rimse {flexmet}

Root Integrated Mean Squared Difference Between FMP IRFs

Description

Compute the root integrated mean squared error (RIMSE) between two FMP IRFs.

Usage

rimse(
  bvec1,
  bvec2,
  ncat = 2,
  c1 = NULL,
  d1 = NULL,
  c2 = NULL,
  d2 = NULL,
  int = int_mat()
)

Arguments

bvec1

Either a vector of FMP item parameters or a function corresponding to a non-FMP IRF. Functions should have exactly one argument, corresponding to the latent trait.

bvec2

Either a vector of FMP item parameters or a function corresponding to a non-FMP IRF. Functions should have exactly one argument, corresponding to the latent trait.

ncat

Number of response categories (first ncat - 1 elemnts of bvec1 and bvec2 are intercepts)

c1

Lower asymptote parameter for bvec1. Ignored if bvec1 is a function.

d1

Upper asymptote parameter for bvec1. Ignored if bvec1 is a function.

c2

Lower asymptote parameter for bvec2. Ignored if bvec2 is a function.

d2

Upper asymptote parameter for bvec2. Ignored if bvec2 is a function.

int

Matrix with two columns, used for numerical integration. Column 1 is a grid of theta values, column 2 are normalized densities associated with the column 1 values

Value

Root integrated mean squared difference between two IRFs (dichotomous items) or expected item scores (polytomous items).

References

Ramsay, J. O. (1991). Kernel smoothing approaches to nonparametric item characteristic curve estimation. Psychometrika, 56, 611–630. doi: 10.1007/BF02294494

Examples

set.seed(2342)
bmat <- sim_bmat(n_items = 2, k = 2, ncat = c(2, 5))$bmat

theta <- rnorm(500)
dat <- sim_data(bmat = bmat, theta = theta, maxncat = 5)

# k = 0
fmp0a <- fmp_1(dat = dat[, 1], k = 0, tsur = theta)
fmp0b <- fmp_1(dat = dat[, 2], k = 0, tsur = theta)


# k = 1
fmp1a <- fmp_1(dat = dat[, 1], k = 1, tsur = theta)
fmp1b <- fmp_1(dat = dat[, 2], k = 1, tsur = theta)


## compare estimated curves to the data-generating curve
rimse(fmp0a$bmat, bmat[1, -c(2:4)])
rimse(fmp0b$bmat, bmat[2, ], ncat = 5)


rimse(fmp1a$bmat, bmat[1, -c(2:4)])
rimse(fmp1b$bmat, bmat[2, ], ncat = 5)