Conceptual Foundations of PLS Path Modeling

Learn what partial least squares path modeling is, distinguishing latent constructs and manifest surrogates, and how path coefficients link these latent variables to outcomes using surrogate measures and ols estimation.

Explore the PLS path modeling technique, a non-normal data, bootstrapped, regression-like method ideal for predictive, exploratory analyses with complex models and formative or dummy variables.

Bootstrapping makes PLS path modeling robust by relaxing distributional assumptions and handling non-normal, skewed data. It supports nominal, ordinal, interval, and ratio scales and remains robust to distributional violations.

In PLS path modeling, apply a rule of ten times the maximum arrows to a latent variable, with a practical floor of 50 to 100 observations; more is better.

Learn why PLS path modeling relies on bootstrap inference instead of parametric tests, plan sample size with Cowan's power tables, and compare to covariance-based chi-square pitfalls.

Explore how partial least squares path modeling uses multiple simultaneous regressions to predict latent variables, contrasting its prediction focus with covariance-based confirmation methods.

Explore how PLS path modeling differentiates formative and reflective indicators, estimates weights via regression, standardizes data, and interprets latent variable scores with error assumptions.

Explore how PLS path modeling handles complex models with many latent and manifest variables, including formative constructs, advantages over covariance-based approaches, and easy use of dummy variables for categorical data.

Explore pls path modeling by distinguishing the inner (structural) and outer (measurement) models, detailing latent variables, indicators, exogenous and endogenous variables, and reflective versus formative constructs.

Develop theory-driven PLS path models before data collection, focusing on linear relationships, interactions, and mediation, while clarifying reflective versus formative measurement and recursive constraints.

Explore bootstrapping and jackknifing as non-parametric resampling methods to assess parameter significance. Explain how data size affects bootstrap and jackknife utility for variance and standard error.

Compare jackknifing and bootstrapping for small data, noting jackknife's conservatism. Learn how standardizing variables enables direct comparison of path coefficients and parameters, with a preview of reflective versus formative items.

Explore the difference between reflective and formative measurement models in PLS path modeling, where latent constructs link to observed variables and error terms influence the predictions.

Explain how measurement error influences prediction, focusing on reflective measurement where item responses regress on a latent variable, yielding factor loadings around 0.7–0.9 and high inter-item correlations.

Explore formative versus reflective constructs in PLS path modeling, highlighting how formative items form the latent construct with weights, potential multi-collinearity, and differing facet coverage.

Demonstrate the difference between formative and reflective measurement items using the drunkenness latent construct. Show exhaustive, distinct formative items (beer, wine, liquor) and reflectively measured indicators, and discuss design-stage implications.

Explore formative versus reflective constructs in PLS path modeling with drunkenness indicators and perceived ease of use, highlighting temporal sequence, item drop, and item intercorrelations.

Examine formative versus reflective constructs in PLS path modeling through a Saudi desktop usage study. Learn how items like time, frequency, applications used, and tasks relate to construct classification.

Distinguish reflective and formative constructs in PLS path modeling, separate usage dimensions as latent variables, and ensure proper measurement item specification and model identification.

Assess the measurement model in PLS path modeling by evaluating outer model reliability and validity, reflective and formative item content validity, and weights, then examine the structural model's predictive quality.

Assess measurement models by analyzing error sources: distinguish random error (reliability) from systematic error (validity) and evaluate reflective items to measure the true value.

Explore internal consistency reliability in PLS path modeling, comparing composite reliability (Dillon‑Goldstein's rho) and Cronbach's alpha, with indicator reliability, AVE, Fornell‑Larcker criterion, and cross‑loadings.

Explore internal consistency reliability in PLS path modeling by comparing Cronbach's alpha and Dylan Goldstein's row, noting bootstrapping and the limitations of alpha with varying indicators.

Assess convergent validity and indicator reliability using Avi (average variance extracted), check how deleting an item affects Avi and composite reliability, and ensure loadings exceed 0.65 with Avi ≥ 0.5.

Learn how to assess discriminant validity in PLS path modeling by locating reliability and validity metrics, including Cronbach's alpha, composite reliability, and indicator reliability via factor loadings.

Examine average variance extracted and its role in assessing discriminant validity in PLS path modeling, using the Fornell-Larcker criterion and cross-loadings to interpret latent variables.

Assess discriminant validity in PLS path modeling by comparing Cronbach's alpha and composite reliability, and applying AVE, Fornell-Larcker (square root of AVE vs correlations), and cross-loadings.

Assess formative indicators by prioritizing content validity and a comprehensive, noncollinear set of indicators, using expert availability and pretest assessments to ensure valid weights and low variance inflation factor.

