---
title: "Quick Start"
author: "Gilles Colling"
date: "`r Sys.Date()`"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{Quick Start}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r setup, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>",
  fig.width = 7,
  fig.height = 5,
  dev = "svglite",
  fig.ext = "svg"
)
library(corrselect)
```

## Installation

```{r, eval = FALSE}
# Install from CRAN
install.packages("corrselect")

# Or install development version from GitHub
# install.packages("pak")
pak::pak("gcol33/corrselect")
```

**Suggested packages** (for extended functionality):

- `lme4`, `glmmTMB`: Mixed-effects models in `modelPrune()`

- `WGCNA`: Biweight midcorrelation (`bicor`)

- `energy`: Distance correlation

- `minerva`: Maximal information coefficient

## What corrselect Does

corrselect identifies and removes redundant variables based on pairwise correlation or association. Given a threshold $\tau$, it finds subsets where all pairwise associations satisfy $|a_{ij}| < \tau$ (see `vignette("theory")` for mathematical formulation).

## Interface Hierarchy

corrselect provides three levels of interface:

### Level 1: Simple Pruning

**corrPrune()** - Removes redundant predictors based on pairwise correlation:

- Returns a single pruned dataset

- No response variable required

- Fast greedy or exact search

**modelPrune()** - Reduces VIF in regression models:

- Returns a single pruned dataset with response

- Iteratively removes high-VIF predictors

- Works with lm, glm, lme4, glmmTMB

### Level 2: Structured Subset Selection

**corrSelect()** - Returns all maximal subsets (numeric data):

- Enumerates all maximal valid subsets satisfying threshold (see `vignette("theory")`)

- Provides full metadata (size, avg_corr, max_corr, min_corr)

- Exact or greedy search

**assocSelect()** - Returns all maximal subsets (mixed-type data):

- Handles numeric, factor, and ordered variables

- Uses appropriate association measures per variable pair

- Exact or greedy search

### Level 3: Low-Level Matrix Interface

**MatSelect()** - Direct matrix input:

- Accepts precomputed correlation/association matrices

- No data preprocessing

- Useful for repeated analyses

## Quick Examples

### corrPrune(): Association-Based Pruning

```{r}
data(mtcars)

# Remove correlated predictors (threshold = 0.7)
pruned <- corrPrune(mtcars, threshold = 0.7)

# Results
cat(sprintf("Reduced from %d to %d variables\n", ncol(mtcars), ncol(pruned)))
names(pruned)
```

Variables removed:

```{r}
attr(pruned, "removed_vars")
```

**How corrPrune() selects among multiple maximal subsets**:

When multiple maximal subsets exist (which is common), `corrPrune()` (in exact mode) selects among them by, in order:

1. **Largest subset size**: Keeping more variables is preferred over keeping fewer

2. **Lowest average absolute correlation**: Among subsets of the same (largest) size, the one with the least redundancy is preferred

3. **Alphabetically first variable names**: A final tiebreaker for deterministic behavior when size and average correlation are both tied

Subset size is checked first, so a smaller subset is never preferred over a larger one even if its average correlation is lower.

To explore **all** maximal subsets instead of just the optimal one, use `corrSelect()` (see below).

### modelPrune(): VIF-Based Pruning

```{r}
# Prune based on VIF (limit = 5)
model_data <- modelPrune(
  formula = mpg ~ .,
  data = mtcars,
  limit = 5
)

# Results
cat("Variables kept:", paste(attr(model_data, "selected_vars"), collapse = ", "), "\n")
cat("Variables removed:", paste(attr(model_data, "removed_vars"), collapse = ", "), "\n")
```

### corrSelect(): Enumerate All Maximal Subsets

```{r}
results <- corrSelect(mtcars, threshold = 0.7)
show(results)
```

Inspect subsets:

```{r}
as.data.frame(results)[1:5, ]  # First 5 subsets
```

Extract a specific subset:

