change_test | R Documentation |

Computes gradient (GR), likelihood ratio (LR), Rao score (RS) and Wald (W) test statistics for hypotheses on parameters expressing change between two time points.

```
change_test(X)
```

`X` |
Data matrix containing the responses of n persons to 2k binary items. Columns 1 to k contain the responses to k items at time point 1, and columns (k+1) to 2k the responses to the same k items at time point 2. |

Assume all items be presented twice (2 time points) to the same persons. The data matrix X has n rows (number of persons) and 2k columns considered as virtual items. Assume a constant shift of item difficulties of each item between the 2 time points represented by one parameter. The shift parameter is the only parameter of interest. Of interest is the test of the hypothesis that the shift parameter equals 0 against the two-sided alternative that it is not equal to zero.

A list of test statistics, degrees of freedom, and p-values.

`test` |
A numeric vector of gradient (GR), likelihood ratio (LR), Rao score (RS), and Wald test statistics. |

`df` |
Degrees of freedom. |

`pvalue` |
A vector of corresponding p-values. |

`call` |
The matched call. |

Fischer, G. H. (1995). The Linear Logistic Test Model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch models: Foundations, Recent Developments, and Applications (pp. 131-155). New York: Springer.

Fischer, G. H. (1983). Logistic Latent Trait Models with Linear Constraints. Psychometrika, 48(1), 3-26.

`invar_test`

, and `LLTM_test`

.

```
## Not run:
# Numerical example with 400 persons and 4 items
# presented twice, thus 8 virtual items
# Data y generated under the assumption that shift parameter equals 0
# (no change from time point 1 to 2)
# design matrix W used only for example data generation
# (not used for estimating in change_test function)
W <- rbind(c(1,0,0,0,0),
c(0,1,0,0,0),
c(0,0,1,0,0),
c(0,0,0,1,0),
c(1,0,0,0,1),
c(0,1,0,0,1),
c(0,0,1,0,1),
c(0,0,0,1,1))
# eta Parameter, first 4 are nuisance, i.e. , easiness parameters of the 4 items
# at time point 1, last one is the shift parameter.
eta <- c(-2,-1,1,2,0)
y <- eRm::sim.rasch(persons = rnorm(400), items = colSums(eta * t(W)))
res <- change_test(X = y)
res$test # test statistics
res$df # degrees of freedoms
res$pvalue # p-values
## End(Not run)
```

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