Methods and comparisons

Method guides and numerical checks

Find a method and its comparison records. Each record identifies the tested outputs, settings and reference. A shared link does not mean every option has been compared.

How to read the comparison labels

Related numerical comparisons check the specific settings and outputs in each record. Main method comparison covers the underlying method, not the additional procedure. Method guide provides instructions where no comparison is linked. Each record names the software versions and whether the check used the desktop app or tested calculations separately.

PLS-SEM and component models

Method or workflowWhat you can exploreComparison resources
GSCA Joint RelationshipsEstimate GSCA interaction terms, formed by multiplying variables, together with squared terms that allow curved relationships. Read effects at the chosen values with intervals from resampled original cases.Related numerical comparisonsGSCA: compare results with independent calculations ↗
Higher-order GSCAEstimate a disjoint two-stage GSCA model: first calculate the specified lower-order scores, then use them in the higher-order model. Refit both stages on resampled original cases and label the relationships by stage.Related numerical comparisonsGSCA: compare results with independent calculations ↗
GSCA adjusted copulasCalculate GSCA scores, then add copula controls to the selected relationship. Repeat both steps when estimating uncertainty.Related numerical comparisonsGSCA: compare results with independent calculations ↗
PLS-SEM AlgorithmCalculate PLS composite scores, structural paths, indicator loadings and weights, together with the model-quality measures needed to interpret them.Related numerical comparisonsPLS-SEM: compare QuickPLS estimates with cSEM ↗
Consistent PLSApply the Consistent PLS correction to reflective measurement models and read the corrected estimates.Related numerical comparisonsConsistent PLS: check the reliability correction ↗PLS-SEM: compare QuickPLS estimates with cSEM ↗
Weighted PLSEstimate a reflective PLS model in which each case contributes according to its positive weight.Related numerical comparisonsWeighted PLS: check estimates and bootstrap intervals ↗
GSCAEstimate a generalized structured component model. Read the component weights, model fit and paths, with optional bootstrap intervals and effects for models without feedback loops.Related numerical comparisonsGSCA: compare results with independent calculations ↗

CFA and covariance-based SEM

Method or workflowWhat you can exploreComparison resources
CB-SEM Model ComparisonFit two saved ordinary maximum-likelihood models again on the same observations. Test specified nested restrictions, or compare AIC and BIC as descriptive evidence.Method guide
CB-SEM Measurement InvarianceFit confirmatory factor analysis (CFA) models jointly for the selected independent groups. Check the same factor pattern (configural), equal loadings (metric) and equal intercepts (scalar) in stages to assess measurement comparability.Method guide
CB-SEM Multigroup AnalysisCompare specified structural paths across independent groups after checking metric invariance, meaning comparable factor loadings. Test planned equality restrictions and estimate uncertainty by resampling within each group and refitting the complete maximum-likelihood model.Method guide
CB-SEM Moderator AnalysisEstimate one interaction between a latent factor, measured through indicators, and an observed variable using conditional likelihood. Estimate uncertainty by resampling whole cases and refitting the complete model.Method guide
CB-SEM Product-Indicator ModerationEstimate a specified interaction between two factors using products of their indicators. Read bootstrap intervals from resampled original cases and, where requested, simple slopes showing the relationship at chosen moderator values.Method guide
CB-SEM / CFAUse maximum likelihood for a single-group reflective CFA measurement model or a latent SEM model without feedback loops. The optional bootstrap refits the model to resampled cases.Related numerical comparisonsFactor and structural models: compare QuickPLS with lavaan ↗Maximum likelihood: check a model with a known solution ↗

