data.sim.rasch: Dataset 'data.sim.rasch' in 'tclboot' Package

In akurz1/tclboot: Conditional Inference in Small Sample Scenarios

Dataset data.sim.rasch in tclboot Package

Description

Datasets of 60 cases of simulated Rasch data of size n * k included in the tclboot package.

Usage

data.sim.rasch

Format

data.sim.rasch has the following format:

List of 5

• eta_list: A list of numeric matrices of size 2 x (k-1), with item parameters as rows and items as columns. The first row refers to CML estimates of item parameters of the restricted (full) model, the second row refers to initial item parameters used to generate the initial input matrix for each case. Note the item parameter of first item is set to 0.

  eta_list : List of 6
$ I :List of 10
$ II :List of 10
$ III:List of 10
$ IV :List of 10
$ V :List of 10
$ VI :List of 10
  

• inputmat_list: A list of numeric input matrices of size n x k for each case with persons as rows, items as columns,

  inputmat_list : List of 6
  

  $ I :List of 10
A-I-10x6 : num [1:10, 1:6] 1 0 1 0 0 1 1 0 0 1 ...
B-I-10x8 : num [1:10, 1:8] 0 0 1 1 1 1 0 0 0 0 ...
C-I-10x10: num [1:10, 1:10] 0 1 1 0 1 1 1 0 0 1 ...
D-I-10x12: num [1:10, 1:12] 1 0 0 1 1 0 1 1 0 1 ...
E-I-10x14: num [1:10, 1:14] 0 0 0 1 1 0 1 0 0 1 ...
F-I-10x16: num [1:10, 1:16] 1 1 1 0 0 1 0 1 0 0 ...
G-I-10x18: num [1:10, 1:18] 1 1 1 0 0 1 0 1 0 0 ...
H-I-10x20: num [1:10, 1:20] 1 1 0 0 1 1 1 0 1 0 ...
I-I-10x25: num [1:10, 1:25] 1 0 1 0 1 1 0 1 1 0 ...
J-I-10x30: num [1:10, 1:30] 0 1 1 0 1 0 1 1 0 0 ...
  

  $ II :List of 10
A-II-15x6 : num [1:15, 1:6] 0 1 0 1 1 1 1 1 1 0 ...
...
J-II-15x30: num [1:15, 1:30] 1 0 1 0 1 0 1 0 1 1 ...
  

  $ III:List of 10
A-III-20x6 : num [1:20, 1:6] 1 0 0 1 1 0 1 1 0 0 ...
...
J-III-20x30: num [1:20, 1:30] 0 0 1 1 0 0 1 1 1 0 ...
  

  $ IV :List of 10
A-IV-25x6 : num [1:25, 1:6] 0 1 1 1 0 1 0 0 0 0 ...
...
J-IV-25x30: num [1:25, 1:30] 0 1 1 0 1 0 1 0 0 0 ...
  

  $ V :List of 10
A-V-30x6 : num [1:30, 1:6] 0 0 1 0 0 0 1 0 1 1 ...
...
J-V-30x30: num [1:30, 1:30] 1 0 0 1 1 0 1 0 0 0 ...
  

  $ VI :List of 10
A-VI-50x6 : num [1:50, 1:6] 0 0 0 0 1 0 0 1 1 1 ...
...
J-VI-50x30: num [1:50, 1:30] 0 1 1 0 1 0 0 0 1 1 ...
  

• score_list: A list of numeric matrices of size k x 10000 for each case, containing in each column the value of score function in each sample drawn.

  score_list : List of 6
$ I :List of 10
$ II :List of 10
$ III:List of 10
$ IV :List of 10
$ V :List of 10
$ VI :List of 10
  

• stat_list: A list of numeric matrices of size 7 x 10000 for each case, containing in rows values of test statistics for each sample drawn. See Details.

  stat_list : List of 6
$ I :List of 10
$ II :List of 10
$ III:List of 10
$ IV :List of 10
$ V :List of 10
$ VI :List of 10
  

• t_list: A list of numeric matrices of size k x 10000 for each case, containing in each column the observed values of sufficient statistic for d computed for each sample drawn.

  t_list : List of 6
$ I :List of 10
$ II :List of 10
$ III:List of 10
$ IV :List of 10
$ V :List of 10
$ VI :List of 10
  

Note: Roman numbers I to VI refer to cases with sample sizes n = 10, 15, 20, 25, 30, 50. Letters A to J refer to cases with number of items k = 6, 8, 10, 12, 14, 16, 18, 20, 25, 30. Total 60 cases.

Details

Bootstrap data was generated by repeated resampling with replacement from an initial data set by a non-parametric bootstrap simulation design. From an initially generated data sample of size n * k, denoted as inputmat, a number of 10.000 bootstrap samples are generated and test statistics are computed.

The initial data sample of size n * k was generated according to the Rasch model, given a vector of initial item parameters. Person parameters were drawn from N(0,1). A sample had to meet the requirements of Fischer (1981) and were not allowed to have any items with only zero or full responses, both in the restricted and unrestricted models.

The initial data sample is then used as input matrix inputmat for the Rasch sampler (Mair & Hatzinger, 2007; Verhelst et al., 2007). A number of B = 10,000 bootstrap samples of size n * k are generated. Each bootstrap sample had to meet the requirements of Fischer (1981) and were not allowed to have any items with only zero or full responses, both in the restricted and unrestricted models.

Finally, the bootstrap replications of the test statistics are obtained for Wald (W), likelihood ratio (LR), Rao score (RS), gradient (GR), test statistic based on absolute values of the score function (abs) and squared elements of the score function (sqs), and an alternative version of the score test (St).

akurz1/tclboot documentation built on Oct. 23, 2022, 9:07 p.m.