EAP's and PV's

[Georg II]

Hi,
1. How are EAP ability estimates different from MLE and WLE?
2. When do we used EAP estimates?
3. How are PV's different from WLE, MLE, and EAP?
4. When do we used PV's?

Thanks
Georh II

[ConQuest]

These are huge questions.  I will do a bit of work on a note that explains the differences, but it will take a while.  In the mean time doing some reading on the web and from other available resources might help.

here are a few points.

1.  maximum likelihood (MLE) and weighted maximum likelihood (WLE) are point estimates that depend only upon the item response model.  The WLE is Warm's improvement on the MLE that is close to an unbiased estimator.

2.  EAP is expected a-posterior, or the expectation of the posterior.  I believe the term was introduced by Bock.  The EAP is a minimum mean squared estimator that is in general biased.  The EAP depends upon both the item response model and the population model. 

3.  PV's are plauible value, they are random draws from the posterior and should be used whenever you wish to undertake analyses with the ability estimates (ie estimate population parameters -- means, variances, covariances, regressions, t-tests and so on)

Ray

[gonzalezdepaz]

Hi:

When I run: show cases ! filetype=excel, estimates=latent><**-xls I get a excel file with next columns:

PV1_D1   PV1_D2   PV1_D3   PV1_D4   PV1_D5   PV2_D1   PV2_D2   PV2_D3   PV2_D4   PV2_D5   PV3_D1   PV3_D2   PV3_D3   PV3_D4   PV3_D5   PV4_D1   PV4_D2   PV4_D3   PV4_D4   PV4_D5   PV5_D1   PV5_D2   PV5_D3   PV5_D4   PV5_D5   EAP_1   Posterior SD_1   EAP_2   Posterior SD_2   EAP_3   Posterior SD_3   EAP_4   Posterior SD_4   EAP_5   Posterior SD_5

What I'm seeking is a make a table with the plausible values of each case in each dimension. What columns I should select?
What are the other columns?

Luis

[m.krell]

Hi Luis,

it seems that you have specified a five-dimensional model. For each dimension, ConQuest estimates five PVs (default). So, the columns are: PV no.1 for dimension no. 1 (PV1_D1), PV no.1 for dimension no. 2 (PV1_D2), ... , PV no.5 for dimension no. 5 (PV5_D5).

[The author of this reply suggested to average the 5 PVs of each domain, but that is incorrect. Never average them, it will give biased results. Instead, you need to compute each statistic 5 times and take the average of the 5 statistics (for example, you compute a mean with each PV and then you average the 5 means). If you need an unbiased shortcut, you can use one of the 5 plausible values. The PISA data analysis manual, second edition (OECD), explains working with plausible values in detail. Eveline Gebhardt]

I hope this short note will help you. For further reading I suggest:

Davier, M. von, Gonzales, E., & Mislevy, R. (2009). What are plausible values and why are they useful? In IERInstitute (Ed.), Issues and Methodologies in Large-Scale Assessments (pp. 9–36). Hamburg & Princeton: IERInstitute.

Wu, M. L. (2005). The role of plausible values in large-scale surveys. Studies in Educational Evaluation, 31, 114–128.

Best wishes
Moritz

[hartmann]

3. How are PV's different from WLE, MLE, and EAP?
4. When do we used PV's?

In a nutshell, all person parameters (WLE, MLE, EAP, PV) provide good estimates of population means. However, WLEs and MLEs overestimate variance, while EAPs underestimate variance. PVs provide a rather accurate estimate to population variance and should be used for analysises of population parameters.

But: PVs are random draws from the posterior distribution and therefore not appropriate as individual ability estimates. For an estimation of individual scores, use MLEs or WLEs.