Model checks and interpretation

Method or workflowWhat you can exploreComparison resources
CCA composite residual diagnosticsCompare observed composite correlations with the correlations reproduced by the model. Inspect their differences, called residuals, as descriptive checks.Method guide
PLS exact-fit assessmentAssess exact fit using specified factor and composite roles, while keeping the original PLS estimates unchanged.Related numerical comparisonsPLS-SEM: compare QuickPLS estimates with cSEM ↗
PLSc exact-fit assessmentAssess measurement and structural fit using specified construct roles, while keeping the original Consistent PLS estimates unchanged.Related numerical comparisonsPLS-SEM: compare QuickPLS estimates with cSEM ↗
Confirmatory Tetrad AnalysisExamine tetrads, which compare products of indicator covariances. Use the available bootstrap tests to assess the specified group of zero-value restrictions.Related numerical comparisonsTetrads: check the values and bootstrap summaries ↗
Importance-Performance Map AnalysisChoose the outcome you want to improve. Compare each preceding construct’s total effect with its performance using the specified indicator ranges.Related numerical comparisonsRegression: compare estimates and uncertainty with statsmodels ↗Importance and performance checked with independent calculations ↗
Blindfolding (Q²)Calculate cross-validated redundancy Q² by leaving out parts of the data for reflective constructs that are outcomes in the model. This checks the omission-based task; use PLSpredict / CVPAT to study prediction for new cases.Related numerical comparisonsPLS-SEM: compare QuickPLS estimates with cSEM ↗
Discriminant Validity — HTMT/HTMT+Check whether eligible pairs of reflective constructs are distinct using HTMT+ and the original signed HTMT. Optional bootstrap intervals and tests use the fixed or configurable settings supported by the selected procedure.Related numerical comparisonsPLS-SEM: compare QuickPLS estimates with cSEM ↗
Global Goodness of FitCalculate the square root of the product of average reflective AVE (average variance extracted) and average endogenous R² (explained variance of outcome constructs). This descriptive index does not establish overall validity, model fit or predictive performance.Related numerical comparisonsPLS-SEM: compare QuickPLS estimates with cSEM ↗

Effects, mediation and endogeneity

Method or workflowWhat you can exploreComparison resources
Gaussian-Copula Endogeneity DiagnosticsUse Gaussian-copula terms to investigate selected PLS paths. Check the required distribution assumptions, alternative fits and adjustments for multiple tests.Method guide
Quadratic Nonlinear EffectsFit a curve by including a predictor and its squared term together. Inspect the curve, the added explained variance and optional bootstrap intervals.Related numerical comparisonsInteraction terms checked after missing-value replacement ↗
PLS-SEM Conditional ProcessEstimate how an indirect PLS relationship changes with a moderator. Supported setups cover the first stage, second stage, both stages, longer paths, groups, weights, higher-order constructs and three-way relationships; use a supported combination of these features.Related numerical comparisonsConditional-process preparation and simulation checks ↗
Interventional MediationUse observed data and specified statistical equations to estimate direct and mediated effects of an intervention. Check the causal assumptions and whether the data contain the comparisons the question requires.Related numerical comparisonsInterventional mediation effects checked independently ↗

Inference and sample planning

Method or workflowWhat you can exploreComparison resources
PLS-SEM BootstrappingUse reproducible case resampling to estimate confidence intervals and statistical significance for the selected PLS-SEM model.Related numerical comparisonsWeighted PLS: check estimates and bootstrap intervals ↗
PLSc Consistent BootstrappingRefit Consistent PLS to each resampled set of cases. Report percentile intervals and bias-corrected and accelerated (BCa) results where their additional requirements are met.Method guide
Structural Path RandomizationApply Freedman-Lane randomization to structural paths in one model, keeping the original PLS construct scores fixed. Report individual path p values without a multiple-testing adjustment, within the stated procedure limits.Method guide
Post-hoc Technical Minimum Sample SizeCalculate a technical minimum sample size after analysis, using the inverse-square-root method and the weakest statistically significant structural path in the linked PLS bootstrap result.Related numerical comparisonsEarlier power formulas checked against SciPy ↗
PLS-SEM Sample Size and PowerPlan sample size for one reflective path between two constructs using normally distributed simulated data. Compare estimated power, the chance of detecting the specified relationship, at the sample sizes you choose.Related numerical comparisonsEarlier power formulas checked against SciPy ↗

