GDINA (version 1.4.2)

autoGDINA: Q-matrix validation, model selection and calibration in one run

Description

autoGDINA conducts a series of CDM analyses within the G-DINA framework. Particularly, the GDINA model is fitted to the data first using the GDINA function; then, the Q-matrix is validated using the function Qval. Based on the suggested Q-matrix, the data is fitted by the G-DINA model again, followed by an item level model selection via the Wald test using modelcomp. Lastly, the selected models are calibrated based on the suggested Q-matrix using the GDINA function. The Q-matrix validation and item-level model selection can be disabled by the users. Possible reduced CDMs for Wald test include the DINA model, the DINO model, A-CDM, LLM and RRUM. See Details for the rules of item-level model selection.

Usage

autoGDINA(dat, Q, modelselection = TRUE, Qvalid = TRUE,
  reducedCDM = c("DINA", "DINO", "ACDM", "LLM", "RRUM"), alpha.level = 0.05,
  modelselectionrule = "simpler", eps = 0.95, GDINA1.option = list(),
  GDINA2.option = list(), CDM.option = list())
# S3 method for autoGDINA
summary(object, ...)

Arguments

dat

A required \(N \times J\) matrix or data.frame consisting of the responses of \(N\) individuals to \(J\) items. Missing values need to be coded as NA.

Q

A required \(J \times K\) item or category and attribute association matrix, wher \(J\) represents the number of items or nonzero categories and \(K\) represents the number of attributes. For binary attributes, entry 1 indicates that the attribute is measured by the item, and 0 otherwise. For polytomous attributes, non-zero elements indicate the level of attributes that are needed for an individual to answer the item correctly (see Chen, & de la Torre, 2013). Note that for polytomous items, the sequential G-DINA model is used and either restricted or unrestricted category-level Q-matrix is needed. In the category-level Q-matrix, the first column gives the item number, which must be numeric and match the number of column in the data. The second column indicates the category number. See Examples.

modelselection

logical; conducting model selection or not?

Qvalid

logical; validate Q-matrix or not? TRUE is the default.

reducedCDM

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

alpha.level

nominal level for the Wald test. The default is 0.05.

modelselectionrule

how to conducted model selection? Possible options include simpler, largestp and DS. See Details.

eps

cut-off value for PVAF if Qvalid=TRUE. The default is 0.95.

GDINA1.option

options for initial G-DINA calibration

GDINA2.option

options for second G-DINA calibration

CDM.option

options for final calibration

object

estimated GDINA object for various S3 methods

...

additional arguments

Value

a list consisting of the following elements:

GDINA1.obj

initial GDINA calibration of class GDINA

GDINA2.obj

second GDINA calibration of class GDINA

Qval.obj

Q validation object of class Qval

Wald.obj

model comparison object of class modelcomp

CDM.obj

Final CDM calibration of class GDINA

Methods (by generic)

• summary: print summary information

Details

After the Wald statistics for each reduced CDM were calculated for each item, the reduced models with p values less than the pre-specified alpha level were rejected. If all reduced models were rejected for an item, the G-DINA model was used as the best model; if at least one reduced model was retained, three diferent rules can be implemented for selecting the best model: when modelselectionrule is simpler: If (a) the DINA or DINO model was one of the retained models, then the DINA or DINO model with the larger p value was selected as the best model; but if (b) both DINA and DINO were rejected, the reduced model with the largest p value was selected as the best model for this item. Note that when the p-values of several reduced models were greater than 0.05, the DINA and DINO models were preferred over the A-CDM, LLM, and R-RUM because of their simplicity. This procedure is originally proposed by Ma, Iaconangelo, and de la Torre (2016). When modelselectionrule is largestp: The reduced model with the largest p-values is selected as the most appropriate model. When modelselectionrule is DS: The reduced model with non-significant p-values but the smallest dissimilarity index is selected as the most appropriate model. Dissimilarity index can be viewed as an effect size measure, which quatifies how dis-similar the reduced model is from the G-DINA model. See Ma, Iaconangelo, and de la Torre (2016).

References

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

See Also

GDINA, modelcomp, Qval

Examples

## Not run: ------------------------------------
# # simulated responses
# Q <- sim10GDINA$simQ
# dat <- sim10GDINA$simdat
# 
# #misspecified Q
# misQ <- Q
# misQ[10,] <- c(0,1,0)
# out1 <- autoGDINA(dat,misQ,modelselectionrule="largestp")
# out1
# summary(out1)
# AIC(out1$CDM.obj)
# 
# 
# 
# #using the other selection rule
# out11 <- autoGDINA(dat,misQ,modelselectionrule="simpler",reducedCDM = c("DINO","DINA"))
# out11
# summary(out11)
# 
# # disable model selection function
# out12 <- autoGDINA(dat,misQ,modelselection=FALSE)
# out12
# summary(out12)
# 
# # -- Only consider some reduced CDMs
# out2 <- autoGDINA(dat,misQ,reducedCDM = c("RRUM","LLM"))
# 
# # Disable Q-matrix validation
# out3 <- autoGDINA(dat = dat, Q = misQ, Qvalid = FALSE,alpha.level=0.01)
# out3
# summary(out3)
## ---------------------------------------------