ExploreModelMatrix

ExploreModelMatrix generates an interactive application for exploring design matrices derived from sample data tables and design formulas to aid in interpreting model coefficients and constructing contrasts in (generalized) linear models.

Key Features:

• Design Matrix Exploration: Given a sample data table and a design formula, the package generates an interactive application for exploration of the resulting design matrix.
• Coefficient Interpretation: The package displays how model coefficients are combined to give fitted values for each combination of predictor variables, allowing users to extract the interpretation of each individual coefficient.
• Linear Contrast Formulation: Users can formulate desired linear contrasts based on the displayed coefficient combinations.
• Model Diagnostics: The interactive interface displays informative characteristics for the regular linear model, including variance inflation factors and the pseudoinverse of the design matrix.
• Static Visualizations: Static visualizations of the design matrix can also be generated.
• Common Design Collection: The package includes a built-in collection of common types of linear model designs.

Scientific Applications:

• Linear Model Interpretation: Assists in thorough understanding of the meaning of individual coefficients in linear and generalized linear models used for modeling observed data and as the basis for hypothesis tests.
• Contrast Construction: Supports formulation of contrasts representing scientific hypotheses of interest in (generalized) linear models.
• Teaching and Self-Learning: Useful for educational purposes in understanding design matrices and linear model diagnostics.
• Complex Model Design Assistance: Aids experienced users in interpreting complex model designs.

Methodology:

Given a sample data table and a desired design formula, the package computes and displays how model coefficients combine to produce fitted values for predictor variable combinations, and calculates variance inflation factors and the pseudoinverse of the design matrix.