Person fit statistics

personfit calculates the Zh values from Drasgow, Levine and Williams (1985) for unidimensional and multidimensional models, as well as the infit and outfit statistics. The returned object is a data.frame consisting either of the tabulated data or full data with the statistics appended to the rightmost columns.

Usage

personfit(
  x,
  method = "EAP",
  Theta = NULL,
  stats.only = TRUE,
  return.resids = FALSE,
  ...
)

Arguments

x

a computed model object of class SingleGroupClass or MultipleGroupClass

method

type of factor score estimation method. See fscores for more detail

Theta

a matrix of factor scores used for statistics that require empirical estimates. If supplied, arguments typically passed to fscores() will be ignored and these values will be used instead

stats.only

logical; return only the person fit statistics without their associated response pattern?

return.resids

logical; return the standardized and unstandardized N by J matrices of person and item residuals? If TRUE will return a named list of each residual type

...

additional arguments to be passed to fscores()

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

Drasgow, F., Levine, M. V., & Williams, E. A. (1985). Appropriateness measurement with polychotomous item response models and standardized indices. British Journal of Mathematical and Statistical Psychology, 38, 67-86.

Reise, S. P. (1990). A comparison of item- and person-fit methods of assessing model-data fit in IRT. Applied Psychological Measurement, 14, 127-137.

Wright B. D. & Masters, G. N. (1982). Rating scale analysis. MESA Press.

See also

itemfit

Author

Phil Chalmers rphilip.chalmers@gmail.com

Examples

if (FALSE) { # \dontrun{

#make some data
set.seed(1)
a <- matrix(rlnorm(20),ncol=1)
d <- matrix(rnorm(20),ncol=1)
items <- rep('2PL', 20)
data <- simdata(a,d, 2000, items)

# first observation responds 1 for most difficult, 0 for easiest
data[1,] <- ifelse(d > 0, 0, 1)

# second observations answers first half as 1 second half as 0
data[2,] <- rep(1:0, each = 10)

x <- mirt(data, 1)
fit <- personfit(x)
head(fit)

# raw/standardized residuals
resid_list <- personfit(x, return.resids=TRUE)
head(resid_list$resid) # unstandardized
head(resid_list$std.resid) # standardized (approximate z-scores)

residuals(x, type = 'score')

# with missing data
data[3, c(1,3,5,7)] <- NA
x.miss <- mirt(data, 1)
fit.miss <- personfit(x.miss)
head(fit.miss)
head(personfit(x.miss, return.resids=TRUE))

#using precomputed Theta
Theta <- fscores(x, method = 'MAP', full.scores = TRUE)
head(personfit(x, Theta=Theta))

# multiple group Rasch model example
set.seed(12345)
a <- matrix(rep(1, 16), ncol=1)
d <- matrix(rnorm(16,0,.7),ncol=1)
itemtype <- rep('dich', nrow(a))
N <- 1000
dataset1 <- simdata(a, d, N, itemtype)
dataset2 <- simdata(a, d, N, itemtype, sigma = matrix(1.5))
dat <- rbind(dataset1, dataset2)

# first observation responds 1 for most difficult, 0 for easiest
dat[1,] <- ifelse(d > 0, 0, 1)

group <- c(rep('D1', N), rep('D2', N))
models <- 'F1 = 1-16'
mod_Rasch <- multipleGroup(dat, models, itemtype = 'Rasch', group = group)
coef(mod_Rasch, simplify=TRUE)
pf <- personfit(mod_Rasch, method='MAP')
head(pf)

  } # }