Description Usage Arguments Details 'lca' model definition Author(s) References See Also Examples
mdirt
fits a variety of item response models with discrete latent variables.
These include, but are not limited to, latent class analysis, multidimensional latent
class models, multidimensional discrete latent class models, DINA/DINO models,
grade of measurement models, and so on.
1 2 3 4 |
data |
a |
model |
number of classes to fit, or alternatively a |
customTheta |
input passed to |
nruns |
a numeric value indicating how many times the model should be fit to the data
when using random starting values. If greater than 1, |
method |
estimation method. Can be 'EM' or 'BL' (see |
covdata |
a data.frame of data used for latent regression models |
formula |
an R formula (or list of formulas) indicating how the latent traits
can be regressed using external covariates in |
optimizer |
optimizer used for the M-step, set to |
return_max |
logical; when |
group |
a factor variable indicating group membership used for multiple group analyses |
GenRandomPars |
logical; use random starting values |
verbose |
logical; turn on messages to the R console |
pars |
used for modifying starting values; see |
technical |
list of lower-level inputs. See |
... |
additional arguments to be passed to the estimation engine. See |
Posterior classification accuracy for each response pattern may be obtained
via the fscores
function. The summary()
function will display
the category probability values given the class membership, which can also
be displayed graphically with plot()
, while coef()
displays the raw coefficient values (and their standard errors, if estimated). Finally,
anova()
is used to compare nested models, while
M2
and itemfit
may be used for model fitting purposes.
The latent class IRT model with two latent classes has the form
P(x = k|θ_1, θ_2, a1, a2) = \frac{exp(a1 θ_1 + a2 θ_2)}{ ∑_j^K exp(a1 θ_1 + a2 θ_2)}
where the θ values generally take on discrete points (such as 0 or 1). For proper identification, the first category slope parameters (a1 and a2) are never freely estimated. Alternatively, supplying a different grid of θ values will allow the estimation of similar models (multidimensional discrete models, grade of membership, etc.). See the examples below.
Phil Chalmers rphilip.chalmers@gmail.com
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
fscores
, mirt.model
, M2
,
itemfit
, boot.mirt
, mirtCluster
,
wald
, coef-method
, summary-method
,
anova-method
, residuals-method
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#LSAT6 dataset
dat <- expand.table(LSAT6)
# fit with 2-3 latent classes
(mod2 <- mdirt(dat, 2))
(mod3 <- mdirt(dat, 3))
summary(mod2)
residuals(mod2)
residuals(mod2, type = 'exp')
anova(mod2, mod3)
M2(mod2)
itemfit(mod2)
# generate classification plots
plot(mod2)
plot(mod2, facet_items = FALSE)
plot(mod2, profile = TRUE)
# available for polytomous data
mod <- mdirt(Science, 2)
summary(mod)
plot(mod)
plot(mod, profile=TRUE)
# classification based on response patterns
fscores(mod2, full.scores = FALSE)