Group comparison and segmentation

Method or workflowWhat you can exploreComparison resources
PLSc Consistent PermutationCompare two groups defined before analysis by repeatedly reassigning their group labels in a reproducible way. Refit the complete Consistent PLS model for every usable assignment.Method guide
MICOM and Multigroup Analysis (PLS / PLSc)Check whether measures are comparable, then compare 2 to 20 groups. Choose ordinary PLS or reflective PLSc and review the group tests and multiple-testing adjustments available for that choice.Related numerical comparisonsGroup comparisons: inspect the estimates checked against cSEM ↗
FIMIX-PLSInvestigate whether the data contain groups you did not specify in advance. Compare different numbers of segments, check repeated starting points and review the chosen grouping before inference.Method guide
PLS-POSLook for groups with better fit under the selected PLS-POS criterion in the data being analysed. Review and save the chosen grouping before continuing to the next analysis. This search does not by itself show better prediction for new cases.Method guide

Prediction and model selection

Method or workflowWhat you can exploreComparison resources
PLS Model ComparisonCompare two compatible saved PLS-SEM models using the same validation folds, or groups of cases left out of fitting. Read prediction accuracy, the paired CVPAT test of prediction error and prediction-oriented BIC together.Method guide
Prediction-Oriented Model SelectionCompare 2 to 20 compatible saved PLS-SEM models using BIC for each outcome equation. See exact ties and outcomes that favour different models, without an automatic overall winner.Method guide
PLSpredict / CVPATPredict indicators of outcome constructs by repeatedly fitting to some cases and testing on cases left out. Use configurable cross-validation and a saved random seed. Choose earliest or direct antecedent information, from constructs preceding the target, and compare with indicator-average (IA) and linear-model (LM) benchmarks.Related numerical comparisonsPrediction: check held-out errors and training-only preparation ↗

Set analysis and observed-data methods

Method or workflowWhat you can exploreComparison resources
Necessary Condition AnalysisAssess whether one numeric observed condition is required for one numeric observed outcome, using ceiling lines and the minimum levels shown in bottleneck tables.Related numerical comparisonsNecessary condition analysis: compare ceilings and requirements ↗
Principal Component AnalysisUse the same standalone PCA procedure for numeric variables or indicators from PLS, CB-SEM or GSCA models. The analysis leaves the SEM model unchanged.Related numerical comparisonsPCA: verify component values and chart output ↗
Fuzzy-set Qualitative Comparative AnalysisTurn original variables or scores published as a dataset through the app into defined sets. Assess whether conditions are necessary or sufficient for the outcome, then inspect truth tables, Boolean solution alternatives and their cases.Related numerical comparisonsfsQCA results compared with QCA and independent calculations ↗fsQCA truth-table cutoffs and preview decisions ↗fsQCA assumptions about unobserved cases and alternative solutions ↗Calibration checked at anchors, cutoffs and between them ↗
RegressionUse ordinary least squares (OLS) for a continuous outcome, binary logistic regression for a strict 0/1 outcome, or a specified path graph for mediation and moderation among observed numeric variables. These routes do not require a latent-variable model.Related numerical comparisonsRegression: compare estimates and uncertainty with statsmodels ↗

