STBIAS=Y causes an approximate correction for estimation bias in JMLE estimates to be applied to measures and calibrations. This is only relevant if an exact probabilistic interpretation of logit differences is required for short tests or small samples. Set STBIAS=NO when using IWEIGHT=, PWEIGHT=, anchoring, IAFILE=, PAFILE=, SAFILE= or artificially lengthened tests or augmented samples, e.g., by replicating item or person response strings.
Fit statistics are computed without this estimation-bias correction. Estimation-bias correction makes the measures more central, generally giving a slight overfit condition to Outfit and Infit. Correct "unbiased" computation of INFIT and OUTFIT needs not only unbiased measures, but also probabilities adjusted for the possibility of extreme score vectors (which is the cause of the estimation bias).
STBIAS=YES instructs Winsteps to compute and apply statistical-bias-correction coefficients to the item difficulties and to the person measures - based on the current data. This becomes complicated for anchor values and scoring tables. With STBIAS=YES, the item anchor values are assumed to be bias-corrected. Consequently bias is applied to make them compatible with JMLE computations for the current data. The resulting person measures are JMLE person estimates, which are biased. So a person bias correction is applied to them.
For the special case of two items for each person, or two persons for each item, please use PAIRED=Yes to correct for bias.
With STBIAS=No, there is no statistical bias correction, so the internal and reported values are the same. The process is
For unanchored item values,
data + internal person estimates => internal item estimates => reported item estimates
For anchored item values,
anchored item values => internal item estimates => reported item estimates
For unanchored person values,
data + internal item estimates => internal person estimates => reported person estimates
For anchored person values,
anchored person values => internal person estimates => reported person estimates
For a scoring table
reported item estimates => internal item estimates => internal person estimates => reported person estimates
With STBIAS= YES, the internal and reported values differ. The process is
Compute bias correction coefficients for item estimates and for person estimates based on the current data.
For unanchored item values,
current data + internal person estimates => internal item estimates => item bias correction => reported item estimates
For anchored item values,
anchored item values => undo item bias correction => internal item estimates => item bias correction => reported item estimates
For unanchored person values,
data + internal item estimates => internal person estimates => person bias correction => reported person estimates
For anchored person values,
anchored person values => undo person bias correction => internal person estimates => person bias correction => reported person estimates
For a scoring table, the process is
reported item estimates => undo item bias correction => internal item estimates => internal person estimates => person bias correction => reported person estimates.
Note: it is seen that this process can result in estimates that are worse than uncorrected JMLE estimates. Consequently it may be advisable not to use STBIAS=YES unless the bias correction is clearly required.
Question: Are JMLE estimates always biased?
Answer: Yes, but the bias becomes inconsequential (less than the standard errors) for tests with more than 20 persons and more than 20 items - www.rasch.org/memo45.htm
Question: Are person estimates in JMLE biased as well as the item difficulty estimates?
Answer: The Rasch model does not know what is a person and what is an item. Smaller person samples for a given test length and shorter tests for a given person sample size generally make the estimation bias worse. Winsteps is constructed so that transposing the rows and columns of the data matrix (with dichotomous items or the Andrich rating scale model) produces statistically the same item and person measures (apart from a change of sign). CMLE and MMLE do not have this property. This transposition property is convenient in those types of analysis where it is not clear what is a "person" and what is an "item" - e.g., a matrix of street intersections and calendar dates with "0" for no traffic accident and "1" for traffic accident. It also enables analysis with a person-based "Partial Credit" model, where each person has a unique rating scale.
Question: Are person estimates obtain from known or anchored item difficulties statistically biased?
Answer: Under these circumstances, estimation is no longer "Joint" (persons and items), but becomes the AMLE (Anchored Maximum Likelihood Estimation) used to estimate person abilities from item difficulties in other estimation methods (CMLE, MMLE, PMLE, etc.)
Question: What is the bias correction used by Winsteps?
Assuming dichotomous, complete data:
Unbiased item estimate = biased estimate * (number of items - 1) / number of items
Unbiased person estimate = biased estimate * (number of persons - 1) / number of persons
Question: what about other data?
An empirical solution is to estimate the Rasch measures from your data. Note down the person S.D.
Then use the Winsteps "Output Files" "simulate data" option to simulate 10 datasets.
Analyze these, and average the person S.D.s
(This process can be automated using Winsteps "BATCH=" capability)
Compare the average with the original estimate person S.D. - this will tell you the size of the bias.
Then apply USCALE= bias correction to the original analysis to obtain unbiased estimates. The unbiased estimates will always be more central (smaller range) than the biased estimates.
Example 1: I have a well-behaved test of only a few items, but I want to correct for statistical estimation bias because I want to me to make exact probabilistic inferences based on differences between logit measures:
STBIAS=Y
Example 2: I have a set of item difficulties from RUMM (or ConQuest or OPLM or ...) and want to construct a score-table that matches the RUMM person measures.
IAFILE = (RUMM item difficulties)
STBIAS = No ; don't change the estimates - use the values RUMM uses
TFILE=*
20 ; Table 20 is the score table
*
...
END LABELS
01010101010101010 ; Dummy data records
10101010101010101 ; so that Winsteps will run
