8.11 Item-level Relative Fit measures (Cont’d)

Code

library(GDINA)
Y <- sim10GDINA$simdat
head(Y)

##      [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10]
## [1,]    1    0    1    1    0    1    1    1    0     1
## [2,]    1    1    1    1    1    1    1    1    0     1
## [3,]    1    1    1    0    1    1    1    0    1     0
## [4,]    1    0    1    1    1    1    1    1    1     0
## [5,]    0    0    1    1    0    0    1    0    0     0
## [6,]    1    0    0    0    0    0    0    1    0     1

Code

Q <- sim10GDINA$simQ
Q

##       [,1] [,2] [,3]
##  [1,]    1    0    0
##  [2,]    0    1    0
##  [3,]    0    0    1
##  [4,]    1    0    1
##  [5,]    0    1    1
##  [6,]    1    1    0
##  [7,]    1    0    1
##  [8,]    1    1    0
##  [9,]    0    1    1
## [10,]    1    1    1

To implement Wald test, we need to fit G-DINA model to the data first.

Code

fit.gdina <- GDINA(Y,Q,model = "GDINA",verbose = 0)

The Wald test can be requested by calling modelcomp function:

Code

mc <- modelcomp(fit.gdina)
mc

## 
## Item-level model selection:
## 
## test statistic: Wald 
## Decision rule: largest p value rule at 0.05 alpha level.
## Adjusted p values were based on holm correction.
## 
##         models pvalues adj.pvalues
## Item 1   GDINA                    
## Item 2   GDINA                    
## Item 3   GDINA                    
## Item 4    RRUM  0.3338           1
## Item 5    DINA  0.7991           1
## Item 6    DINO  0.8077           1
## Item 7    ACDM  0.6123           1
## Item 8    RRUM    0.32           1
## Item 9     LLM  0.9021           1
## Item 10   RRUM  0.5674           1

To extract the Wald statistics,

Code

extract(mc,what = "stats")

##           DINA   DINO   ACDM    LLM  RRUM
## Item 4   52.80 164.91  10.78  4.429  0.93
## Item 5    0.45 342.82 150.80 40.142 21.03
## Item 6  211.44   0.43  99.90 23.768 42.35
## Item 7   93.09  58.96   0.26  3.344  9.46
## Item 8   14.47 167.27  36.59 12.110  0.99
## Item 9   48.19 102.18   2.30  0.015  3.61
## Item 10  91.71 194.74  11.99  7.011  2.94

To extract the p values,

Code

extract(mc,what = "pvalues")

##          DINA DINO  ACDM    LLM   RRUM
## Item 4  0e+00 0.00 0.001 0.0353 0.3338
## Item 5  8e-01 0.00 0.000 0.0000 0.0000
## Item 6  0e+00 0.81 0.000 0.0000 0.0000
## Item 7  0e+00 0.00 0.612 0.0675 0.0021
## Item 8  7e-04 0.00 0.000 0.0005 0.3200
## Item 9  0e+00 0.00 0.129 0.9021 0.0574
## Item 10 0e+00 0.00 0.018 0.1353 0.5674

To extract the Wald-selected models, we can use extract() function:

Code

wald.model <- extract(mc,what = "selected.model")

To fit the selected models to the data, call GDINA function again:

Code

fit.wald <- GDINA(Y,Q,model = wald.model$models,verbose = 0)