The per-class-interval breakdown behind an item's item-trait chi-square, as dissected in Andrich and Marais (2019, ch. 13): for every class interval the size, the maximum and mean person location, the standardised residual between observed and expected interval means, its squared chi-square component, the observed and expected means (OM, EV), the sample-size-free effect size ES = (OM - EV)/sqrt(mean V), and per response category the observed proportion (OBS.P), the mean model probability (EST.P), and the observed conditional threshold proportion (OBS.T), the proportion scoring k among those scoring k - 1 or k.
Arguments
- fit
A fitted object from
rasch.- item
Item name or index.
Value
A list with item, location, the intervals
data frame, the categories data frame, the whole-sample observed
mean ave, and the item's total chisq, df, and
p. Intervals with fewer than 2 responders are shown but carry no
chi-square contribution (used = FALSE), matching the item-trait
computation.
Examples
set.seed(1)
d <- seq(-1.5, 1.5, length.out = 6)
X <- matrix(rbinom(400 * 6, 1, plogis(outer(rnorm(400), d, "-"))), 400, 6)
colnames(X) <- paste0("I", 1:6)
chisq_detail(rasch(X), "I3")$intervals
#> interval n theta_max theta_mean obs_mean exp_value residual
#> 1 1 52 -1.61901055 -1.61901055 0.07692308 0.1962929 -2.1671803
#> 2 2 67 -0.73551099 -0.73551099 0.38805970 0.3714206 0.2818740
#> 3 3 118 0.01710555 0.01710555 0.54237288 0.5563815 -0.3062983
#> 4 4 78 0.75817394 0.75817394 0.78205128 0.7246324 1.1352375
#> 5 5 43 1.61003743 1.61003743 0.93023256 0.8604966 1.3198477
#> chisq es used
#> 1 4.69667044 -0.30053383 TRUE
#> 2 0.07945293 0.03443639 TRUE
#> 3 0.09381862 -0.02819704 TRUE
#> 4 1.28876421 0.12854034 TRUE
#> 5 1.74199785 0.20127488 TRUE