Qval (version 1.2.1)

fit: Calculate fit indeces

Description

Calculate relative fit indices (-2LL, AIC, BIC, CAIC, SABIC) and absolute fit indices (\(M_2\) test, \(RMSEA_2\), SRMSR) using the modelfit function in the GDINA package.

Usage

fit(Y, Q, model = "GDINA")

Value

An object of class list. The list contains various fit indices:

npar

The number of parameters.

-2LL

The Deviance.

AIC

The Akaike information criterion.

BIC

The Bayesian information criterion.

CAIC

The consistent Akaike information criterion.

SABIC

The Sample-size Adjusted BIC.

M2

A vector consisting of \(M_2\) statistic, degrees of freedom, significance level, and \(RMSEA_2\) (Liu, Tian, & Xin, 2016).

SRMSR

The standardized root mean squared residual (SRMSR; Ravand & Robitzsch, 2018).

Arguments

Y

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

Q

A required binary \(I\) × \(K\) matrix containing the attributes not required or required master the items. The ith row of the matrix is a binary indicator vector indicating which attributes are not required (coded by 0) and which attributes are required (coded by 1) to master item \(i\).

model

Type of model to be fitted; can be "GDINA", "LCDM", "DINA", "DINO", "ACDM", "LLM", or "rRUM". Default = "GDINA".

Author

Haijiang Qin <[e-mail]>

References

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.

Examples

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")

## calculate fit indices
fit.indices <- fit(Y = example.data$dat, Q = example.Q, model = "GDINA")
print(fit.indices)