```{r}
subset_data <- corrSubset(results, mtcars, which = 1)
names(subset_data)
```

### assocSelect(): Mixed-Type Data

```{r}
# Create mixed-type data
df <- data.frame(
  x1 = rnorm(100),
  x2 = rnorm(100),
  cat1 = factor(sample(c("A", "B", "C"), 100, replace = TRUE)),
  ord1 = ordered(sample(1:5, 100, replace = TRUE))
)

# Handle mixed types automatically
results_mixed <- assocSelect(df, threshold = 0.5)
show(results_mixed)

# Verify all pairwise associations are below threshold
cat("Max pairwise association:", max(results_mixed@max_corr), "\n")
```

## Protecting Variables

Use `force_in` to ensure specific variables are always retained:

```{r}
# Force "mpg" to remain in all subsets
pruned_force <- corrPrune(
  data = mtcars,
  threshold = 0.7,
  force_in = "mpg"
)

# Verify forced variable is present
"mpg" %in% names(pruned_force)
```

## Threshold Selection

Common thresholds: **0.5** (strict), **0.7** (moderate, recommended default), **0.9** (lenient).

Lower thresholds are stricter because they allow fewer variable pairs to coexist, resulting in smaller subsets. Higher thresholds permit stronger correlations, retaining more variables.

For detailed threshold selection strategies including visualization techniques, VIF guidelines, and sensitivity analysis, see `vignette("advanced")`.

## Interface Selection Guide

| Scenario | Function | Key Parameters |
|----------|----------|----------------|
| Quick dimensionality reduction | `corrPrune()` | `threshold`, `mode` |
| Model-based refinement | `modelPrune()` | `limit` (VIF threshold), `engine` |
| Enumerate all maximal subsets | `corrSelect()` | `threshold` |
| Mixed-type data | `assocSelect()` | `threshold` |
| Precomputed matrices | `MatSelect()` | `threshold`, `method` |
| Protect key variables | Any function | `force_in` |

## Quick Reference

### corrPrune()

Removes redundant predictors based on pairwise correlation.

```r
corrPrune(data, threshold = 0.7, measure = "auto", mode = "auto",
          force_in = NULL, by = NULL, group_q = 1, max_exact_p = 100)
```

| Parameter | Description | Default |
|-----------|-------------|---------|
| `data` | Data frame or matrix | *required* |
| `threshold` | Maximum allowed correlation | `0.7` |
| `measure` | Correlation type: `"auto"`, `"pearson"`, `"spearman"`, `"kendall"`, `"bicor"`, `"distance"`, `"maximal"` | `"auto"` |
| `mode` | Algorithm: `"auto"`, `"exact"`, `"greedy"` | `"auto"` |
| `force_in` | Variables that must be retained | `NULL` |
| `by` | Column name(s) for grouped pruning | `NULL` |
| `group_q` | Quantile for aggregating group correlations (0-1] | `1` |
| `max_exact_p` | Max predictors for exact search when `mode = "auto"` | `100` |

**Returns**: Data frame with pruned variables. Attributes: `selected_vars`, `removed_vars`.

### modelPrune()

Iteratively removes predictors with high VIF from a regression model.
```r
modelPrune(formula, data, engine = "lm", criterion = "vif",
           limit = 5, force_in = NULL, max_steps = NULL, ...)
```

| Parameter | Description | Default |
|-----------|-------------|---------|
| `formula` | Model formula (e.g., `y ~ .`) | *required* |
| `data` | Data frame | *required* |
| `engine` | `"lm"`, `"glm"`, `"lme4"`, `"glmmTMB"`, or custom | `"lm"` |
| `criterion` | `"vif"` or `"condition_number"` | `"vif"` |
| `limit` | Maximum allowed diagnostic value | `5` |
| `force_in` | Variables that must be retained | `NULL` |

**Returns**: Pruned data frame. Attributes: `selected_vars`, `removed_vars`, `final_model`.

### corrSelect()

Enumerates all maximal subsets satisfying correlation threshold (numeric data).

