mirt (version 1.42)

RCI: Model-based Reliable Change Index

Description

Computes an IRT version of the "reliable change index" (RCI) proposed by Jacobson and Traux (1991) but modified to use IRT information about scores and measurement error (see Jabrayilov, Emons, and Sijtsma (2016). Main benefit of the IRT approach is the inclusion of response pattern information in the pre/post data score estimates, as well as conditional standard error of measurement information.

Usage

RCI(
  mod_pre,
  predat,
  postdat,
  mod_post = mod_pre,
  cutoffs = NULL,
  rxx.method = "pooled",
  rxx.pre = NULL,
  rxx.post = NULL,
  SD.pre = NULL,
  SD.post = NULL,
  Fisher = FALSE,
  ...
)

Arguments

mod_pre

single-group model fitted by mirt. If not supplied the information will be extracted from the data input objects to compute the classical test theory version of the RCI statistics

predat

a vector (if one individual) or matrix/data.frame of response data to be scored, where each individuals' responses are included in exactly one row

postdat

same as predat, but with respect to the post/follow-up measurement

mod_post

(optional) IRT model for post-test if different from pre-test; otherwise, the pre-test model will be used

cutoffs

optional vector of length 2 indicating the type of cut-offs to report (e.g., c(-1.96, 1.96) reflects the 95 percent z-score type cut-off)

rxx.method

which method to use for pooling the reliability information. Currently supports 'pooled' to pool the pre-post reliability estimates (default) or 'pre' for using just the pre-test

rxx.pre

CTT reliability of pretest. If not supplied will be computed using coefficient alpha from predat

rxx.post

same as rxx.pre, but for post-test data

SD.pre

standard deviation of pretest. If not supplied will be computed from predat

SD.post

same as SD.pre, but for the post-test data

Fisher

logical; use the Fisher/expected information function to compute the SE terms? If FALSE the SE information will be extracted from the select fscores method (default). Only applicable for unidimensional models

...

additional arguments passed to fscores

Author

Phil Chalmers

References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. tools:::Rd_expr_doi("10.18637/jss.v048.i06")

Jacobson, N. S., & Truax, P. (1991). Clinical significance: A statistical approach to defining meaningful change in psychotherapy research. Journal of Consulting and Clinical Psychology, 59, 12-19.

Jabrayilov, R. , Emons, W. H. M., & Sijtsma, K. (2016). Comparison of Classical Test Theory and Item Response Theory in Individual Change Assessment. Applied Psychological Measurement, 40 (8), 559-572.

Examples

if (FALSE) {

# simulate some data
N <- 1000
J <- 20     # number of items
a <- matrix(rlnorm(J,.2,.3))
d <- rnorm(J)

theta <- matrix(rnorm(N))
dat_pre <- simdata(a, d, itemtype = '2PL', Theta = theta)

# first 3 cases decrease by 1/2
theta2 <- theta - c(1/2, 1/2, 1/2, numeric(N-3))
dat_post <- simdata(a, d, itemtype = '2PL', Theta = theta2)

mod <- mirt(dat_pre)

# all changes using fitted model from pre data
RCI(mod, predat=dat_pre, postdat=dat_post)

# single response pattern change using EAP information
RCI(mod, predat=dat_pre[1,], postdat=dat_post[1,])

# WLE estimator with Fisher information for SE (see Jabrayilov et al. 2016)
RCI(mod, predat = dat_pre[1,], postdat = dat_post[1,],
    method = 'WLE', Fisher = TRUE)

# multiple respondents
RCI(mod, predat = dat_pre[1:6,], postdat = dat_post[1:6,])

# include large-sample z-type cutoffs
RCI(mod, predat = dat_pre[1:6,], postdat = dat_post[1:6,],
    cutoffs = c(-1.96, 1.96))

######
# CTT version by omitting IRT model (easiest to use complete dataset)
RCI(predat = dat_pre, postdat = dat_post)

# CTT version with pre-computed information
RCI(predat = dat_pre[1:6,], postdat = dat_post[1:6,],
    rxx.pre=.6, rxx.post=.6, SD.pre=2, SD.post=3,
    cutoffs = c(-1.96, 1.96))

# just pre-test rxx
RCI(predat = dat_pre[1:6,], postdat = dat_post[1:6,],
    rxx.pre=.6, SD.pre=2, rxx.method = 'pre')

############################
# Example where individuals take completely different item set pre-post
#   but prior calibration has been performed to equate the items

dat <- key2binary(SAT12,
  key = c(1,4,5,2,3,1,2,1,3,1,2,4,2,1,5,3,4,4,1,4,3,3,4,1,3,5,1,3,1,5,4,5))

mod <- mirt(dat)

# with N=5 individuals under investigation
predat <- postdat <- dat[1:5,]
predat[, 17:32] <- NA
postdat[, 1:16] <- NA

head(predat)
head(postdat)

RCI(mod, predat, postdat)

}