Item Characteristic Curves with Class Intervals

Plots Item Characteristic Curves (ICCs) for Bayesian Rasch-family models fitted with brms. Each item panel shows the model-expected item score curve (with a credible interval ribbon) overlaid with observed average item scores computed within class intervals. Optionally, observed scores can be split by a grouping variable to visually assess differential item functioning (DIF).

Usage

plot_icc(
  model,
  item_var = item,
  person_var = id,
  items = NULL,
  n_intervals = 5,
  theta_range = c(-4, 4),
  n_points = 200,
  center = TRUE,
  prob = 0.95,
  ncol = NULL,
  line_size = 0.8,
  ribbon_alpha = 0.3,
  point_size = 2.5,
  dif_var = NULL,
  dif_data = NULL,
  dif_labels = NULL,
  dif_stats = TRUE,
  min_n = 5,
  palette = NULL
)

Arguments

model: A fitted brmsfit object from an ordinal IRT model (e.g., family = acat) or a dichotomous model (family = bernoulli()).
item_var: An unquoted variable name identifying the item grouping variable in the model data. Default is item.
person_var: An unquoted variable name identifying the person grouping variable in the model data. Default is id.
items: An optional character vector of item names to plot. If NULL (the default), all items are plotted.
n_intervals: Integer. The number of class intervals into which persons are binned along the sum score. Default is 5.
theta_range: A numeric vector of length 2 specifying the range of theta for the expected curve. Default is c(-4, 4).
n_points: Integer. Number of evenly spaced theta values for computing the expected curve. Default is 200.
center: Logical. If TRUE (the default), the scale is recentered so the grand mean of item thresholds = 0, consistent with plot_targeting.
prob: Numeric in $(0, 1)$. Width of the credible interval ribbon around the expected curve. Default is 0.95.
ncol: Integer. Number of columns in the faceted layout. If NULL, chosen automatically.
line_size: Numeric. Line width for the expected curve. Default is 0.8.
ribbon_alpha: Numeric in $[0, 1]$. Transparency of the credible interval ribbon. Default is 0.3.
point_size: Numeric. Size of observed score points. Default is 2.5.
dif_var: An optional unquoted variable name for a grouping variable to assess DIF visually. If supplied, observed scores are computed separately per group and coloured accordingly.
dif_data: An optional data frame containing the DIF variable. Required when dif_var is specified and the variable was not part of the model formula (since brms drops unused variables from model$data). Must have the same rows and row order as the original model data.
dif_labels: An optional character vector of labels for the DIF groups. If NULL, factor levels are used.
dif_stats: Logical. If TRUE (the default when dif_var is specified), the partial gamma coefficient for each item is annotated in the plot panel. The partial gamma measures the strength of DIF, stratified by total score.
min_n: Integer. Minimum number of persons required in a class interval for the observed mean to be plotted. Intervals with fewer persons are dropped to avoid unstable estimates. Default is 5.
palette: An optional character vector of colors. If NULL, viridis colors are used.

Value

A ggplot object.

Details

This is the Bayesian analogue of ICCplot() from the iarm package, using the class interval method.

Expected curve: For each item, the expected item score $E_i(\theta)$ is computed for a dense grid of theta values using the posterior draws of item thresholds. For the adjacent category (PCM/acat) family: $$E_i(\theta) = \sum_{c=0}^{K} c \cdot P_{ic}(\theta)$$ where $P_{ic}$ are the category probabilities. For dichotomous items, $E_i(\theta) = P_i(\theta)$.

The posterior mean of $E_i(\theta)$ is plotted as a line, with a credible interval ribbon showing the prob interval across posterior draws.

Class intervals: Following the approach in iarm::ICCplot(), persons are binned into class intervals by their ordinal sum score (the sufficient statistic in Rasch models), not by their EAP theta estimate. Within each interval, the mean observed item response is computed and plotted at the theta value corresponding to the mean sum score in that interval, obtained by inverting the posterior-mean expected total score function. Persons with extreme sum scores (0 and maximum) are excluded from the class intervals, as their theta positions cannot be estimated.

Uncertainty around observed points: For each class interval, the standard error of the mean observed response is computed and displayed as error bars showing $\pm 1.96$ SE. These reflect sampling variability of the observed mean within each bin.

DIF overlay: When dif_var is specified, observed scores are computed separately for each level of the DIF variable, producing group-specific points connected by lines. Deviations between groups that track alongside each other (but offset from the expected curve) suggest uniform DIF. Crossing group lines suggest non-uniform DIF.

Partial gamma: When dif_stats = TRUE (default when DIF is requested), the Goodman-Kruskal partial gamma coefficient is displayed in each item panel. This measures the ordinal association between item response and DIF group, stratified by total score. Values near 0 indicate no DIF; values near $\pm 1$ indicate strong DIF. The computation reuses the concordant/discordant pair counting algorithm from gk_gamma.

Examples

# \donttest{
library(brms)
library(dplyr)
library(tidyr)
library(tibble)
library(ggplot2)

# --- Partial Credit Model ---

df_pcm <- eRm::pcmdat2 %>%
  mutate(across(everything(), ~ .x + 1)) %>%
  rownames_to_column("id") %>%
  pivot_longer(!id, names_to = "item", values_to = "response")

fit_pcm <- brm(
  response | thres(gr = item) ~ 1 + (1 | id),
  data   = df_pcm,
  family = acat,
  chains = 4, cores = 2, iter = 1000 # use more iter and cores
)
#> Compiling Stan program...
#> Error in .fun(model_code = .x1): Boost not found; call install.packages('BH')

# Basic ICC plot with 5 class intervals
plot_icc(fit_pcm)
#> Error: object 'fit_pcm' not found

# Select specific items, more intervals
plot_icc(fit_pcm, items = c("I1", "I2"), n_intervals = 5)
#> Error: object 'fit_pcm' not found

# With DIF overlay and partial gamma annotation

# same dataset, adding a `gender` DIF variable
df_pcm <- eRm::pcmdat2 %>%
  mutate(across(everything(), ~ .x + 1)) %>%
  rownames_to_column("id") %>%
  mutate(gender = sample(c("M", "F"), nrow(.), TRUE)) %>% 
  pivot_longer(!c(id,gender), names_to = "item", values_to = "response")
  
plot_icc(fit_pcm, dif_var = gender, dif_data = df_pcm,
         dif_labels = c("Female", "Male"), n_intervals = 5)
#> Error: object 'fit_pcm' not found
# }

Usage

Arguments

Value

Details

See also

Examples