GDINA (version 2.0.8)

modelcomp: Item-level model comparison using Wald, LR or LM tests

Description

This function evaluates whether the saturated G-DINA model can be replaced by reduced CDMs without significant loss in model data fit for each item using the Wald test, likelihood ratio (LR) test or Lagrange multiplier (LM) test. For Wald test, see de la Torre and Lee (2013), and Ma, Iaconangelo and de la Torre (2016) for details. For LR test and a two-step LR approximation procedure, see Sorrel, de la Torre, Abad, and Olea (2017) and Ma (2017). For LM test, which is only applicable for DINA, DINO and ACDM, see Sorrel, Abad, Olea, de la Torre, and Barrada (2017). This function also calculates the dissimilarity between the reduced models and the G-DINA model, which can be viewed as a measure of effect size (Ma, Iaconangelo & de la Torre, 2016).

Usage

modelcomp(GDINA.obj = NULL, method = "Wald", items = "all",
  p.adjust.methods = "bonferroni", models = c("DINA", "DINO", "ACDM", "LLM",
  "RRUM"), DS = FALSE, Wald.args = list(SE.type = 2, varcov = NULL),
  LR.args = list(LR.approx = FALSE), LM.args = list(reducedMDINA = NULL,
  reducedMDINO = NULL, reducedMACDM = NULL, SE.type = 2))
# S3 method for modelcomp
extract(object, what = c("stats", "pvalues",
  "adj.pvalues", "df", "DS", "models"), digits = 4, ...)
# S3 method for modelcomp
summary(object, ...)

Arguments

GDINA.obj

An estimated model object of class GDINA

method

method for item level model comparison; can be wald, LR or LM.

items

a vector of items to specify the items for model comparsion

p.adjust.methods

adjusted p-values for multiple hypothesis tests. This is conducted using p.adjust function in stats, and therefore all adjustment methods supported by p.adjust can be used, including "holm", "hochberg", "hommel", "bonferroni", "BH" and "BY". See p.adjust for more details. "bonferroni" is the default.

models

a vector specifying which reduced CDMs are possible reduced CDMs for each item. The default is "DINA","DINO","ACDM","LLM",and "RRUM".

DS

whether dissimilarity index should be calculated? FALSE is the default.

Wald.args

a list of options for Wald test including (1) SE.type giving the type of covariance matrix for the Wald test; by default, it uses outer product of gradient based on incomplete information matrix; (2) varcov for user specified variance-covariance matrix. If supplied, it must be a list, giving the variance covariance matrix of success probability for each item or category. The default is NULL, in which case, the estimated variance-covariance matrix from the GDINA function is used.

LR.args

a list of options for LR test including for now only LR.approx, which is either TRUE or FALSE, indicating whether a two-step LR approximation is implemented or not.

LM.args

a list of options for LM test including reducedMDINA, reducedMDINO, and reducedMACDM for DINA, DINO and ACDM estimates from the GDINA function; SE.type specifies the type of covariance matrix.

object

object of class modelcomp for various S3 methods

what

argument for S3 method extract indicating what to extract; It can be "wald" for wald statistics, "wald.p" for associated p-values, "df" for degrees of freedom, and "DS" for dissimilarity between G-DINA and other CDMs.

digits

How many decimal places in each number? The default is 4.

...

additional arguments

Value

an object of class modelcomp. Elements that can be extracted using extract method include

stats

Wald or LR statistics

pvalues

p-values associated with the test statistics

adj.pvalues

adjusted p-values

df

degrees of freedom

DS

dissimilarity between G-DINA and other CDMs

Methods (by generic)

• extract: extract various elements from modelcomp objects

• summary: print summary information

References

de la Torre, J., & Lee, Y. S. (2013). Evaluating the wald test for item-level comparison of saturated and reduced models in cognitive diagnosis. Journal of Educational Measurement, 50, 355-373.

Ma, W., Iaconangelo, C., & de la Torre, J. (2016). Model similarity, model selection and attribute classification. Applied Psychological Measurement, 40, 200-217.

Ma, W. (2017). A Sequential Cognitive Diagnosis Model for Graded Response: Model Development, Q-Matrix Validation,and Model Comparison. Unpublished doctoral dissertation. New Brunswick, NJ: Rutgers University.

Sorrel, M. A., Abad, F. J., Olea, J., de la Torre, J., & Barrada, J. R. (2017). Inferential Item-Fit Evaluation in Cognitive Diagnosis Modeling. Applied Psychological Measurement, 41, 614-631.

Sorrel, M. A., de la Torre, J., Abad, F. J., & Olea, J. (2017). Two-Step Likelihood Ratio Test for Item-Level Model Comparison in Cognitive Diagnosis Models. Methodology, 13, 39-47.

See Also

GDINA, autoGDINA

Examples

# NOT RUN {
dat <- sim10GDINA$simdat
Q <- sim10GDINA$simQ
# --- GDINA model ---#
fit <- GDINA(dat = dat, Q = Q, model = "GDINA")
fit

###################
#
# Wald test
#
###################

w <- modelcomp(fit)
w
# wald statistics
extract(w,"stats")
#p values
extract(w,"pvalues")

##########################
#
# LR and Two-step LR test
#
##########################

lr <- modelcomp(fit,models = c("DINA","DINO"),method = "LR")
lr
TwostepLR <- modelcomp(fit,items =c(6:10),method = "LR",LR.args = list(LR.approx = TRUE))
TwostepLR

##########################
#
# LM test
#
##########################

dina <- GDINA(dat = dat, Q = Q, model = "DINA")
dino <- GDINA(dat = dat, Q = Q, model = "DINO")
acdm <- GDINA(dat = dat, Q = Q, model = "ACDM")
lm <- modelcomp(method = "LM",LM.args=list(reducedMDINA = dina,
reducedMDINO = dino, reducedMACDM  = acdm))
lm


# }