fit.RdCalculate relative fit indices (-2LL, AIC, BIC, CAIC, SABIC) and absolute fit indices (\(M_2\) test)
using the testfit function in the GDINA package.
fit(Y, Q, model = "GDINA")A required N × I matrix or data.frame consisting of the responses of N
individuals to I items. Missing values should be coded as NA.
A required binary I × K matrix containing the attributes not required or required
, coded as 0 or 1, to master the items. The ith row of the matrix is a binary indicator vector
indicating which attributes are not required (coded as 0) and which attributes are required
(coded as 1) to master item i.
Type of model to be fitted; can be "GDINA", "LCDM", "DINA", "DINO",
"ACDM", "LLM", or "rRUM". Default = "GDINA".
An object of class list. The list contains various fit indices:
The number of parameters.
The Deviance.
The Akaike information criterion.
The Bayesian information criterion.
The consistent Akaike information criterion.
The Sample size Adjusted BIC.
A vector consisting of \(M_2\) statistic, degrees of freedom, significance level, and \(RMSEA_2\) (Liu, Tian, & Xin, 2016).
The standardized root mean squared residual (SRMSR; Ravand & Robitzsch, 2018).
Khaldi, R., Chiheb, R., & Afa, A.E. (2018). Feed-forward and Recurrent Neural Networks for Time Series Forecasting: Comparative Study. In: Proceedings of the International Conference on Learning and Optimization Algorithms: Theory and Applications (LOPAL 18). Association for Computing Machinery, New York, NY, USA, Article 18, 1–6. DOI: 10.1145/3230905.3230946.
Liu, Y., Tian, W., & Xin, T. (2016). An application of M2 statistic to evaluate the fit of cognitive diagnostic models. Journal of Educational and Behavioral Statistics, 41, 3–26. DOI: 10.3102/1076998615621293.
Ravand, H., & Robitzsch, A. (2018). Cognitive diagnostic model of best choice: a study of reading comprehension. Educational Psychology, 38, 1255–1277. DOI: 10.1080/01443410.2018.1489524.
set.seed(123)
library(Qval)
## generate Q-matrix and data to fit
K <- 5
I <- 30
example.Q <- sim.Q(K, I)
IQ <- list(
P0 = runif(I, 0.0, 0.2),
P1 = runif(I, 0.8, 1.0)
)
example.data <- sim.data(Q = example.Q, N = 500, IQ = IQ, model = "GDINA", distribute = "horder")
#> distribute = horder
#> model = GDINA
#> number of attributes: 5
#> number of items: 30
#> num of examinees: 500
#> average of P0 = 0.102
#> average of P1 = 0.905
#> theta_mean = -0.064 , theta_sd = 0.994
#> a = 1.5 1.5 1.5 1.5 1.5
#> b = 0 -0.75 -1.5 1.5 0.75
## calculate fit indices
fit.indices <- fit(Y = example.data$dat, Q = example.Q, model = "GDINA")
#>
Iter = 1 Max. abs. change = 0.47924 Deviance = 15962.63
Iter = 2 Max. abs. change = 0.13841 Deviance = 13443.96
Iter = 3 Max. abs. change = 0.07686 Deviance = 13314.35
Iter = 4 Max. abs. change = 0.03944 Deviance = 13292.46
Iter = 5 Max. abs. change = 0.02354 Deviance = 13286.48
Iter = 6 Max. abs. change = 0.02056 Deviance = 13283.80
Iter = 7 Max. abs. change = 0.01822 Deviance = 13282.25
Iter = 8 Max. abs. change = 0.01478 Deviance = 13281.32
Iter = 9 Max. abs. change = 0.01097 Deviance = 13280.79
Iter = 10 Max. abs. change = 0.00756 Deviance = 13280.47
Iter = 11 Max. abs. change = 0.00494 Deviance = 13280.26
Iter = 12 Max. abs. change = 0.00311 Deviance = 13280.13
Iter = 13 Max. abs. change = 0.00191 Deviance = 13280.04
Iter = 14 Max. abs. change = 0.00116 Deviance = 13279.97
Iter = 15 Max. abs. change = 0.00070 Deviance = 13279.93
Iter = 16 Max. abs. change = 0.00048 Deviance = 13279.89
Iter = 17 Max. abs. change = 0.00038 Deviance = 13279.87
Iter = 18 Max. abs. change = 0.00030 Deviance = 13279.85
Iter = 19 Max. abs. change = 0.00024 Deviance = 13279.83
Iter = 20 Max. abs. change = 0.00019 Deviance = 13279.82
Iter = 21 Max. abs. change = 0.00016 Deviance = 13279.81
Iter = 22 Max. abs. change = 0.00013 Deviance = 13279.80
Iter = 23 Max. abs. change = 0.00011 Deviance = 13279.79
Iter = 24 Max. abs. change = 0.00009 Deviance = 13279.79
print(fit.indices)
#> $npar
#> [1] 149
#>
#> $`-2LL`
#> [1] 13279.78
#>
#> $AIC
#> [1] 13577.78
#>
#> $BIC
#> [1] 14205.76
#>
#> $CAIC
#> [1] 14354.76
#>
#> $SABIC
#> [1] 13732.82
#>
#> $M2
#> M2 df p.value RMSEA2
#> 307.4313228 316.0000000 0.6245266 0.0000000
#>
#> $SRMSR
#> [1] 0.02965562
#>