Description Usage Arguments Value Author(s) References Examples

A function to estimate marginal and test reliability from estimated item response theory models.

1 | ```
irtreliability(input, model, cats, relcoef = "trc", nquad = 49, SE = TRUE)
``` |

`input` |
An object of class SingleGroupClass from package mirt. |

`model` |
A character vector indicating the item response theory model used, options are "GPCM" and "3-PL". |

`cats` |
A numeric vector indicating the number of possible categories for each item. |

`relcoef` |
A character vector indicting which reliability coefficients to calculate, options are "mrc" for the marginal reliability coefficient and "trc" for the test reliability coefficient. |

`nquad` |
The number of Gauss-Hermite quadrature points to be used. |

`SE` |
A logical vector denoting whether the standard errors for the reliability coefficient estimates should be calculated. |

An S4 object of class 'relout' which includes the following slots

`est` |
The estimated coefficient. |

`cov` |
The estimated variance. |

`pder` |
The partial derivatives of the coefficient with respect to the item parameters. |

`type` |
The type of coefficient. |

Andersson, B. and Xin, T. (2018). Large Sample Confidence Intervals for Item Response Theory Reliability Coefficients. *Educational and Psychological Measurement*, 78, 32-45.

Cheng, Y., Yuan, K.-H. and Liu, C. (2012). Comparison of reliability measures under factor analysis and item response theory. *Educational and Psychological Measurement*, 72, 52-67.

Green, B. F., Bock, R. D., Humphreys, L. G., Linn, R. L. and Reckase, M. D. (1984). Technical guidelines for assessing computerized adaptive tests. *Journal of Educational Measurement*, 21, 347-360.

Kim, S. (2012). A note on the reliability coefficients for item response model-based ability estimates. *Psychometrika*, 77, 153-162.

Kim, S. and Feldt, L. S. (2010). The estimation of the IRT reliability coefficient and its lower and upper bounds, with comparisons to CTT reliability statistics. *Asia Pacific Education Review*, 11, 179-188.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
#Generate 2-PL data
set.seed(14)
akX <- runif(15, 0.5, 2)
bkX <- rnorm(15)
data2pl <- matrix(0, nrow = 1000, ncol = 15)
for(i in 1:1000){
ability <- rnorm(1)
data2pl[i,1:15] <- (1 / (1 + exp(-akX *(ability - bkX)))) > runif(15)
}
#Estimate the 2-PL IRT model with package mirt
library(mirt)
sim2pl <- mirt(data.frame(data2pl), 1, "gpcm", SE = TRUE)
mrc2pl <- irtreliability(sim2pl, "GPCM", rep(2, 15), relcoef = "mrc")
trc2pl <- irtreliability(sim2pl, "GPCM", rep(2, 15))
``` |

```
Loading required package: stats4
Loading required package: lattice
Iteration: 1, Log-Lik: -8451.768, Max-Change: 0.49027
Iteration: 2, Log-Lik: -8336.191, Max-Change: 0.25156
Iteration: 3, Log-Lik: -8312.465, Max-Change: 0.13431
Iteration: 4, Log-Lik: -8305.747, Max-Change: 0.07985
Iteration: 5, Log-Lik: -8303.312, Max-Change: 0.04955
Iteration: 6, Log-Lik: -8302.352, Max-Change: 0.02996
Iteration: 7, Log-Lik: -8301.823, Max-Change: 0.01076
Iteration: 8, Log-Lik: -8301.766, Max-Change: 0.00714
Iteration: 9, Log-Lik: -8301.743, Max-Change: 0.00473
Iteration: 10, Log-Lik: -8301.730, Max-Change: 0.00176
Iteration: 11, Log-Lik: -8301.728, Max-Change: 0.00115
Iteration: 12, Log-Lik: -8301.727, Max-Change: 0.00076
Iteration: 13, Log-Lik: -8301.727, Max-Change: 0.00034
Iteration: 14, Log-Lik: -8301.726, Max-Change: 0.00030
Iteration: 15, Log-Lik: -8301.726, Max-Change: 0.00019
Iteration: 16, Log-Lik: -8301.726, Max-Change: 0.00016
Iteration: 17, Log-Lik: -8301.726, Max-Change: 0.00014
Iteration: 18, Log-Lik: -8301.726, Max-Change: 0.00010
Iteration: 19, Log-Lik: -8301.726, Max-Change: 0.00008
Calculating information matrix...
```

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