Further fsQCA and QCA tools

Method or workflowWhat you can exploreComparison resources
Save a study and named specificationsSave the research question and dataset with named fsQCA analysis setups. Keep each set of calibration, threshold and case choices separate from the result calculated from it.Method guide
Inspect a truth table before minimizationInspect observed and unobserved condition combinations, their case counts, consistency and PRI before simplifying the truth table. Follow each row to its cases and refresh the preview when analysis choices change.Related numerical comparisonsfsQCA truth-table cutoffs and preview decisions ↗
Read solution alternatives and their casesRead one whole fsQCA solution at a time, checking its pathways, case memberships, consistency and coverage. Core/peripheral labels require the specified compatible pair of solutions.Related numerical comparisonsfsQCA results compared with QCA and independent calculations ↗
Compare outcome presence and absenceCalculate the outcome and its absence separately, then compare selected whole solutions using compatible original cases and calibration. The absence solution is not obtained by reversing the presence formula.Method guide
Plan and inspect fsQCA robustness scenariosCompare a named fsQCA baseline with planned changes to calibration, thresholds or case inclusion. Examine formulas, fit and memberships while keeping every scenario's completion status visible.Method guide
Create an fsQCA report from a saved resultCreate an fsQCA report for a selected completed result, alternative or expression. Save the research explanation, settings and case evidence with that selection, then check the exported output.Method guide
Counterfactual reasoning and simplifying assumptionsInspect unobserved combinations, justified exclusions and stated expectations about condition directions. Compare the simplifying assumptions behind selected outcome-presence and outcome-absence solutions, including any remaining conflicts.Related numerical comparisonsfsQCA assumptions about unobserved cases and alternative solutions ↗
Compound necessity with AND, OR and NOTTest whether the outcome requires a named AND, OR or NOT expression. Read necessity consistency, coverage and relevance with the cases that support or contradict the proposed requirement.Related numerical comparisonsCombined necessary conditions checked with exact fractions ↗
Crisp, piecewise, bell/valley and indirect calibrationTurn raw values into memberships using crisp, piecewise, bell/plateau, valley or the named indirect binomial-logit calibration. Check the reference values (anchors), boundary memberships and fit diagnostics before interpreting the truth table.Related numerical comparisonsCalibration checked at anchors, cutoffs and between them ↗
Multi-value QCA for nominal categoriesMap exact category labels to named levels and select the outcome categories to explain. Read conservative and parsimonious solution alternatives while keeping category codes distinct from numerical distances.Related numerical comparisonsMulti-value QCA: every classification in a small example ↗
Temporal transformations and conservative QCACreate lags (earlier values), event-order conditions or changes between stated endpoints. Inspect the original rows behind each value. Use at least one generated temporal column in conservative temporal QCA.Related numerical comparisonsTime-based set calculations and panel summaries checked ↗
Panel and cluster set-fit diagnosticsCheck necessity or sufficiency fit across all observations, within each unit and between clusters for the selected targets. Inspect case lists, missing periods and subgroup measures that are undefined alongside the summary.Related numerical comparisonsTime-based set calculations and panel summaries checked ↗
Multiple-outcome studies with independent specificationsRun several outcomes from one dataset. Select a solution for each completed analysis and keep each outcome’s settings and case decisions visible.Related numerical comparisonsSeparate outcomes and larger fsQCA workloads checked ↗
Coincidence Analysis (CNA)Search for combinations of conditions sufficient for an outcome and the larger formulas they form. Specify the data type, causal order and search limits, then inspect the cases and whether the search finished.Related numerical comparisonsCoincidence Analysis: set fit and logical search checked ↗
Comparison scope

The published checks do not include an executed cna 4.0.3 package comparison or a matched run of the current Store app.

Exact binomial checks for crisp truth-table rowsCalculate exact upper-tail binomial probabilities: the chance of at least the observed number of successes under a stated reference probability. Use eligible crisp truth-table rows and chosen frequency rules. Keep the original row classification separate from the diagnostic decision.Related numerical comparisonsBinomial probabilities for crisp truth-table rows checked ↗
Expanded fsQCA and resource estimatesEstimate the resources needed for a larger fsQCA specification before calculating. Inspect the selected alternatives and cases, and distinguish a completed result from a calculation stopped by resource limits or cancellation.Related numerical comparisonsSeparate outcomes and larger fsQCA workloads checked ↗

Further modelling and research tasks

Method or workflowWhat you can exploreComparison resources
Measurement quality and automatic model fitRead loadings, weights, reliability, average variance extracted (AVE), eligible HTMT pairs and collinearity (overlap among indicators or predictors) according to each indicator block's role. Read the automatically reported descriptive fit measures alongside those checks.Main method comparisonPLS-SEM: compare QuickPLS estimates with cSEM ↗
Mediation in PLS-SEMCalculate each indirect effect along a PLS path, add them for the total indirect effect, then add direct paths for the total effect. Use a bootstrap that refits the complete model to estimate uncertainty.Main method comparisonPLS-SEM: compare QuickPLS estimates with cSEM ↗
Two-way and three-way PLS moderationEstimate two-way and three-way PLS interactions together with their required main effects and lower-order interactions. Read the resulting effects at specified moderator values on the chosen scale.Main method comparisonGSCA: compare results with independent calculations ↗Interaction terms checked after missing-value replacement ↗
Higher-order PLS modelsEstimate supported higher-order PLS models, which describe broader concepts through lower-order dimensions, using repeated, extended, embedded or disjoint approaches. Inspect both levels separately and check the inputs used at each stage.Main method comparisonPLS-SEM: compare QuickPLS estimates with cSEM ↗
Comparison scope

The linked comparison checks the underlying PLS calculation. It does not by itself check the higher-order model preparation, stage-specific results or a bootstrap that refits both stages.