Assess formative indicators' validity and reliability by comparing with existing reflective measures, examining external validity, and addressing variance inflation factors to ensure construct accuracy in PLS path modeling.

Evaluate collinearity of formative indicators using the five-threshold; if below five, proceed; else examine weights and outer loadings, keeping items with outer loading ≥50%.

Assess the measurement model for reflective indicators, ensuring composite reliability at least 0.71 and loadings at least 0.71, then evaluate structural model for predictive quality with R-squared and significant coefficients.

Assess formative indicators by checking convergent validity with AVE above 0.50, discriminant validity via cross-correlations and square roots of AVE, and examining weights and outer loadings for significance.

Learn how bootstrapping enables inference in PLS path modeling by resampling with replacement to build distributions of parameter estimates, yielding confidence intervals and significance without normality assumptions.

Explore bootstrapping as a versatile resampling method to estimate parameters and standard errors, compare it with jackknifing, and apply it to a correlation between IQ and course grades.

Bootstrapping in conceptual foundations of PLS path modeling resamples the data 200 to 500 times to estimate the distribution, standard error, and significance of correlations and test statistics.

Learn how bootstrap t tests assess parameter significance using bootstrap samples, degrees of freedom, one- and two-tailed tests, and practical thresholds for quick judgments.

Execute bootstrap on a data matrix X with n observations and m manifest variables to test the significance of path coefficients in PLS path modeling via the POS algorithm.

Use bootstrap to generate 5000 mixed samples with replacement from the original nine records. Run a PLS path model to estimate coefficients, weights, and loadings, revealing approximately normal bootstrap distributions.

Explore bootstrapping to estimate the behavioral intention–to–use path, obtain factor loadings and latent variable scores, and assess significance with repeated resampling.

Bootstrapping in PLS path modeling demonstrates that increasing bootstrap samples yields near normal distributions of path coefficients, enabling reliable standard errors, p-values, and confidence intervals.

Examine bootstrapping for partial least squares path modeling, estimating inner and outer path coefficients across thousands of samples, and testing significance with mean, standard error, and t values.

Explore sign-change options in bootstrapping, including no sign changes, individual sign changes, and construct-level flips, and how these choices affect the significance and standard error of parameter estimates.

Compare latent variable loadings across samples in the inner model to decide when to flip loadings, using conservative to construct-level sign-change approaches for bootstrap-based path significance.

Explore bootstrapping for sign changes in PLS path modeling, comparing conservative, liberal, and in-between estimates; assess significant path coefficients using empirical t-values and confidence intervals.

Introduce the principles and mechanics of the pls path modeling algorithm. Identify sources of unexpected results—data issues, theory issues, and method bias.

Examine a simple plx example model to see how the plx algorithm estimates weights, loadings, path coefficients, and latent variable scores for formative and reflective blocks.

Estimate latent variable scores with the PLS algorithm through iterative inner and outer weight updates, converging on stable estimates for the measurement and structural model parameters.

Explore how the PLS algorithm begins with two initialization routines and how they influence early imputed values and path coefficients, causing sign changes between smart PLS and pos graph.

Explore how the PLS algorithm initializes the outer model with equal indicator weights, iterates Stage One to converge on stable latent scores, then estimates loadings and path coefficients via regression.

Compute initial estimates for three latent variables by applying linear combinations of indicator values across 100 survey observations. Demonstrate initialization for formative and reflective measurement models in PLS path modeling.

Examine how initialization schemes flip signs in the PLS step 0, changing customer satisfaction and loyalty, and contrast low Meller's minus-one last indicator with SMART PLS's plus-one rule.

During stage 1, we estimate inner path weights using standardized data and one of three weighting schemes, with the factor weighting scheme insensitive to direction and based on correlations.

Explains step 2 of the PLS algorithm, using inside approximation and inner weights to refine latent variable scores, leveraging outer information and covariance to converge phase 1 estimates.

Establish outer weights in step three by using reflective simple regressions of indicators on the latent score and formative multiple regressions of the latent score on indicators, using standardized data.

Update latent variable scores using the new outer weights from Step Three by forming a linear combination of indicator values, applying reflective and formative measurement models in the outside approximation.

Describe the PLS stop criterion and convergence in stage 1, updating outer weights and latent variable scores, and switch to stage 2 when outer weight changes fall below a threshold.

This lecture describes stage 2 of the PLS algorithm, using stable latent scores to estimate outer loadings, outer weights, and inner path coefficients.

Explore how the PLS algorithm estimates final parameters, including disturbance terms, outer loadings and weights, inner path coefficients via simultaneous regressions, and direct and indirect effects with standardized coefficients.

