﻿ STBIAS= correct for estimation bias

# STBIAS= correct for statistical estimation bias = No

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 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.

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: No. Erling Andersen (1973) demonstrates that JMLE is biased for specific formulations and conceptualizations of data for which CMLE is unbiased. However, Andersen neglects to point out that under other formulations and conceptualizations of the same data, JMLE is unbiased and CMLE is biased. The essential contrast between the formulations is this. Does each item rank-order the persons by performance (CMLE unbiased), or is each item a paired-comparison with each person (JMLE unbiased)?

Andersen, E. B. Conditional inference for multiple-choice questionnaires. British Journal of Mathematical and Statistical Psychology, 1973, 26, 31-44.

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. So Erling Andersen's logic for demonstrating statistical item-bias (inconsistency) for an infinite sample with two items applies in the same way to person statistical-bias (inconsistency) with an infinitely long test and two persons. 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 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.

Question: Are person estimates obtain from known or anchored item difficulties statistically biased?

Answer: Yes, but only slightly. The problem with JMLE is not that persons and items are estimated simultaneously but that the possibility of infinite score vectors is not eliminated from the estimation space (as Haberman demonstrates in his "Analysis of Qualitative Data"). Even when the items are anchored, the possibility of infinite person score vectors remains, so that person measures estimated from anchored items are statistically biased.

Example 1: I have a well-behaved test of only a few items, but I want to adjust for statistical estimation bias correction 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 ; RUMM does not correct for statistical bias in its person measures

TFILE=*

20  ; Table 20 is the score table

*

(Dummy data records)

01010101010101010 ; so that Winsteps will run.

10101010101010101

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