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Return model implied residuals for linear dependencies between items or at the person level.
If the latent trait density was approximated (e.g., Davidian curves, Empirical histograms, etc)
then passing use_dentype_estimate = TRUE
will use the internally saved quadrature and
density components (where applicable).
# S4 method for SingleGroupClass
residuals(
object,
type = "LD",
df.p = FALSE,
full.scores = FALSE,
QMC = FALSE,
printvalue = NULL,
tables = FALSE,
verbose = TRUE,
Theta = NULL,
suppress = 1,
theta_lim = c(-6, 6),
quadpts = NULL,
fold = TRUE,
technical = list(),
...
)
an object of class SingleGroupClass
or
MultipleGroupClass
. Bifactor models are automatically detected and utilized for
better accuracy
type of residuals to be displayed.
Can be either 'LD'
or 'LDG2'
for a local dependence matrix based on the
X2 or G2 statistics (Chen & Thissen, 1997), 'Q3'
for the statistic proposed by
Yen (1984), 'JSI'
for the jack-knife statistic proposed Edwards et al. (2018),
'exp'
for the expected values for the frequencies of every response pattern,
and 'expfull'
for the expected values for every theoretically observable response pattern.
For the 'LD' and 'LDG2' types, the upper diagonal elements represent the standardized
residuals in the form of signed Cramers V coefficients
logical; print the degrees of freedom and p-values?
logical; compute relevant statistics for each subject in the original data?
logical; use quasi-Monte Carlo integration? If quadpts
is omitted the
default number of nodes is 5000
a numeric value to be specified when using the res='exp'
option. Only prints patterns that have standardized residuals greater than
abs(printvalue)
. The default (NULL) prints all response patterns
logical; for LD type, return the observed, expected, and standardized residual tables for each item combination?
logical; allow information to be printed to the console?
a matrix of factor scores used for statistics that require empirical estimates (i.e., Q3).
If supplied, arguments typically passed to fscores()
will be ignored and these values will
be used instead
a numeric value indicating which parameter local dependency combinations to flag as being too high. Absolute values for the standardized estimates greater than this value will be returned, while all values less than this value will be set to NA
range for the integration grid
number of quadrature nodes to use. The default is extracted from model (if available) or generated automatically if not available
logical; apply the sum 'folding' described by Edwards et al. (2018) for the JSI statistic?
list of technical arguments when models are re-estimated (see mirt
for details)
additional arguments to be passed to fscores()
Chalmers, R., P. (2012). mirt: A Multidimensional Item Response Theory Package for the R Environment. Journal of Statistical Software, 48(6), 1-29. 10.18637/jss.v048.i06
Chen, W. H. & Thissen, D. (1997). Local dependence indices for item pairs using item response theory. Journal of Educational and Behavioral Statistics, 22, 265-289.
Edwards, M. C., Houts, C. R. & Cai, L. (2018). A Diagnostic Procedure to Detect Departures From Local Independence in Item Response Theory Models. Psychological Methods, 23, 138-149.
Yen, W. (1984). Effects of local item dependence on the fit and equating performance of the three parameter logistic model. Applied Psychological Measurement, 8, 125-145.
# NOT RUN {
# }
# NOT RUN {
x <- mirt(Science, 1)
residuals(x)
residuals(x, tables = TRUE)
residuals(x, type = 'exp')
residuals(x, suppress = .15)
residuals(x, df.p = TRUE)
# Pearson's X2 estimate for goodness-of-fit
full_table <- residuals(x, type = 'expfull')
head(full_table)
X2 <- with(full_table, sum((freq - exp)^2 / exp))
df <- nrow(full_table) - extract.mirt(x, 'nest') - 1
p <- pchisq(X2, df = df, lower.tail=FALSE)
data.frame(X2, df, p, row.names='Pearson-X2')
# above FOG test as a function
PearsonX2 <- function(x){
full_table <- residuals(x, type = 'expfull')
X2 <- with(full_table, sum((freq - exp)^2 / exp))
df <- nrow(full_table) - extract.mirt(x, 'nest') - 1
p <- pchisq(X2, df = df, lower.tail=FALSE)
data.frame(X2, df, p, row.names='Pearson-X2')
}
PearsonX2(x)
# extract results manually
out <- residuals(x, df.p = TRUE, verbose=FALSE)
str(out)
out$df.p[1,2]
# with and without supplied factor scores
Theta <- fscores(x)
residuals(x, type = 'Q3', Theta=Theta)
residuals(x, type = 'Q3', method = 'ML')
# Edwards et al. (2018) JSI statistic
N <- 250
a <- rnorm(10, 1.7, 0.3)
d <- rnorm(10)
dat <- simdata(a, d, N=250, itemtype = '2PL')
mod <- mirt(dat, 1)
residuals(mod, type = 'JSI')
residuals(mod, type = 'JSI', fold=FALSE) # unfolded
# LD between items 1-2
aLD <- numeric(10)
aLD[1:2] <- rnorm(2, 2.55, 0.15)
a2 <- cbind(a, aLD)
dat <- simdata(a2, d, N=250, itemtype = '2PL')
mod <- mirt(dat, 1)
# JSI executed in parallel over multiple cores
mirtCluster()
residuals(mod, type = 'JSI')
# }
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