# How to build a library of standart datasets and their Rasch estimates

Let’s build a library of standard datasets and their Rasch estimates. These can be used to confirm that Rasch software is functioning correctly and also for teaching about Rasch estimation.
————————————————————————————————————– Estimation method:
AMLE = Anchored Maximum Likelihood Estimation (MLE for estimating person abilities with known item difficulties)
CMLE = Conditional Maximum Likelihood Estimation (R- eRm, WINMIRA)
JMLE = Joint Maximum Likelihood Estimation (R-mixRasch, Winsteps) – no correction for estimation bias
MMLE = Marginal Maximum Likelihood Estimation (R-ltm, ConQuest)
PMLE = Pairwise Maximum Likelihood Estimation (R-pairwise, RUMM2030)
WMLE = Warm’s Mean Likelihood Estimation (applied to MLE estimates) All estimates are in logits. The estimate for column 1 (item 1) is set to 0.0 logits.
————————————————————————————————————–Standard dataset 1: Complete dichotomous dataset of 2 columns (items) and 2 rows (persons): 0,1 1,0 All Rasch estimation methods: column estimates: 0.0, 0.0 ; row estimates: 0.0, 0.0.
————————————————————————————————————– Standard dataset 2: Complete dichotomous dataset of 2 columns (items) and 3 rows (persons): 0,1 1,0 0,1
CMLE column estimates: 0.00000, -0.69315 AMLE row estimates: -0.34658, -0.34658, -0.34658
JMLE column estimates: 0.00000, -1.38629 JMLE row estimates: -0.69315, -0.69315, -0.69315
MMLE column estimates: 0.00000, -1.38629 AMLE row estimates: -0.69315, -0.69315, -0.69315
PMLE column estimates: 0.00000, -0.69315 AMLE row estimates: -0.34658, -0.34658, -0.34658
————————————————————————————————————–Standard dataset 3: Complete dichotomous dataset of 3 columns (items) and 3 rows (persons): 1,0,0 0,1,1 0,1,1
CMLE column estimates: 0.00000, -1.00505, -1.00505 AMLE row estimates: -1.40449, 0.05635, 0.05635 WMLE row estimates: -1.17098, -0.18498, -0.18498
JMLE column estimates: 0.00000, -1.56593, -1.56593 JMLE row estimates: -1.84142, -0.27549, -0.27549 WMLE row estimates: -1.63506, -0.50850, -0.50850
MMLE column estimates: 0.00000, -1.38629, -1.38629 AMLE row estimates: -1.69820, -0.17070, -0.17070 WMLE row estimates: -1.48169, -0.40644, -0.40644
PMLE column estimates: 0.00000, -0.69315, -0.69315 AMLE row estimates: -1.17436, 0.24746, 0.24746 WMLE row estimates: -0.93166, 0.00210, 0.00210
————————————————————————————————————–Standard Dataset 4: Rating Scale 8 persons (rows) respond to 8 items (columns) on a 0-3 rating scale:
`1000000000210203020011130101212300122033021103330012333303333332`
or
`1,0,0,0,0,0,0,00,0,2,1,0,2,0,30,2,0,0,1,1,1,30,1,0,1,2,1,2,30,0,1,2,2,0,3,30,2,1,1,0,3,3,30,0,1,2,3,3,3,30,3,3,3,3,3,3,2`
The row (column) totals are 1, 8, 8, 10, 11, 13, 15, 20
This data matrix is symmetric. In principle, person (row) and item (column) standard deviations (S.D.) are the same.
1000 persons (rows) respond to 5 items (columns) scored 0-1:
The data matrix is here.
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