Simulates data under the Joint Hierarchical Model and plots the resulting response accuracy. The plot type depends on `level` and `by.theta`:
- **Person, by distribution**: Histogram of total correct scores across persons. - **Person, by theta**: Mean total score as a function of ability \(\theta\), shown as a bar chart binned by \(\theta\). - **Item, by distribution**: Density of \(P(X = 1)\) across persons for each item, with the item-wise median marked. - **Item, by theta**: Item characteristic curves (ICCs), showing \(P(X = 1)\) as a function of \(\theta\) for each item, with a dashed line at the item difficulty \(\beta\).
Data are generated via [sim.jhm.data()] with `scale = FALSE`.
Usage
plot_RA(
design = NULL,
level = "item",
by.theta = TRUE,
N = 1000,
K = 30,
mu.person = c(0, 0),
mu.item = c(1, 0, 0.5, 1),
meanlog.sigma2 = log(0.6),
cov.m.person = matrix(c(1, 0.4, 0.4, 1), ncol = 2, byrow = FALSE),
cov.m.item = matrix(c(1, 0, 0, 0, 0, 1, 0, 0.4, 0, 0, 1, 0, 0, 0.4, 0, 1), ncol = 4,
byrow = TRUE),
sd.item = c(0.2, 1, 0.2, 0.5),
sdlog.sigma2 = 0,
item.pars.m = NULL,
cor2cov.item = FALSE
)Arguments
- design
Optional list or `"sspLNIRT.design"` object holding the data-generating design. When supplied, its fields are used for any design-related argument the caller did not pass explicitly (`K`, `mu.person`, `mu.item`, `meanlog.sigma2`, `cov.m.person`, `cov.m.item`, `sd.item`, `sdlog.sigma2`, `item.pars.m`, `cor2cov.item`). Caller- supplied arguments always take precedence. Extra fields in `design` (e.g. `thresh`, `out.par`, `seed`) are ignored, so the object returned in `$design` by [get_sspLNIRT()] or [optim_sample()] can be passed directly. Default `NULL` (use the function defaults / caller arguments).
- level
Character. `"person"` for person-level aggregates or `"item"` for item-level curves / distributions.
- by.theta
Logical. If `TRUE`, the x-axis is \(\theta\); if `FALSE`, a marginal distribution is shown.
- N
Integer. Sample size (number of persons) for the simulated data. Default is 1000.
- K
Integer. Test length (number of items). Default is 10.
- mu.person
Numeric vector of length 2. Population means of \((\theta, \zeta)\).
- mu.item
Numeric vector of length 4. Population means of \((\alpha, \beta, \varphi, \lambda)\).
- meanlog.sigma2
Numeric. Mean of the log-normal distribution for \(\sigma^2\) (on the log scale).
- cov.m.person
2x2 symmetric matrix. Covariance matrix of \((\theta, \zeta)\).
- cov.m.item
4x4 symmetric matrix. Covariance (or correlation) matrix of \((\alpha, \beta, \varphi, \lambda)\). See `cor2cov.item`.
- sd.item
Numeric vector of length 4. Standard deviations of \((\alpha, \beta, \varphi, \lambda)\). Required when `cor2cov.item = TRUE`.
- sdlog.sigma2
Numeric. Standard deviation of the log-normal distribution for \(\sigma^2\). Default is 0.
- item.pars.m
Matrix with 4 columns or `NULL`. If supplied, item parameters are held fixed instead of drawn from the truncated MVN.
- cor2cov.item
Logical. If `TRUE`, `cov.m.item` is treated as a correlation matrix and converted using `sd.item`.
Examples
if (FALSE) { # \dontrun{
plot_RA(level = "person", by.theta = TRUE, N = 500, K = 20)
plot_RA(level = "item", by.theta = FALSE, N = 1000, K = 5,
mu.item = c(1, 0, 0.5, 1), sd.item = c(0.2, 0.5, 0.2, 0.5))
# Pass a design object retrieved from get_sspLNIRT() (or optim_sample()):
res <- get_sspLNIRT(thresh = 0.10, out.par = "alpha",
K = 30, mu.alpha = 1,
meanlog.sigma2 = log(0.6), rho = 0.4)
plot_RA(res$design, level = "item", by.theta = TRUE)
} # }