Reviewers may reject Winsteps and its estimation method, JMLE, because they are "inconsistent", quoting perhaps
Christensen (2012) "“Estimation of the item parameters using the joint likelihood function leads to inconsistent item parameter estimates because the number of parameters increases with the number of persons”, and recommending CMLE or MMLE
Response: It is true that JMLE (UMLE, UCON) is statistically inconsistent for infinite data. For finite data this is seen as "estimation bias". During many discussions/arguments in the 1970s and 1980s it was discovered that the JMLE estimation bias is inconsequential for most datasets and can easily be corrected where it is consequential . See, for instance, www.rasch.org/memo45.htm which appeared in Applied Psychological Measurement 12 (3) pp. 315-318, September 1988. and, more recently, "Overall, the differences between the results produced with the three estimation methods [CMLE, JMLE, MMLE] were negligible, and the discrepancies observed between datasets were attributable to the software choice as opposed to the estimation method." in Nicklin C., Vitta J.P. (2022) Assessing Rasch measurement estimation methods across R packages with yes/no vocabulary test data. Language Testing.
Of course, MMLE is estimation-biased if the person distribution mismatches the assumed person theta distribution (which it always does, empirical data never matches a theoretical distribution, - as the reviewer implicitly admits). CMLE, as usually implemented, is estimation-biased for the person measures (thetas) - see my note in Rasch Measurement Transactions - www.rasch.org/rmt/rmt331.pdf "CMLE – a Problem, its Solution and a Useful Approximation". Further depending on the nature of your data and analysis, CMLE and MMLE may be impossible to implement.
In my experience over 40 years JMLE estimation bias is only consequential for pairwise data, so Winsteps has a special command for this unique situation: "PAIREDdata=Yes". In other situations, I recommend against bias correction, STBIAScorrection=Yes in Winsteps, because of its side-effects. For instance, only for uncorrected JMLE can we complete this loop: raw person and item scores with original data -> item estimates and person estimates -> original person and item raw scores. This is important if we intend to predict person raw scores and item p-values for future data from the current estimates.
Every estimation method has advantages and disadvantages. A somewhat obscure disadvantage, and almost irrelevant for practical purposes, is the lack of "statistical consistency" of JMLE estimates. Here is the idea. Suppose we had an infinite amount of data, and used JMLE to estimate the parameter values from it. Would those parameter values be the "true" values of the parameters? The answer is no! The worst case is a test of only two dichotomous items. If the true difference between the difficulties of the two items is one logit. JMLE would report two logits difference! This indicates that JMLE is "statistical inconsistent". However, this two-to-one "estimation bias" is easy to correct. We simply divide all the estimates by two! In Winsteps, this is done automatically with the instruction "PAIRED=Yes". With longer tests, the correction is (number of items-1)/(number of items), corrected by STBIAS=YES. For longer tests, this correction quickly becomes meaninglessly small.
In fact, even for short tests, the correction for estimation bias is unnecessary unless we need to make very exact inferences about small logit differences. However, we discover that the correction is smaller than the standard errors of the estimates. We are in the situation that Quality-Control guru, W. E. Deming, pointed out is over-correction when applied to industrial machinery. We are trying to adjust the estimation process within its area of uncertainty. The result, Deming demonstrated, is that the outcome of the process becomes worse, not better!
Estimation bias, the practical consequence of statistical inconsistency, does not change the hierarchy of item difficulties and person abilities. So, if you are applying a user-friendly rescaling (USCALE=) to the logit values, the estimation bias is entirely inconsequential.
On the other hand, estimation methods that are statically consistent (with infinite data), such as CMLE, MMLE, PMLE, can also have estimation bias (with finite data) depending on the characteristics of those data. For instance, MMLE imposes a theoretical distribution of person abilities on the person parameters. This may or may not be a good match to the actual distribution of those parameters. PMLE uses the data in an uneven way during the estimation process resulting in estimation bias. CMLE, MMLE and PMLE are all asymmetric in the way they estimate the item and person parameters. This is fine if we think of a fixed set of items and a potentially infinite sample of persons, but in other applications of Rasch measurement, both the "items" and "persons" are fixed, or both the "items" and "persons" are potentially infinite. JMLE is symmetric in its estimates. Transpose the data matrix, and the absolute differences between the estimates for specific items and/or specific persons do not change. For those other estimation methods, those differences do change.
