Numerical benchmarks

PLS-SEM: compare QuickPLS estimates with cSEM

Partial least squares structural equation modelling (PLS-SEM) estimates relationships between constructs and their indicators. These tests compare QuickPLS with cSEM, an independent R package, across several calculation settings. A separate installed-app test also checks individual scores and model diagnostics.

Consistent PLS: check the reliability correction

Consistent partial least squares (PLSc) adjusts ordinary PLS estimates using a reliability estimate. These tests check both valid corrections and cases where the correction cannot be calculated. They compare results with cSEM, an independent R package, and with independent formulas where the programs use different loading definitions.

Weighted PLS: check estimates and bootstrap intervals

Weighted partial least squares (PLS) gives some observations more influence through case weights. These tests check its estimates and confidence intervals after missing indicator values are replaced with the ordinary observed means. Bootstrap samples repeat that preparation and fitting, so the reference checks the same sequence.

Factor and structural models: compare QuickPLS with lavaan

Confirmatory factor analysis checks a proposed measurement model. Covariance-based structural models also estimate relationships between variables or factors. These tests compare QuickPLS results with lavaan, an independent R package, after matching the model and the definitions of its reported statistics.

Maximum likelihood: check a model with a known solution

Maximum likelihood (ML) chooses estimates that best account for the observed data under a specified model. This test fits a model with an independently calculated answer in QuickPLS. It checks the estimates, the calculations used to find them and the calculations used to measure their uncertainty.

GSCA: compare results with independent calculations

Compare generalized structured component analysis (GSCA) paths, loadings and weights with cSEM and independent mathematical calculations. Each reflective, mixed-measurement, higher-order or joint-relationship model is assessed against its matching reference.

Importance and performance checked with independent calculations

Importance-performance map analysis (IPMA) compares a construct's relationship with a chosen target and its score on a defined scale. A construct is a concept represented in the model. This test checks the target, the constructs leading to it, total effects and performance scaling, using the same definitions as the reference.

Group comparisons: inspect the estimates checked against cSEM

MICOM checks whether composite measurement is comparable across groups. Multigroup analysis (MGA) compares model estimates between groups. This test checks selected group and pooled-data results against cSEM, an independent R package. It does not independently repeat every permutation or bootstrap fit.

Tetrads: check the values and bootstrap summaries

A tetrad is a difference between products of covariances, which describe how pairs of indicators vary together. These tests check the tetrad values directly and then check bias-corrected bootstrap summaries. They keep that summary arithmetic separate from independently fitting every resample.

Prediction: check held-out errors and training-only preparation

A prediction test fits a model on training observations and checks its predictions on observations left out of that fit. This comparison reconstructs the same data splits and learns preparation steps from training data only. It then compares the errors for the same held-out observations using matching reference models and error definitions.

Interaction terms checked after missing-value replacement

An interaction term combines variables to represent a relationship that changes with another variable. This comparison checks how QuickPLS replaces missing values, centres and scales the source variables, and then forms the term. The order matters: multiplying first and filling in missing products later can give a different answer.

Earlier power formulas checked against SciPy

This comparison checks an earlier power calculation made from already observed model estimates. It uses a normal approximation, which calculates probabilities from a bell-shaped distribution. Agreement with SciPy checks the arithmetic; it does not validate the current simulation procedure for choosing a sample size before a study.

Interventional mediation effects checked independently

This test checks three effect estimates from g-computation, a method that uses fitted statistical models to calculate average outcomes under specified settings. The independent calculation uses the same fixed synthetic dataset and model definitions. It checks the numerical answers; a causal interpretation still depends on assumptions about the study.

Regression: compare estimates and uncertainty with statsmodels

Linear regression models a numeric outcome. Binary logistic regression models the probability of an outcome with two categories. These tests compare QuickPLS with statsmodels, an independent Python package, using matching predictors, outcome coding, intercept choices and standard-error calculations.

PCA: verify component values and chart output

Principal component analysis (PCA) summarises variation in a set of variables using components. This unrotated example fixes two components, compares QuickPLS with an independent matrix calculation and checks the installed output. It also records how a precision issue was corrected.

Necessary condition analysis: compare ceilings and requirements

Necessary condition analysis (NCA) examines whether a condition sets a minimum requirement for an outcome. These checks compare the estimated boundary, or ceiling, and the resulting bottleneck requirements with the R NCA package. A separate Store app test checks importing data, calculating a result and saving it.

fsQCA results compared with QCA and independent calculations

These comparisons check fuzzy-set qualitative comparative analysis (fsQCA) results: truth-table decisions, alternative solutions, consistency and coverage. The four tests include a saved QuickPLS result checked by independent mathematics, selected comparisons with the QCA package for R, and an example calculated in the installed app.

fsQCA truth-table cutoffs and preview decisions

A truth-table row can change classification when its value falls exactly on a cutoff. These tests check that QuickPLS applies the stated inclusion rules at those boundaries and prepares the same data for the preview and final calculation.

fsQCA assumptions about unobserved cases and alternative solutions

In fuzzy-set qualitative comparative analysis (fsQCA), a counterfactual assumption says what would happen for a combination of conditions that is absent from the data. These tests check how such combinations are classified, how the simplest solutions are found, and how alternative solutions are paired. They follow the reasoning behind the final expression.

Combined necessary conditions checked with exact fractions

A necessary condition is expected to be present whenever the outcome is present. Compound necessity asks the same question about conditions joined by AND, OR or NOT. This reference combines their fuzzy memberships and calculates the necessity measures independently using exact fractions, without copying the app calculation.

Calibration checked at anchors, cutoffs and between them

Calibration converts observed values into memberships, which express how strongly each case belongs to a set. These tests check the values at the chosen anchors, between them and at the outer ends of the calibration curve. They also check unavailable inputs. An independent calculation with extra decimal precision supplies the expected answers.

Multi-value QCA: every classification in a small example

Multi-value qualitative comparative analysis, or multi-value QCA, works with conditions that can have several categories. This reference checks every classification within a small, explicitly defined set of category combinations. The category codes are treated as labels, so a higher number does not imply a larger measured amount.

Time-based set calculations and panel summaries checked

These tests check whether a value from an earlier occasion belongs to the right unit, whether event order can be traced to the original rows, and whether panel summaries describe the intended observations. The time-based transformations and the pooled, within-unit and between-cluster summaries are checked separately.

Coincidence Analysis: set fit and logical search checked

Coincidence Analysis (CNA) searches for logical relationships among conditions and outcomes. These tests check the memberships, set-fit measures and rules used to find formulas, including whether a simpler formula meets the criteria. They also check whether the search finished, because an unfinished search cannot establish a complete set of solutions.

Binomial probabilities for crisp truth-table rows checked

This diagnostic asks how unusual a crisp truth-table row's outcome count would be under a chosen probability. It uses whole-number counts of trials and successes and calculates the upper-tail probability. The test checks that arithmetic using exact fractions; it does not treat fuzzy memberships as binary trials or adjust for testing many rows.

Separate outcomes and larger fsQCA workloads checked

These tests examine how fuzzy-set qualitative comparative analysis (fsQCA) handles separately specified outcomes and larger analyses. Each outcome must keep its own set definitions, settings and included cases. The larger-workload checks examine resource estimates, cancellation and clear reporting when a search cannot finish.