# classify individuals either with the largest posterior probability.....
fs <- fscores(mod2)
head(fs)
classes <- matrix(1:2, nrow(fs), 2, byrow=TRUE)
class_max <- classes[t(apply(fs, 1, max) == fs)]
table(class_max)
# ... or by probability sampling (closer to estimated class proportions)
class_prob <- apply(fs, 1, function(x) sample(1:2, 1, prob=x))
table(class_prob)
# plausible value imputations for stocastic classification in both classes
pvs <- fscores(mod2, plausible.draws=10)
tabs <- lapply(pvs, function(x) apply(x, 2, table))
tabs[[1]]
# fit with random starting points (run in parallel to save time)
mirtCluster()
mod <- mdirt(dat, 2, nruns=10)
#--------------------------
# Grade of measurement model
# define a custom Theta grid for including a 'fuzzy' class membership
(Theta <- matrix(c(1, 0, .5, .5, 0, 1), nrow=3 , ncol=2, byrow=TRUE))
(mod_gom <- mdirt(dat, 2, customTheta = Theta))
summary(mod_gom)
#-----------------
# Multidimensional discrete latent class model
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))
# define Theta grid for three latent classes
(Theta <- matrix(c(0,0,0, 1,0,0, 0,1,0, 0,0,1, 1,1,0, 1,0,1, 0,1,1, 1,1,1),
ncol=3, byrow=TRUE))
(mod_discrete <- mdirt(dat, 3, customTheta = Theta))
summary(mod_discrete)
# Located latent class model
model <- mirt.model('C1 = 1-32
C2 = 1-32
C3 = 1-32
CONSTRAIN = (1-32, a1), (1-32, a2), (1-32, a3)')
(mod_located <- mdirt(dat, model, customTheta = diag(3)))
summary(mod_located)
#-----------------
### DINA model example
# generate some suitable data for a two dimensional DINA application
# (first columns are intercepts)
set.seed(1)
Theta <- expand.table(matrix(c(1,0,0,0, 200,
1,1,0,0, 200,
1,0,1,0, 100,
1,1,1,1, 500), 4, 5, byrow=TRUE))
a <- matrix(c(rnorm(15, -1.5, .5), rlnorm(5, .2, .3), numeric(15), rlnorm(5, .2, .3),
numeric(15), rlnorm(5, .2, .3)), 15, 4)
guess <- plogis(a[11:15,1]) # population guess
slip <- 1 - plogis(rowSums(a[11:15,])) # population slip
dat <- simdata(a, Theta=Theta, itemtype = 'lca')
# first column is the intercept, 2nd and 3rd are attributes
theta <- matrix(c(1,0,0,
1,1,0,
1,0,1,
1,1,1), 4, 3, byrow=TRUE)
theta <- cbind(theta, theta[,2] * theta[,3]) #DINA interaction of main attributes
model <- mirt.model('Intercept = 1-15
A1 = 1-5
A2 = 6-10
A1A2 = 11-15')
mod <- mdirt(dat, model, customTheta = theta)
coef(mod)
summary(mod)
M2(mod) # fits well
cfs <- coef(mod, simplify=TRUE)$items[11:15,]
cbind(guess, estguess = plogis(cfs[,1]))
cbind(slip, estslip = 1 - plogis(rowSums(cfs)))
### DINO model example
theta <- matrix(c(1,0,0,
1,1,0,
1,0,1,
1,1,1), 4, 3, byrow=TRUE)
# define theta matrix with negative interaction term
theta <- cbind(theta, -theta[,2] * theta[,3])
model <- mirt.model('Intercept = 1-15
A1 = 1-5, 11-15
A2 = 6-15
Yoshi = 11-15
CONSTRAIN = (11,a2,a3,a4), (12,a2,a3,a4), (13,a2,a3,a4),
(14,a2,a3,a4), (15,a2,a3,a4)')
mod <- mdirt(dat, model, customTheta = theta)
coef(mod, simplify=TRUE)
summary(mod)
M2(mod) #doesn't fit as well, because not the generating model
#------------------
#multidimensional latent class model
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))
# 5 latent classes within 2 different sets of items
model <- mirt.model('C1 = 1-16
C2 = 1-16
C3 = 1-16
C4 = 1-16
C5 = 1-16
C6 = 17-32
C7 = 17-32
C8 = 17-32
C9 = 17-32
C10 = 17-32
CONSTRAIN = (1-16, a1), (1-16, a2), (1-16, a3), (1-16, a4), (1-16, a5),
(17-32, a6), (17-32, a7), (17-32, a8), (17-32, a9), (17-32, a10)')
theta <- diag(10)
mod <- mdirt(dat, model, customTheta = theta)
coef(mod, simplify=TRUE)
summary(mod)
#------------------
# multiple group with constrained group probabilities
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))
group <- rep(c('G1', 'G2'), each = nrow(SAT12)/2)
Theta <- diag(2)
# the latent class parameters are technically located in the (nitems + 1) location
model <- mirt.model('A1 = 1-32
A2 = 1-32
CONSTRAINB = (33, c1)')
mod <- mdirt(dat, model, group = group, customTheta = Theta)
coef(mod, simplify=TRUE)
summary(mod)
## End(Not run)
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