---
title: "A Workflow for Variance-Aware Michaelis-Menten Analysis"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{A Workflow for Variance-Aware Michaelis-Menten Analysis}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

`inferMM` targets a common enzyme-kinetic workflow: fit a Michaelis-Menten
curve, compare plausible working variance functions, and summarize inference in
a way that is less sensitive to heteroscedasticity than ordinary nonlinear least
squares alone. The same interface also supports clustered assay layouts in
which repeated measurements within a core, plate, or sample may be correlated.

## Single-curve fitting

```{r}
library(inferMM)

one_curve <- subset(sdl_demo, enzyme == "1111")

fit <- fit_mm(
  x = one_curve$s_uM,
  y = one_curve$v_uM_per_min,
  variance = "sqrt"
)

summary(fit)

fit_auto <- fit_mm(
  x = one_curve$s_uM,
  y = one_curve$v_uM_per_min,
  variance = "auto",
  power_selection = "quasi_aic"
)

summary(fit_auto)
```

The fitted object supports extraction of coefficients, Wald confidence
intervals, bootstrap confidence intervals, and predictions.

```{r}
coef(fit)
confint(fit)
set.seed(1)
confint(fit, method = "bootstrap", B = 99)
head(predict(fit, newdata = seq(0, 80, length.out = 6), interval = "prediction"))
```

For a one-step console summary plus a 95\% confidence band, use:

```{r, eval = FALSE}
report_mm(fit, interval_type = "confidence")
set.seed(1)
report_mm(fit, method = "bootstrap", B = 99,
          interval_type = "confidence")
```

## Screening working variance models

```{r}
screen <- screen_mm(
  x = one_curve$s_uM,
  y = one_curve$v_uM_per_min,
  power_values = c(0.4, 0.6),
  include_auto = TRUE,
  quiet = TRUE
)

screen$table[, c("model", "selected_model", "quasi_aic", "quasi_bic", "rmse")]
```

The screening table is ordered by quasi-AIC, with quasi-BIC and RMSE reported
as secondary summaries.

## Grouped analyses

For real enzyme panels we often fit many curves at once and then compare the
best model within each group.

```{r}
grouped <- group_mm(
  data = sdl_demo,
  s = "s_uM",
  v = "v_uM_per_min",
  groups = "enzyme",
  variance_models = c("constant", "log", "sqrt", "cuberoot"),
  power_values = c(0.4, 0.6),
  include_auto = TRUE,
  quiet = TRUE
)

head(grouped$comparison$best_by_group[, c("group_label", "model", "selected_model", "quasi_aic", "quasi_bic", "rmse")])
```

To visualize the current best model for each group, use the grouped plotting
method.

```{r, eval = FALSE}
plot(grouped, interval_type = "confidence")
```

## Clustered repeated measurements

For repeated or clustered assays, `cluster_mm()` uses a Ma-Genton-style
working covariance with a random effect on `Vmax` and a low-dimensional
residual variance function. The bundled `alves_demo` data illustrate the
interface on a small soil-enzyme panel.

```{r}
cluster_fit <- cluster_mm(
  data = subset(alves_demo, enzyme == "BG"),
  s = "substrate_conc",
  v = "activity",
  cluster = "core",
  variance = "sqrt"
)

summary(cluster_fit)
confint(cluster_fit)
head(predict(cluster_fit, newdata = seq(0, 700, length.out = 6),
             interval = "confidence"))
```

Because the bundled example contains only three cores, the printed summary
reports point estimates by default and treats interval output as an explicit
sensitivity analysis.

## Simulation

```{r}
set.seed(100)
sim_dat <- simulate_mm_data(variance_shape = "hill", error = "skewed")
head(sim_dat)
```

The package is intentionally lightweight: it relies only on base and
recommended R packages, while keeping the workflow close to the heteroscedastic
and clustered Michaelis-Menten analyses used in the companion methodology
paper.