability to identify misspecified models
    • Nonpparmatric characteristic
      • has no distributional assumption which affects how significance levels are calculated
      • bootstrapping is implemented to create distribution basedon data and then significane levels are derived
    • Sample size
      • converges in smaller sample size, but does not have advantage in detecting statistical significance - bootstrapping does not provide more statistical power
      • sample size has to be large enough to support conclusion
    • Model complexity
      • shift from individual variable and parameter to package and aggregated parameters
    • On the robustness of parameter estimates
      • comparison between CB-SEM and PLS-SEM
        • when taking CCB-SEM as standard, PLS-SEM estimations are known as PLS-SEM bias - estimations of CB-SEM and PLS-SEM do approximate the same.
        • indicators are assumed to contain measurement error and their estimates are usually overestimated because of adjustment of measurement error
        • because indicators (which are overestimated because of measurement error) are used to estimate constructs there is also measurement error in endogenous constructs which results in estimates that are underestimated
      • PLS-SEM is more general in estimating indicators as a set
      • in PLS-SEM because more information is used in estimating individual indicators, construct estimation is specific because of these adjustments
      • CB-SEM estimates of construct need to remain broader because no adjustment in individual indicator
    • Choice between the Covariance- and Variance- Based SEM method
      • CB-SEM focus on structural relationship (theory). CB-SEM loss predictive ability which does not reduce theory importance

    Algorithm Options and Parameter Setting

    • Indicator Mode
    • Weighting Scheme
    • Initial weighting values
    • Stopping criteria - percentage consider convergence
    • Maximum number of iterations

    Code

    Chapter 4: Assesssing PLS-SEM Results - Part I: Evaluation of the Reflective Measurment Models

    Summary

    Code

    Chapter 5: Assesssing PLS-SEM Results - Part II: Evaluation of the Formative Measurment Models

    Summary

    Code

    Chapter 6: Assesssing PLS-SEM Results - Part III: Evaluation of the Structural Model

    Summary

    Code

    Chapter 7: Mediator and Moderator analysis

    Summary

    Code

    Chapter 8: Outlook on Advanced Methods

    Summary

    Code