Prototype mixed models explorer

[jbkunst]

What this adds

• new mixed-models/ draft app following the repository structure
• simulated grouped data with four underlying structures: none, random intercept, random slope, intercept + slope
• five fitted-model choices: complete pooling, no pooling, random intercept, random slope, intercept + slope
• mathematical data-generating and fitted-model formulas plus the corresponding lm() / lmer() syntax
• base R main plot with simulated truth and fitted relationships
• base R diagnostics for residuals, Q-Q, random effects, shrinkage, and variance components
• technical model check for optimizer convergence and singular fits

Learning goal

Keep data generation separate from model specification, then make partial pooling visible through shrinkage of group-specific intercept/slope estimates toward the population effects.

Status

Draft app on purpose. The site build skips it while the interaction and statistical story are being tested. No Highcharter/proxy yet.

Local check

shiny::runApp("mixed-models")

The current connector environment does not provide an R runtime, so this PR has been reviewed statically but not executed here yet.