Description Usage Arguments Details Value Warning Author(s) See Also Examples

Performs a Likelihood Ratio Test between two nested IRT models.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
## S3 method for class 'gpcm'
anova(object, object2, simulate.p.value = FALSE,
B = 200, verbose = getOption("verbose"), seed = NULL, ...)
## S3 method for class 'grm'
anova(object, object2, ...)
## S3 method for class 'ltm'
anova(object, object2, ...)
## S3 method for class 'rasch'
anova(object, object2, ...)
## S3 method for class 'tpm'
anova(object, object2, ...)
``` |

`object` |
an object inheriting from either class |

`object2` |
an object inheriting from either class |

`simulate.p.value` |
logical; if |

`B` |
the number of Bootstrap samples. |

`verbose` |
logical; if |

`seed` |
the seed to be used during the parametric Bootstrap; if |

`...` |
additional arguments; currently none is used. |

`anova.gpcm()`

also includes the option to estimate the *p*-value of the LRT using a parametric Bootstrap approach.
In particular, `B`

data sets are simulated under the null hypothesis (i.e., under the generalized partial credit model
`object`

), and both the null and alternative models are fitted and the value of LRT is computed. Then the *p*-value is
approximate using *[1 + {\# T_i > T_{obs}}]/(B + 1),* where *T_{obs}*
is the value of the likelihood ratio statistic in the original data set, and *T_i* the value of the statistic in the *i*th
Bootstrap sample.

In addition, when `simulate.p.value = TRUE`

objects of class `aov.gpcm`

have a method for the `plot()`

generic function
that produces a QQ plot comparing the Bootstrap sample of likelihood ration statistic with the asymptotic chi-squared distribution. For instance,
you can use something like the following: `lrt <- anova(obj1, obj2, simulate.p.value = TRUE); plot(lrt)`

.

An object of either class `aov.gpcm`

, `aov.grm`

, class `aov.ltm`

or class `aov.rasch`

with components,

`nam0` |
the name of |

`L0` |
the log-likelihood under the null hypothesis ( |

`nb0` |
the number of parameter in |

`aic0` |
the AIC value for the model given by |

`bic0` |
the BIC value for the model given by |

`nam1` |
the name of |

`L1` |
the log-likelihood under the alternative hypothesis ( |

`nb1` |
the number of parameter in |

`aic1` |
the AIC value for the model given by |

`bic1` |
the BIC value for the model given by |

`LRT` |
the value of the Likelihood Ratio Test statistic. |

`df` |
the degrees of freedom for the test (i.e., the difference in the number of parameters). |

`p.value` |
the |

The code does not check if the models are nested! The user is responsible to supply nested models in order the LRT to be valid.

When `object2`

represents a three parameter model, note that the
null hypothesis in on the boundary of the parameter space for the guessing parameters. Thus, the Chi-squared reference
distribution used by these function might not be totally appropriate.

Dimitris Rizopoulos [email protected]

`GoF.gpcm`

,
`GoF.rasch`

,
`gpcm`

,
`grm`

,
`ltm`

,
`rasch`

,
`tpm`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 | ```
## LRT between the constrained and unconstrained GRMs
## for the Science data:
fit0 <- grm(Science[c(1,3,4,7)], constrained = TRUE)
fit1 <- grm(Science[c(1,3,4,7)])
anova(fit0, fit1)
## LRT between the one- and two-factor models
## for the WIRS data:
anova(ltm(WIRS ~ z1), ltm(WIRS ~ z1 + z2))
## An LRT between the Rasch and a constrained
## two-parameter logistic model for the WIRS data:
fit0 <- rasch(WIRS)
fit1 <- ltm(WIRS ~ z1, constraint = cbind(c(1, 3, 5), 2, 1))
anova(fit0, fit1)
## An LRT between the constrained (discrimination
## parameter equals 1) and the unconstrained Rasch
## model for the LSAT data:
fit0 <- rasch(LSAT, constraint = rbind(c(6, 1)))
fit1 <- rasch(LSAT)
anova(fit0, fit1)
## An LRT between the Rasch and the two-parameter
## logistic model for the LSAT data:
anova(rasch(LSAT), ltm(LSAT ~ z1))
``` |

drizopoulos/ltm documentation built on April 19, 2018, 2:37 a.m.

Embedding an R snippet on your website

Add the following code to your website.

For more information on customizing the embed code, read Embedding Snippets.