PLS and PLSc with covariance or correlation inputCalculate supported PLS or PLSc estimates from a covariance or correlation matrix. Supply the variable order, sample size and scale information. Individual case scores and resampling require the original observations.Main method comparisonPLS-SEM: compare QuickPLS estimates with cSEM ↗
Weighted PLS preparation and inferencePrepare positive case weights and handle missing values using the selected weighted-PLS procedure. Read bootstrap uncertainty, usable resamples and effective sample size, which accounts for the unequal case contributions, under that weight definition.Main method comparisonWeighted PLS: check estimates and bootstrap intervals ↗
Ordinary least-squares regressionFit an OLS model for a continuous outcome. Read coefficients in outcome units, confidence intervals, prediction errors (residuals), overlap among predictors (collinearity) and model fit.Main method comparisonRegression: compare estimates and uncertainty with statsmodels ↗
Binary logistic regressionFit binary logistic regression for an outcome coded 0/1. Read log-odds, odds ratios and predicted probabilities on their different scales. Check whether fitting converged and whether separation prevents finite estimates.Main method comparisonRegression: compare estimates and uncertainty with statsmodels ↗
Bootstrapping OLS and logistic regressionResample cases and refit the selected OLS or logistic model. Read coefficient intervals with the usable and failed fit counts. In logistic resamples, check for loss of an outcome class or separation that prevents finite estimates.Method guide
Observed-variable path analysis and PROCESS-style modelsConnect regression equations to study mediation and moderation among observed variables. Read the effects using the equations, units and moderator values you specified.Method guide
Bootstrap inference for PROCESS-style pathsRefit the complete PROCESS-style equation system to resampled cases to assess indirect and conditional effects. Read percentile, bias-corrected and accelerated (BCa), and supported nested studentized intervals with their settings and fit counts.Method guide
Confirmatory factor analysisFit the factor measurement model specified by your theory. Inspect loadings, factor relationships, unexplained indicator variation (residual variances), standard errors and fit. CFA evaluates that factor model rather than extracting principal components.Main method comparisonFactor and structural models: compare QuickPLS with lavaan ↗Maximum likelihood: check a model with a known solution ↗
CB-SEM and CFA case bootstrappingResample individual cases and fit the complete selected CFA or CB-SEM model again. Read intervals with the requested, usable and failed refits.Method guide
CB-SEM from covariance and correlation matricesCalculate supported CB-SEM estimates from a covariance or correlation matrix. Specify sample size, variable order, how covariances were calculated and the required scales. Bootstrapping individual cases requires the original observations.Main method comparisonFactor and structural models: compare QuickPLS with lavaan ↗Maximum likelihood: check a model with a known solution ↗
Covariance-based maximum-likelihood estimationFit supported continuous linear CB-SEM models from covariances, including means when needed. Check whether estimation converged and inspect the calculation details when investigating a precision issue.Main method comparisonFactor and structural models: compare QuickPLS with lavaan ↗Maximum likelihood: check a model with a known solution ↗
CB-SEM constraints and defined parametersApply supported restrictions to model parameters and calculate expressions based on the estimates. Distinguish estimated values, values fixed in advance and values derived from other estimates. Report each expression with the uncertainty available for it.Main method comparisonFactor and structural models: compare QuickPLS with lavaan ↗Maximum likelihood: check a model with a known solution ↗
CB-SEM direct, indirect and total effectsCalculate defined direct, indirect and total effects from a CB-SEM structural model. Use uncertainty for the specified effect rather than multiplying the endpoints of coefficient intervals.Main method comparisonFactor and structural models: compare QuickPLS with lavaan ↗Maximum likelihood: check a model with a known solution ↗
Combined IPMA and NCA (cIPMA)Combine the PLS importance-performance map with NCA requirements for a chosen outcome target. Read the minimum necessary levels and count cases below them, using the stated score range.Main method comparisonRegression: compare estimates and uncertainty with statsmodels ↗Importance and performance checked with independent calculations ↗