Explore inner weighting schemes in PLS path modeling—path, factor, and centroid—and why the path scheme, the default, maximizes variance in predicted latent variables; avoid centroid with second-order models.

Analyze inner weighting schemes in PLS path modeling—path weighting, factor weighting, and centroid—using covariance and correlation to estimate inner weights and maximize predictive r-squared.

Explore the blindfolding procedure in PLS path modeling, including uppercase Q squared for predictive relevance and lowercase q squared as the blindfolding effect size.

Explain how blindfolding tests predictive relevance in PLS path modeling by omitting x3_1, x3_2, x3_3 and predicting Y3 from inner and outer models using the POS algorithm.

Use blindfolding in PLS path modeling: set an omission distance to avoid omitting records, perform three rounds to predict missing values, and derive predictive relevance with the Stone-Geisser Q² measure.

Explore the mechanics of blindfolding in PLS path modeling, using mean replacement for omitted items to estimate PAF weights and loadings across three rounds, predicting missing values.

Compute q-squared predictive relevance with the blindfolding procedure by squaring and summing predicted versus actual errors and mean-centered deviations to assess model performance.

Compute Q squared to assess predictive relevance via blindfolding, comparing full versus partial models to measure each latent variable's contribution; classify effects as no, weak, moderate, or strong.

Explore mediation in pls path modeling, distinguish direct and indirect effects, and apply Baron and Kenny criteria for path a, b, and c to identify complete or partial mediation.

Learn how to test mediation in simple path models, differentiate full, partial, and suppressor effects, and apply Baren and Kennie's guidelines and Sobel tests (with bootstrapping as a robust alternative).

Critique the Sobol test for mediation in PLX path models. Highlight non-normal product distribution and promote bootstrap methods by Preacher and Hayes to estimate the indirect effect.

Explore how to test mediation using Sobel and VAF, calculate indirect and direct effects from path a, b, and c, and distinguish partial, full, and suppressor mediation with VAF interpretation.

Joe Hare outlines how to decide a mediator in pls path modeling by separating three variables, testing direct and indirect effects, assessing variance accounted for, and ensuring reliable mediator measurement.

Explain testing mediation in PLS path modeling via the indirect effect a×b, c vs c′, and bootstrapping, then describe moderation as an interaction altering the X to Y path.

Explore mediated moderation and moderated mediation, showing how an interaction term (the product of A and B) influences paths A, B, and C', and how moderators shape mediation.

This lecture revisits an e-commerce model testing how perceived usefulness, trust, and intrinsic enjoyment shape online shopping attitudes, examining telepresence and perceived social presence in a Second Life experiment.

Explore how telepresence affects enjoyment and trust directly, with perceived social presence mediating these effects, and examine partial mediation and moderated mediation across Second Life user groups.

Explore complex mediation in partial least squares path modeling by comparing experienced and inexperienced groups, assessing path coefficients, indirect effects, and moderated mediation through Sobol and bootstrapping methods.

Compare two-group path differences by estimating the same model on split samples, and assess significance with permutation methods over parametric approaches, while evaluating measurement invariance and standard errors.

Explore bootstrapping in PLS path modeling, estimating path coefficients across 200 resamples, comparing standard errors between inexperienced and experienced groups, and using F-tests for significance.

Learn how to test group differences and moderated mediation in pls path modeling using f tests and Satterthwaite's approach, comparing experienced and inexperienced groups on perceived social presence and enjoyment.

Explore how telepresence moderates the effect of perceived social presence on enjoyment using the product-indicator approach within a global PLS path modeling framework, including standardization and interaction-term construction.

Run the PLS path model to estimate the interaction between telepresence and perceived social presence on enjoyment, revealing a significant negative interaction that weakens telepresence's effect, regardless of predictor order.

Explore moderation as the interaction of latent variables in path modeling, detailing the product indicator approach for continuous X and M and approaches for formative or two-stage cases.

Learn to model moderation by Z on x’s effect on y using the product indicator approach and assess interaction significance.

Examine the product indicator approach within a TAM variant, showing how perceived usefulness and intrinsic enjoyment interact to shape intention to use electronic mail.

Explore how product indicators and an interaction term shape path coefficients in PLS path modeling, with perceived usefulness often stronger than enjoyment and a negative, significant interaction changes R-squared.

Apply the two-stage approach to compute inner model coefficients and outer loadings from latent variable scores, enabling interaction tests with formative constructs using a product term and a second-stage regression.

Examine the group differences approach for testing moderation in PLS path models, with categorical and continuous moderators, and cautions against dichotomizing metrics. Explore moderated mediation and path coefficients.