Model-based Reliable Change Index

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,
  SEM.pre = NULL,
  SEM.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)
SEM.pre: standard error of measurement for the pretest. This can be used instead of rxx.pre and SD.pre
SEM.post: (optional) standard error of measurement for the post-test. Using this will create a pooled version of the SEM; otherwise, SEM.post = SEM.pre
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
verbose: logical; include extra information in the printout?

References

Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. 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.

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples


if (FALSE) { # \dontrun{

# 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
    # Requires either sample or population SEM's as input
(istats <- itemstats(dat_pre)$overall)
SEM.alpha <- istats$SEM.alpha    # SEM estimate of dat_pre

# assumes SEM.post = SEM.pre
RCI(predat = dat_pre, postdat = dat_post, SEM.pre=SEM.alpha)

# include cutoffs
RCI(predat = dat_pre, postdat = dat_post, SEM.pre=SEM.alpha,
    cutoffs=c(-1.96, 1.96))

# allows SEM.post != SEM.pre
(istats.post <- itemstats(dat_post)$overall)
SEM.alpha.post <- istats.post$SEM.alpha

RCI(predat = dat_pre, postdat = dat_post,
   SEM.pre=SEM.alpha, SEM.post=SEM.alpha.post)


############################
# 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)

} # }