DTMR Fraction Data (Bradshaw et al., 2014)
This is a simulated dataset of the DTMR fraction data described in Bradshaw, Izsak, Templin and Jacobson (2014).
data(data.dtmr)
The format is:
List of 5 $ data : num [1:5000, 1:27] 0 0 0 0 0 1 0 0 1 1 ... ..- attr(*, "dimnames")=List of 2 .. ..$ : NULL .. ..$ : chr [1:27] "M1" "M2" "M3" "M4" ... $ q.matrix :'data.frame': 27 obs. of 4 variables: ..$ RU : int [1:27] 1 0 0 1 1 0 1 0 0 0 ... ..$ PI : int [1:27] 0 0 1 0 0 1 0 0 0 0 ... ..$ APP: int [1:27] 0 1 0 0 0 0 0 1 1 1 ... ..$ MC : int [1:27] 0 0 0 0 0 0 0 0 0 0 ... $ skill.distribution:'data.frame': 16 obs. of 5 variables: ..$ RU : int [1:16] 0 0 0 0 0 0 0 0 1 1 ... ..$ PI : int [1:16] 0 0 0 0 1 1 1 1 0 0 ... ..$ APP : int [1:16] 0 0 1 1 0 0 1 1 0 0 ... ..$ MC : int [1:16] 0 1 0 1 0 1 0 1 0 1 ... ..$ freq: int [1:16] 1064 350 280 406 196 126 238 770 14 28 ... $ itempars :'data.frame': 27 obs. of 7 variables: ..$ item : chr [1:27] "M1" "M2" "M3" "M4" ... ..$ lam0 : num [1:27] -1.12 0.59 -2.07 -1.19 -1.67 -3.81 -0.73 -0.62 -0.09 0.28 ... ..$ RU : num [1:27] 2.24 0 0 0.65 1.52 0 1.2 0 0 0 ... ..$ PI : num [1:27] 0 0 1.7 0 0 2.08 0 0 0 0 ... ..$ APP : num [1:27] 0 1.27 0 0 0 0 0 4.25 2.16 0.87 ... ..$ MC : num [1:27] 0 0 0 0 0 0 0 0 0 0 ... ..$ RU.PI: num [1:27] 0 0 0 0 0 0 0 0 0 0 ... $ sim_data :function (N, skill.distribution, itempars) ..- attr(*, "srcref")='srcref' int [1:8] 1 13 20 1 13 1 1 20 .. ..- attr(*, "srcfile")=Classes 'srcfilecopy', 'srcfile' <environment: 0x00000000298a8ed0>
The attribute definition are as follows
RU: Referent units
PI: Partitioning and iterating attribute
APP: Appropriateness attribute
MC: Multiplicative Comparison attribute
Simulated dataset according to Bradshaw et al. (2014).
Bradshaw, L., Izsak, A., Templin, J., & Jacobson, E. (2014). Diagnosing teachers' understandings of rational numbers: Building a multidimensional test within the diagnostic classification framework. Educational Measurement: Issues and Practice, 33, 2-14.
## Not run:
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# EXAMPLE 1: Model comparisons data.dtmr
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data(data.dtmr, package="CDM")
data <- data.dtmr$data
q.matrix <- data.dtmr$q.matrix
I <- ncol(data)
#*** Model 1: LCDM
# define item wise rules
rule <- rep( "ACDM", I )
names(rule) <- colnames(data)
rule[ c("M14","M17") ] <- "GDINA2"
# estimate model
mod1 <- CDM::gdina( data, q.matrix, linkfct="logit", rule=rule)
summary(mod1)
#*** Model 2: DINA model
mod2 <- CDM::gdina( data, q.matrix, rule="DINA" )
summary(mod2)
#*** Model 3: RRUM model
mod3 <- CDM::gdina( data, q.matrix, rule="RRUM" )
summary(mod3)
#--- model comparisons
# LCDM vs. DINA
anova(mod1,mod2)
## Model loglike Deviance Npars AIC BIC Chisq df p
## 2 Model 2 -76570.89 153141.8 69 153279.8 153729.5 1726.645 10 0
## 1 Model 1 -75707.57 151415.1 79 151573.1 152088.0 NA NA NA
# LCDM vs. RRUM
anova(mod1,mod3)
## Model loglike Deviance Npars AIC BIC Chisq df p
## 2 Model 2 -75746.13 151492.3 77 151646.3 152148.1 77.10994 2 0
## 1 Model 1 -75707.57 151415.1 79 151573.1 152088.0 NA NA NA
#--- model fit
summary( CDM::modelfit.cor.din( mod1 ) )
## Test of Global Model Fit
## type value p
## 1 max(X2) 7.74382 1.00000
## 2 abs(fcor) 0.04056 0.72707
##
## Fit Statistics
## est
## MADcor 0.00959
## SRMSR 0.01217
## MX2 0.75696
## 100*MADRESIDCOV 0.20283
## MADQ3 0.02220
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# EXAMPLE 2: Simulating data of structure data.dtmr
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data(data.dtmr, package="CDM")
# draw sample of N=200
set.seed(87)
data.dtmr$sim_data(N=200, skill.distribution=data.dtmr$skill.distribution,
itempars=data.dtmr$itempars)
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