Advanced Analyses in MerQur: From VARCOMP to Bayesian Linear

Abstract

Advanced statistical analyses encompass methods that go beyond classical regression and comparison tests: decomposing variance components, flexibly modelling non-linear relationships, focusing on outliers or different quantiles, handling censored and naturally bounded data, testing conceptual mediation and structural path models, integrating prior information through Bayesian inference, and managing missing data through multiple imputation. This study introduces in detail the 15 analyses offered in MerQur’s ⚡ Advanced category: VARCOMP (Variance Components Analysis), GAM (Generalised Additive Models), Non-Linear Regression, Robust Regression (M-estimator), Quantile Regression, Regularised Regression (LASSO/Ridge/ElasticNet), Partial Least Squares (PLS), Probit Regression, Tobit Regression (Censored), Conditional Logit, Bayesian Linear Regression, Mediation Analysis, Path Analysis, Discriminant Analysis (LDA/QDA), and Multiple Imputation. For each: (i) mathematical basis and application context, (ii) required assumptions, (iii) form fields and parameters in MerQur, (iv) reported statistics and outputs, and (v) interpretation guidance for a typical research question. This family — from variance components to Bayesian inference — fundamentally expands the methodological repertoire of academic researchers. The ⚡ Advanced category is the concrete manifestation of MerQur’s claim to “GUI-based advanced analysis”: these methods, which would each require learning a separate package in the R/Python ecosystem, are gathered within a single graphical interface.