mcdina: Multiple Choice DINA Model

In CDM: Cognitive Diagnosis Modeling

Multiple Choice DINA Model

Description

The function mcdina implements the multiple choice DINA model (de la Torre, 2009; see also Ozaki, 2015; Chen & Zhou, 2017) for multiple groups. Note that the dataset must contain integer values 1,…, K_j for each item. The multiple choice DINA model assumes that each item category possesses different diagnostic capacity. Using this modeling approach, different distractors of a multiple choice item can be of different diagnostic value. The Q-matrix can also contain integer values which allows the definition of polytomous attributes.

Usage

mcdina(dat, q.matrix, group=NULL, itempars="gr", weights=NULL,
    skillclasses=NULL, zeroprob.skillclasses=NULL,
    reduced.skillspace=TRUE, conv.crit=1e-04,
    dev.crit=0.1, maxit=1000, progress=TRUE)

## S3 method for class 'mcdina'
summary(object, digits=4, file=NULL,  ...)

## S3 method for class 'mcdina'
print(x, ...)

Arguments

dat	A required N \times J data matrix containing integer responses (1, 2, …, K) of N respondents to J test items.
q.matrix	A required matrix specifying which item category is intended to measure which skill. The Q-matrix has K+2 columns for a model with K skills. In the first column should be the item index, in the second column the category integer and the rest of the columns contains the 'ordinary' Q-matrix specification. See data.cdm01$q.matrix for the layout of such a Q-matrix.
group	An optional vector of group identifiers for multiple group estimation.
itempars	A character or a character vector of length J indicating whether item parameters should separately estimated within each group. The default is "gr", for group-invariant item parameters choose "jo".
weights	An optional vector of sample weights.
skillclasses	An optional matrix for determining the skill space. The argument can be used if a user wants less than the prespecified number of 2^K skill classes.
zeroprob.skillclasses	An optional vector of integers which indicates which skill classes should have zero probability. Default is NULL (no skill classes with zero probability).
reduced.skillspace	An optional logical indicating whether the skill space should be reduced to cover only bivariate associations among skills (see Xu & von Davier, 2008).
conv.crit	Convergence criterion for change in item parameter values
dev.crit	Convergence criterion for change in deviance values
maxit	Maximum number of iterations.
progress	An optional logical indicating whether the function should print the progress of iteration in the estimation process.
object	Object of class mcdina.
digits	Number of digits to display in summary.mcdina
file	Optional file name for a file in which summary should be sinked.
x	Object of class mcdina
...	Further arguments to be passed.

Details

The multiple choice DINA model defines for each item category jc the necessary skills to master this attribute. Therefore, the vector of skills \bold{α} is transformed into item-specific latent responses η_{j} which are functions of \bold{α} and Q-matrix entries q_{jc} (just like in the DINA model). If there are K_j item categories for item j, then there exist at most K_j values of the latent response η_j.

The multiple choice DINA model estimates the item response function as

P( X_{nj}=k | η_{nj}=l )=p_{jkl}

with the constraint ∑_k p_{jkl}=1 .

Value

A list with following entries

item	Data frame with item parameters
posterior	Individual posterior distribution
likelihood	Individual likelihood
ic	List with information criteria
q.matrix	Used Q-matrix
pik	Array of item-category probabilities
delta	Array of item parameters
se.delta	Array of standard errors of item parameters
itemstat	Data frame containing item definitions
n.ik	Array of expected counts
deviance	Deviance
attribute.patt	Probabilities of latent classes
attribute.patt.splitted	Splitted attribute pattern
skill.patt	Marginal skill probabilities
MLE.class	Classified skills for each student (MLE)
MAP.class	Classified skills for each student (MAP)
EAP.class	Classified skills for each student (EAP)
dat	Used dataset
skillclasses	Used skill classes
group	Used group identifiers
lc	Data frame containing definitions of each item category
lr	Data frame containing the relation of each latent class and each item category
iter	Number of iterations
itempars	Used specification of item parameter estimation type
converged	Logical indicating whether convergence was achieved.

Note

If dat and q.matrix correspond to the 'ordinary format' which is used in gdina, then the function mcdina will detect it and convert it into the necessary format (see Example 2).

References

Chen, J., & Zhou, H. (2017) Test designs and modeling under the general nominal diagnosis model framework. PLoS ONE 12(6), e0180016.

de la Torre, J. (2009). A cognitive diagnosis model for cognitively based multiple-choice options. Applied Psychological Measurement, 33, 163-183.

Ozaki, K. (2015). DINA models for multiple-choice items with few parameters: Considering incorrect answers. Applied Psychological Measurement, 39(6), 431-447.

Xu, X., & von Davier, M. (2008). Fitting the structured general diagnostic model to NAEP data. ETS Research Report ETS RR-08-27. Princeton, ETS.

See Also

See din for estimating the DINA/DINO model and gdina for estimating the GDINA model.

Examples

#############################################################################
# EXAMPLE 1: Multiple choice DINA model for data.cdm01 dataset
#############################################################################

data(data.cdm01, package="CDM")

dat <- data.cdm01$data
group <- data.cdm01$group
q.matrix <- data.cdm01$q.matrix

#*** Model 1: Single group model
mod1 <- CDM::mcdina( dat=dat, q.matrix=q.matrix )
summary(mod1)

#*** Model 2: Multiple group model with group-invariant item parameters
mod2 <- CDM::mcdina( dat=dat, q.matrix=q.matrix, group=group, itempars="jo")
summary(mod2)

## Not run: 
#*** Model 3: Multiple group model with group-specific item parameters
mod3 <- CDM::mcdina( dat=dat, q.matrix=q.matrix, group=group, itempars="gr")
summary(mod3)

#*** Model 4: Multiple group model with some group-specific item parameters
itempars <- rep("jo", ncol(dat))
itempars[ c( 2, 7, 9) ] <- "gr" # set items 2,7 and 9 group specific
mod4 <- CDM::mcdina( dat=dat, q.matrix=q.matrix, group=group, itempars=itempars)
summary(mod4)

#*** Model 5: Reduced skill space

# define skill classes
skillclasses <- scan(nlines=1)  # read only one line
    0 0 0    1 0 0    0 1 0    0 0 1    1 1 0     1 1 1
skillclasses <- matrix( skillclasses, ncol=3, byrow=TRUE )
mod5 <- CDM::mcdina( dat, q.matrix=q.matrix, group=group0,  skillclasses=skillclasses )
summary(mod5)

#*** Model 6: Reduced skill space with setting zero probabilities
#             for some latent classes

# set probabilities of classes P101 P011 (6th and 7th class) to zero
zeroprob.skillclasses <- c(6,7)
mod6 <- CDM::mcdina( dat, q.matrix, group=group, zeroprob.skillclasses=zeroprob.skillclasses )
summary(mod6)

#############################################################################
# EXAMPLE 2: Using the mcdina function for estimating the DINA model
#############################################################################

data(sim.dina, package="CDM")
data(sim.qmatrix, package="CDM")

# estimate the DINA model
mod <- CDM::mcdina( sim.dina, q.matrix=sim.qmatrix )
summary(mod)

#############################################################################
# EXAMPLE 3: MCDINA model with polytomous attributes
#############################################################################

data(data.cdm02, package="CDM")
dat <- data.cdm02$data
q.matrix <- data.cdm02$q.matrix

# estimate model with polytomous attribute B1
mod1 <- CDM::mcdina( dat, q.matrix=q.matrix )
summary(mod1)

## End(Not run)

CDM documentation built on Aug. 25, 2022, 5:08 p.m.