For a really useful, introductory article on Plausible Values see the paper by Professor Margaret Wu in Rasch Measurement Transactions:

https://www.rasch.org/rmt/rmt182c.htm

Some key understandings:

**Plausible values are probability estimates of the ‘posterior distribution’**

“The simplest way to describe plausible values is to say that plausible values are some kind of student ability estimates. There are some differences between plausible values and the θ (student ability parameter) as in the usual 1, 2 or 3-PL item response models. Instead of directly estimating a student's θ, we now estimate a probability distribution for a student's θ. That is, instead of obtaining a point-estimate for θ, we now come up with a range of possible values for a student's θ, with associated likelihood of each of these values. Plausible values are random draws from this (estimated) distribution for a student's θ (I will call this distribution "the posterior distribution").”

**The apparent paradox – use one set of plausible values (one random draw) – not the mean of the plausible values**

Recall that plausible values are random draws from each student's posterior distribution. The collection of posterior distributions for all students, put together, gives us an estimate of the population distribution, g(θ). Therefore, we can regard the collection of plausible values (over all students) as a sampling distribution from g(θ)). This is an important statement, and some results follow from this statement:

(1) Population characteristics (e.g., mean, variance, percentiles) can be constructed using plausible values.

(2) Suppose we generate 5 plausible values for each student, and form 5 sets of plausible values (set 1 contains the first plausible value for each student; set 2 contains the second plausible value for each student, etc.). Then each set is equally as good for estimating population characteristics, as each set forms a sampling distribution of g(θ). It follows that, even if we only use one plausible value per student to estimate population characteristics, we still have unbiased estimates, in contrast to using each student's EAP estimates (mean of plausible values for each student) and getting biased estimates. So the apparent paradox is that using one random draw (PV) from the posterior distribution is better than using the mean of the posterior, in terms of getting unbiased estimates.

**The relationship between plausible values and student / person ability estimates:**

*“Note:* For ordinary estimates, plausible values are values from the error distribution of the estimate. If you have each person's estimate (measure, location) and its standard error, then plausible values are values selected at random from a normal distribution with its mean at the estimated measure and with standard deviation equal to the standard error. You can generate these with Excel or other statistical software.”

Reference: Wu (2004) Plausible Values __Rasch Measurement Transactions__ Vol. 18; No. 2, p. 976 - 978