Scree plot of the residual components with parallel analysis

Eigenvalues of the residual correlation matrix for the leading components, with a model-simulated parallel-analysis reference: responses are simulated from the calibrated model (observed missingness kept), every person is re-estimated, and the residual eigenvalues recomputed. Because estimating the person locations couples the residuals within a person, this reference sits above the classical random-normal one and is calibrated under the fitted model (Raiche 2005; Chou & Wang 2010). Observed eigenvalues above the reference suggest structure beyond what the model itself produces.

Usage

plot_scree(fit, n_components = 10, parallel = TRUE, reps = 20)

Arguments

fit

A fitted object from rasch.

n_components

Number of leading components to display.

parallel

Draw the parallel-analysis reference line.

reps

Model-simulated replicates for the reference.

Value

Called for its plotting side effect; invisibly the eigen table.

References

Raiche, G. (2005). Critical eigenvalue sizes in standardized residual principal components analysis. Rasch Measurement Transactions, 19(1), 1012.

Chou, Y.-T., & Wang, W.-C. (2010). Checking dimensionality in item response models with principal component analysis on standardized residuals. Educational and Psychological Measurement, 70(5), 717-731.

Examples

set.seed(1)
d <- seq(-2, 2, length.out = 8)
X <- matrix(rbinom(500 * 8, 1, plogis(outer(rnorm(500), d, "-"))), 500, 8)
colnames(X) <- paste0("I", 1:8)
plot_scree(rasch(X))