# Extending meow: Writing Your Own Modules

The whole point of `meow` is that you can drop your own algorithms into a shared simulation harness and compare them, on equal footing, against competing methods. This vignette is meant to serve as the authoritative reference for the three kinds of modules you can write: data loaders, item selection functions, and parameter update functions.

# The simulation state

A single `meow` simulation is a conducted with one call to `meow()`, which repeatedly alternates between an item selection step and a parameter update step until no further items are administered. For speed and flexibility, the simulation state is represented internally with matrices:

Object | Type | Meaning
--- | --- | ---
`R` | respondents x items matrix | The (potential) response of every respondent to every item.
`admin` | respondents x items integer | `0` if an item has not been administered; a positive value if it has.
`pers` | data frame | Person parameter estimates. First column `id`, then one column per parameter.
`item` | data frame | Item parameter estimates. First column `item`, then one column per parameter.
`adj_mat` | items x items matrix | Item co-exposure counts (see `construct_adj_mat()`).

Two design choices are important to make clear:

- Responses and simulation state are matrices. The full matrix of possible item responses, `R`, is unchanging throughout the simulation. The simulation state, `admin`, functions as a mask for this total response matrix. Items where `admin == 0` have not yet been administered, and items where `admin > 0` have. The positive values in `admin` additionally encode the order in which items were administered, which order-sensitive algorithms can use.
- Parameters are data frames. This preserves the flexibility to carry arbitrary person or item parameters: add a column to `pers` or `item` and it flows through the simulation untouched while still interacting with existing selection and update functions.

If you need to work with long data frames inside your module, call `meow_long(R, admin)` to get the administered responses as an `id`/`item`/`resp` data frame, ordered by respondent and administration order. While this enables `tidyverse`-style operations, this will likely come at a significant efficiency cost.

    R <- matrix(c(1, 0, 1, 1), nrow = 2)
    admin <- matrix(c(1L, 0L, 2L, 1L), nrow = 2)
    meow_long(R, admin)
    #>   id item resp
    #> 1  1    1    1
    #> 2  1    2    1
    #> 3  2    2    1

# Data loaders

A data loader sets up a simulation. It takes any arguments you like (passed through `data_args`) and returns a list with three elements:

- `resp`: a long data frame with columns `id`, `item`, and `resp`.
- `pers_tru`: true person parameters; first column `id`, then parameter names.
- `item_tru`: true item parameters; first column `item`, then parameter names.

`meow()` turns `resp` into the response matrix `R` once, before the loop starts, so the loader’s only job is to produce the bank of potential responses and the ground-truth parameter values. Below, we implement a data loader that draws respondent abilities from two normal distributions. Note the call to `set.seed(NULL)` to clear the seed before item selection and parameter updates.

    data_two_groups <- function(N_per_group = 50, N_items = 40, data_seed = 1) {
      set.seed(data_seed)
      N <- 2 * N_per_group
      theta <- c(stats::rnorm(N_per_group, -0.5), stats::rnorm(N_per_group, 0.5))
      b <- stats::rnorm(N_items)
      pers_tru <- data.frame(id = seq_len(N), theta = theta)
      item_tru <- data.frame(item = seq_len(N_items), b = b, a = 1)

      p <- stats::plogis(outer(theta, b, "-"))
      resp_mat <- matrix(stats::rbinom(length(p), 1, p), nrow = N)
      resp <- data.frame(
        id = rep(seq_len(N), each = N_items),
        item = rep(seq_len(N_items), times = N),
        resp = as.vector(t(resp_mat))
      )
      set.seed(NULL)
      list(resp = resp, pers_tru = pers_tru, item_tru = item_tru)
    }

    str(data_two_groups(N_per_group = 3, N_items = 4), max.level = 1)
    #> List of 3
    #>  $ resp    :'data.frame':    24 obs. of  3 variables:
    #>  $ pers_tru:'data.frame':    6 obs. of  2 variables:
    #>  $ item_tru:'data.frame':    4 obs. of  3 variables:

Reserved argument names a loader must not use are the ones the harness supplies to the other modules: `pers`, `item`, `R`, `admin`, `adj_mat`, and `select_seed`.