```r
corrSelect(df, threshold = 0.7, method = NULL, force_in = NULL,
           cor_method = "pearson", ...)
```

| Parameter | Description | Default |
|-----------|-------------|---------|
| `df` | Data frame (numeric columns only) | *required* |
| `threshold` | Maximum allowed correlation | `0.7` |
| `method` | Algorithm: `"bron-kerbosch"`, `"els"` | auto |
| `cor_method` | `"pearson"`, `"spearman"`, `"kendall"`, `"bicor"`, `"distance"`, `"maximal"` | `"pearson"` |
| `force_in` | Variables required in all subsets | `NULL` |

**Returns**: `CorrCombo` object with properties: `subset_list`, `avg_corr`, `min_corr`, `max_corr`.

### assocSelect()

Enumerates all maximal subsets for mixed-type data (numeric, factor, ordered).

```r
assocSelect(df, threshold = 0.7, method = NULL, force_in = NULL,
            method_num_num = "pearson", method_num_ord = "spearman",
            method_ord_ord = "spearman", ...)
```

| Parameter | Description | Default |
|-----------|-------------|---------|
| `df` | Data frame (any column types) | *required* |
| `threshold` | Maximum allowed association | `0.7` |
| `method_num_num` | Numeric-numeric: `"pearson"`, `"spearman"`, etc. | `"pearson"` |
| `method_num_ord` | Numeric-ordered: `"spearman"`, `"kendall"` | `"spearman"` |
| `method_ord_ord` | Ordered-ordered: `"spearman"`, `"kendall"` | `"spearman"` |

**Returns**: `CorrCombo` object.

### MatSelect()

Direct matrix interface for precomputed correlation/association matrices.

```r
MatSelect(mat, threshold = 0.7, method = NULL, force_in = NULL, ...)
```

| Parameter | Description | Default |
|-----------|-------------|---------|
| `mat` | Symmetric correlation/association matrix | *required* |
| `threshold` | Maximum allowed value | `0.7` |
| `method` | Algorithm: `"bron-kerbosch"`, `"els"` | auto |
| `force_in` | Variables required in all subsets | `NULL` |

**Returns**: `CorrCombo` object.

### corrSubset()

Extracts a specific subset from a `CorrCombo` result.

```r
corrSubset(res, df, which = "best", keepExtra = FALSE)
```

| Parameter | Description | Default |
|-----------|-------------|---------|
| `res` | `CorrCombo` object from `corrSelect`/`assocSelect`/`MatSelect` | *required* |
| `df` | Original data frame | *required* |
| `which` | Subset index or `"best"` (largest size, then lowest avg correlation) | `"best"` |
| `keepExtra` | Include non-numeric columns in output? | `FALSE` |

**Returns**: Data frame containing only the selected variables.

## Troubleshooting

**"No valid subsets found" error**
- Threshold too strict: all variable pairs exceed it

- Solution: Increase threshold or use `force_in` to keep at least one variable

**VIF computation fails in modelPrune()**
- Perfect multicollinearity (R² = 1) present

- Solution: Use `corrPrune(threshold = 0.99)` first to remove near-duplicates

**Forced variables conflict**
- Variables in `force_in` are too highly correlated with each other

- Solution: Increase threshold or reduce `force_in` set

**Slow performance with many variables**
- Exact mode is exponential for large p

- Solution: Use `mode = "greedy"` for p > 25

For comprehensive troubleshooting with code examples, see `vignette("advanced")`, Section 5.

## See Also

- `vignette("workflows")` - Complete real-world workflows (ecological, survey, genomic, mixed models)

- `vignette("advanced")` - Algorithmic control and custom engines

- `vignette("comparison")` - Comparison with caret, Boruta, glmnet

- `vignette("theory")` - Theoretical foundations and formulation

- `?corrPrune`, `?modelPrune`, `?corrSelect`, `?assocSelect`, `?MatSelect`

## Session Info

```{r}
sessionInfo()
```
