reglca function

Regularized Latent Class Analysis

Estimates the regularized latent class model for dichotomous responses based on regularization methods (Chen, Liu, Xu, & Ying, 2015; Chen, Li, Liu, & Ying, 2017). The SCAD and MCP penalty functions are available.

reglca(dat, nclasses, weights=NULL, group=NULL, regular_type="scad",
   regular_lam=0, sd_noise_init=1, item_probs_init=NULL, class_probs_init=NULL,
   random_starts=1, random_iter=20, conv=1e-05, h=1e-04, mstep_iter=10,
   maxit=1000, verbose=TRUE, prob_min=.0001)

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

Arguments

• dat: Matrix with dichotomous item responses. NAs are allowed.

• nclasses: Number of classes

• weights: Optional vector of sampling weights

• group: Optional vector for grouping variable

• regular_type: Regularization type. Can be scad or mcp. See gdina for more information.

• regular_lam: Regularization parameter $\lambda$

• sd_noise_init: Standard deviation for amount of noise in generating random starting values

• item_probs_init: Optional matrix of initial item response probabilities

• class_probs_init: Optional vector of class probabilities

• random_starts: Number of random starts

• random_iter: Number of initial iterations for random starts

• conv: Convergence criterion

• h: Numerical differentiation parameter

• mstep_iter: Number of iterations in the M-step

• maxit: Maximum number of iterations

• verbose: Logical indicating whether convergence progress should be displayed

• prob_min: Lower bound for probabilities in estimation

• object: A required object of class gdina, obtained from a call to the function gdina.

• digits: Number of digits after decimal separator to display.

• file: Optional file name for a file in which summary

  should be sinked.

• ...: Further arguments to be passed.

Details

The regularized latent class model for dichotomous item responses assumes $C$

latent classes. The item response probabilities $P(X_i=1|c)=p_{ic}$ are estimated in such a way such that the number of different $p_{ic}$ values per item is minimized. This approach eases interpretability and enables to recover the structure of a true (but unknown) cognitive diagnostic model.

Returns

A list containing following elements (selection):

• item_probs: Item response probabilities

• class_probs: Latent class probabilities

• p.aj.xi: Individual posterior

• p.xi.aj: Individual likelihood

• loglike: Log-likelihood value

• Npars: Number of estimated parameters

• Nskillpar: Number of skill class parameters

• G: Number of groups

• n.ik: Expected counts

• Nipar: Number of item parameters

• n_reg: Number of regularized parameters

• n_reg_item: Number of regularized parameters per item

• item: Data frame with item parameters

• pjk: Item response probabilities (in an array)

• N: Number of persons

• I: Number of items

References

Chen, Y., Liu, J., Xu, G., & Ying, Z. (2015). Statistical analysis of Q-matrix based diagnostic classification models. Journal of the American Statistical Association, 110, 850-866.

Chen, Y., Li, X., Liu, J., & Ying, Z. (2017). Regularized latent class analysis with application in cognitive diagnosis. Psychometrika, 82, 660-692.

See Also

See also the gdina and slca functions for regularized estimation.

Examples

## Not run:

#############################################################################
# EXAMPLE 1: Estimating a regularized LCA for DINA data
#############################################################################

#---- simulate data
I <- 12  # number of items
# define Q-matrix
q.matrix <- matrix(0,I,2)
q.matrix[ 1:(I/3), 1 ] <- 1
q.matrix[ I/3 + 1:(I/3), 2 ] <- 1
q.matrix[ 2*I/3 + 1:(I/3), c(1,2) ] <- 1
N <- 1000  # number of persons
guess <- rep(seq(.1,.3,length=I/3), 3)
slip <- .1
rho <- 0.3  # skill correlation
set.seed(987)
dat <- CDM::sim.din( N=N, q.matrix=q.matrix, guess=guess, slip=slip,
           mean=0*c( .2, -.2 ), Sigma=matrix( c( 1, rho,rho,1), 2, 2 ) )
dat <- dat$dat

#--- Model 1: Four latent classes without regularization
mod1 <- CDM::reglca(dat=dat, nclasses=4, regular_lam=0, random_starts=3,
               random_iter=10, conv=1E-4)
summary(mod1)

#--- Model 2: Four latent classes with regularization and lambda=.08
mod2 <- CDM::reglca(dat=dat, nclasses=4, regular_lam=0.08, regular_type="scad",
               random_starts=3, random_iter=10, conv=1E-4)
summary(mod2)

#--- Model 3: Four latent classes with regularization and lambda=.05 with warm start

# "warm start" -> use initial parameters from fitted model with higher lambda value
item_probs_init <- mod2$item_probs
class_probs_init <- mod2$class_probs
mod3 <- CDM::reglca(dat=dat, nclasses=4, regular_lam=0.05, regular_type="scad",
               item_probs_init=item_probs_init, class_probs_init=class_probs_init,
               random_starts=3, random_iter=10, conv=1E-4)
## End(Not run)