# Item selection functions

An item selection function decides which item to administer next. The standard signature is

    select_fun <- function(pers, item, R, admin, adj_mat, ...) { ... }

and it returns an administration matrix with the cells that correspond to newly chosen items marked non-zero. You only need to add items; the harness records the administration order for you, so setting a cell to `TRUE` or `1` is enough. Leave previously administered cells as they were. To stop administering items (a stopping rule), simply return `admin` unchanged — the simulation halts when an iteration adds nothing.

Here we present a complete custom selector that administers the easiest remaining item to each respondent, seeding the first five items in the bank on the first iteration:

    select_easiest <- function(pers, item, R, admin, adj_mat = NULL) {
      if (!any(admin != 0)) {       # first iteration: seed five items
        admin[, seq_len(min(5, ncol(admin)))] <- 1L
        return(admin)
      }
      difficulty <- item$b
      for (i in which(rowSums(admin == 0) > 0)) {
        remaining <- which(admin[i, ] == 0)
        pick <- remaining[which.min(difficulty[remaining])]
        admin[i, pick] <- 1L
      }
      admin
    }

A few tools we use that may be helpful to designing your own selection functions:

- `admin[i, ] == 0` gives the pool of unadministered items for respondent `i`.
- `rowSums(admin == 0) > 0` identifies respondents who still have items they have not yet responded to.
- Setting `admin[i, pick] <- 1L` administers item `pick` to respondent `i`.

If you prefer to compute on long data, `meow_long(R, admin)` is always available (but discouraged).

# Parameter update functions

A parameter update function re-estimates parameters from the administered responses. Its signature is

    update_fun <- function(pers, item, R, admin, ...) { ... }

and it returns a list with two elements, `pers` and `item`, the updated data frames of parameter estimates. The administered responses are `R[admin != 0]`, and their respondent and item indices can be found from `which(admin != 0, arr.ind = TRUE)`.

This custom updater nudges each ability toward the current proportion correct, without touching any item parameters:

    update_pct_correct <- function(pers, item, R, admin, rate = 0.5) {
      idx <- which(admin != 0, arr.ind = TRUE)
      person <- idx[, 1]
      resp <- R[idx]
      pct <- tapply(resp, person, mean)
      target <- stats::qlogis(pmin(pmax(pct, 0.02), 0.98)) # logit of proportion
      pers$theta[as.integer(names(target))] <-
        (1 - rate) * pers$theta[as.integer(names(target))] + rate * target
      list(pers = pers, item = item)
    }

# Putting it together

Custom modules plug into `meow()` exactly like the bundled ones. Extra arguments are passed through `select_args`, `update_args`, and `data_args`.

    sim <- meow(
      select_fun  = select_easiest,
      update_fun  = update_pct_correct,
      data_loader = data_two_groups,
      data_args   = list(N_per_group = 25, N_items = 20),
      update_args = list(rate = 0.3),
      fix         = "item"
    )

    head(sim$results[, 1:4])
    #>   iter pers_theta_1_est pers_theta_2_est pers_theta_3_est
    #> 1    1        0.1216395       -0.1216395      -0.12163953
    #> 2    2        0.2930918       -0.2930918      -0.08514767
    #> 3    3        0.2914689       -0.4800515      -0.14590799
    #> 4    4        0.3572759       -0.4892837      -0.25538328
    #> 5    5        0.3170362       -0.4094417      -0.38671245
    #> 6    6        0.2219253       -0.4082487      -0.39233825

The output object has the same shape no matter which modules you use: a `results` data frame (one row per iteration, an `est` and `bias` column for each parameter), a list of adjacency matrices in `adj_mats`, and the true parameters in `pers_tru` and `item_tru`. That consistency is what lets you reuse analysis and plotting code across studies; see `vignette("intro-viz")`.

# Checklist

- Data loaders return `list(resp, pers_tru, item_tru)` with long `resp`.
- Item selection functions take `(pers, item, R, admin, adj_mat, ...)` and return an administration matrix with new cells marked non-zero.
- Parameter update functions take `(pers, item, R, admin, ...)` and return `list(pers, item)`.
- Use `admin != 0` (or `meow_administered()`) for the administered mask, and `meow_long()` if you want long data frames.
- Do not attempt to un-administer items.
- Implement stopping rules by declining to administer additional items for completed individuals. Once `admin` doesn’t change between iterations, the simulation will terminate.