Multiple-condition NCA and effect-size sensitivityCompare several possible necessary conditions using the same complete cases, specified analysis bounds and outcome targets. Inspect the minimum required levels for each condition and optional CE-FDH effect-size sensitivity.Main method comparisonNecessary condition analysis: compare ceilings and requirements ↗
Choosing a PCA retention ruleChoose how many PCA components to keep using the Kaiser criterion, a fixed count or cumulative variance. Read optional rotation and parallel-analysis results separately from that selected retention rule.Main method comparisonPCA: verify component values and chart output ↗
Out-of-sample prediction with PLSpredictCalculate prediction errors for individual indicators using cases left out of fitting. Compare predictions for the same targets with indicator-average and linear-model benchmarks under the same validation plan.Main method comparisonPrediction: check held-out errors and training-only preparation ↗
Cross-validated predictive ability testingTest paired differences in prediction error for the same cases left out of fitting. State the error measure, which model is subtracted from which and the benchmark. Keep individual-indicator findings separate from the combined result.Main method comparisonPrediction: check held-out errors and training-only preparation ↗
Measurement invariance of composites (MICOM)Check measurement comparability in separate MICOM stages: common group settings, comparable composite composition, and equal composite means and variances. Distinguish partial from full invariance.Main method comparisonGroup comparisons: inspect the estimates checked against cSEM ↗
PLS multigroup analysisCompare ordinary PLS parameters directly across groups using the supported pairwise test or overall group test. Report measurement comparability, group order and any adjustment for multiple tests.Main method comparisonGroup comparisons: inspect the estimates checked against cSEM ↗
Consistent PLS multigroup analysisCompare corrected PLSc parameters across groups using uncertainty estimates and tests supported for reflective PLSc. Check failed corrections and keep this setup distinct from the separate two-group permutation procedure.Method guide
Missing data with interactions and generated termsHandle missing values in original variables before constructing supported interactions or other generated terms. Inspect the means used during preparation, the included cases and the resulting terms together.Main method comparisonInteraction terms checked after missing-value replacement ↗
Importance-performance analysis after OLSCompare positive or negative OLS coefficients in their original units with predictor and control performance on defined 0 to 100 ranges. Use the same complete cases for both.Main method comparisonRegression: compare estimates and uncertainty with statsmodels ↗
Durbin–Watson residual autocorrelationCheck whether regression prediction errors (residuals) are related to neighbouring errors in the chosen row order. Select the available probability calculation and state that ordering.Main method comparisonRegression: compare estimates and uncertainty with statsmodels ↗
Groups, equal-weight scores and metrics in PROCESSChoose the subgroup to analyse and define scores by averaging equally weighted indicators where needed. Then fit the regression equations for the observed variables.Method guide
Adjusted Gaussian copulas in PROCESS equationsAdd the chosen adjusted Gaussian-copula controls to specific regression equations in the observed-variable model.Method guide
Parallel analysis for component retentionCompare the strength of each observed PCA component with components produced from simulated independent, normally distributed data. Use this comparison to help decide how many components to keep.Main method comparisonPCA: verify component values and chart output ↗
Kaiser-normalized varimax rotationRotate at least two retained PCA components to make their loading pattern easier to read. This orthogonal rotation keeps the axes at right angles; inspect the separate rotated loadings and scores.Main method comparisonPCA: verify component values and chart output ↗
CE-FDH effect-size sensitivity analysisCheck how the CE-FDH necessity effect changes at the chosen joint-distribution thresholds, using the same sample and analysis range. The method guide explains these threshold choices.Main method comparisonNecessary condition analysis: compare ceilings and requirements ↗

Reading a comparison

A method guide explains how to run and interpret an analysis. An accuracy check gives the results of a particular test, including the software versions and settings used.

How comparisons are made ↗