Comparing Methods to Recalibrate Drifting Items in Computerized
Adaptive Testing
Recalibrating Drifting CAT Items 12
Comparing Methods to Recalibrate Drifting Items in Computerized
Adaptive Testing
James Masters
Pearson VUE
[email protected]
Timothy Muckle
National Board on Certification and Recertification of Nurse
Anesthetists
[email protected]
Brian Bontempo
Mountain Measurement, Inc.
[email protected]
Introduction
Computerized Adaptive Testing (CAT) involves the construction of
a test dynamically so that the difficulty of each item administered
is targeted to the estimated ability of the candidate. Before an
item can be administered operationally, item parameters (e.g., item
difficulty) must be estimated empirically. Typically, newly
developed items, called experimental, pretest, or pilot items are
embedded into the operational CAT so that they are randomly
administered to examinees amongst the real or operational CAT
items. The experimental items are not scored and the response data
collected are used to estimate the item parameters through IRT
calibration. Once estimated, the item parameters are assigned to
their corresponding items, a process referred to as “anchoring.”
Operational CAT item pools are composed of these calibrated items,
and examinee ability is estimated during the test using the
anchored item parameters.
In an operational computer adaptive test, there are situations
(such as item overexposure or changes in the curriculum or
training, sampling error) when an item’s difficulty (or set of
items’ difficulty) has changed significantly from the difficulty
calculated when the item was originally pilot tested. This
phenomenon, known as item parameter drift, can be the result of
both test and non test design factors such as item overexposure or
a change in the curriculum or training. A test that suffers from
item parameter drift may inaccurately estimate examinees’ ability
(Wells, Subkoviak, Serlin, 2002) and must be remedied. Therefore,
test makers try to detect items that exhibit drift in item
difficulty and reconcile the discrepant estimates.
Monitoring the stability of IRT parameters as a psychometric
practice is well-established in the literature (Goldstein, 1983,
Bock, Muraki, & Pfeiffenberger, 2005; DeMars, 2004; Donoghue
& Isham, 1998; Ito & Sykes, 1994; Sykes & Ito, 1993,
Do, Chuah, & Drasgow, 2005). One metric that is used to
evaluate the stability of Rasch item difficulty calibrations is the
Winsteps (Linacre, 2009) displacement statistic. In any analysis
featuring anchored items, Winsteps simultaneously estimates an
unanchored item difficulty for each of the anchored items. The
displacement statistic is computed simply as the difference between
the anchored difficulty value and the estimated difficulty that
would be obtained if the item were left unanchored. Readers are
referred to Linacre (2009) and Wright & Stone (1999) for
technical details on parameter estimation in Winsteps. Typically,
large-scale certification programs flag items that display large
amounts of drift and begin resolving the problem. Regardless of how
drifting items have been identified, rectification of parameter
drift (in a 1-parameter CAT environment) can be accomplished in one
of two ways:
· Option # 1 (Fresh Pilot): Deactivate (remove from operational
use) drifted items and re-administer the items as pilot items.
Compute a new item difficulty estimate from the new pilot data.
· Option #2 (Adjusted Operational): Adjust the item difficulty
using the Winsteps displacement statistic calculated from the
operational data. Essentially, this is the same as using the value
that would be obtained by recalibrating the item using the current
operational data.
The examinee ability distribution of the sample for these two
options varies greatly. The ability distribution of examinees who
are administered pilot items (Option #1) is normal. The ability
distribution of candidates who are administered operational CAT
items (Option #2) is extremely leptokurtic. For items that are
drifting (displacing), the mean of this ability distribution may be
quite different than the true difficulty of the item. This
mis-targeting of the candidates to the item may be such that it is
impossible to determine the true difficulty of the item without
additional data (Ito & Sykes, 1994). Since the ability
distribution of the Option #1 sample is similar to the ability
distribution of the sample obtained when the item was initially
pilot tested, the more conservative approach is to pilot test the
item again and calculate a new item difficulty estimate.
While re-piloting may be the safer route, this process is costly
and time consuming. In many cases, re-administration of a drifted
item in the pilot stage may not be possible if the pilot test is
already filled with newly constructed items. Conversely, it is
possible that drifted items placed back in the pilot pool will
prevent other newly written items from being piloted in a timely
manner. In these situations, it would be ideal if the drifted item
could remain in operational use, with the item calibration
“adjusted” or updated using the free-estimation value from the
operational data (Option #2). However, the advisability of this
alternative has not yet been investigated.
The purpose of this study is to determine the extent to which an
adjustment to the item difficulty, using the displacement statistic
calculated from the operational data, is comparable to a new item
difficulty estimate calculated from fresh pilot test data.
Methods
The data for this study came from a large-scale, variable-length
CAT that is administered to about 100,000 examinees annually.
Operational pools for this examination are rotated periodically.
Somewhere near the end of an operational pool’s administration
cycle, an item analysis is conducted in order to evaluate the
performance of the items. Operational items are evaluated for
parameter drift, while pilot items are evaluated to determine
whether they meet pre-existing statistical criteria (difficulty,
goodness-of-fit, point-to-measure correlation). In order to be
flagged for significant displacement, an operational item must
exhibit the following conditions on two consecutive operational
pools:
· be administered to at least 200 examinees
· have an absolute displacement greater than or equal to 0.5
logits
· have a standardized displacement (absolute displacement
divided by the Standard Error of Measurement [SEM] associated with
the free item difficulty estimate) greater than or equal to 2.0
logits.
The following analyses focus on 152 operational items that
exhibited significant displacement in at least two of three
operational pools that were available. As the procedures of this
testing program dictate, all of these items were removed from
operational use and re-administered as pilot items. These items
comprised a portion of a pilot pool administered from June to
December, 2008 where they were administered to an average of 450
examinees who were taking the test for the first time. Upon
completion of the pilot pool’s administration, an item analysis was
conducted, resulting in a new calibration for each of the
items.
The analyses which follow compare the “adjusted” operational
item difficulty (adding original anchor to the displacement
statistic) to the “fresh” item calibration from the re-pilot stage.
Two types of analyses were conducted. The first was a correlation
and the second was a t-test with pooled standard error:
where
is the adjusted difficulty estimate from the operational
data,
is the difficulty estimate from the pilot data,
is the standard error associated with the adjusted difficulty
estimate from the operational data,
is the standard error associated with the difficulty estimate
from the pilot data,
n0 is the sample size from the operational data, and
np is the sample size from the pilot data.
Using the results of the t-tests, each difficulty estimate was
placed into three categories:
· No significant difference found between fresh difficulty and
adjusted item difficulty
· Fresh difficulty was significantly greater than the adjusted
item difficulty
· Adjusted item difficulty was significantly greater than the
fresh item difficulty
The results of these categorizations were tabulated and
interpreted. Where an item was found to drift on two consecutive
pools, two t-tests were conducted, comparing fresh pilot
calibration to both the Pool 1 and Pool 2 adjusted operational
calibrations.
Results
Figure 1 is a scatter plot of the various adjusted operational
and fresh pilot calibrations plotted against the initial item
calibration. This figure illustrates the narrow range of item
difficulty for the items in the sample. The fact that there is no
linear shape to the plot also reveals the degree to which the items
had drifted since their initial calibration.
-------------------
Figure 1 about here
-------------------
Figure 2 shows another scatter plot. This is an identity plot of
the adjusted operational calibrations plotted against the fresh
pilot calibration. This plot shows how similar the results were for
both methods. A correlation matrix for the item calibrations is
displayed in Table 1. The correlation between the initial
calibration and the various rectification methods was between .4
and .7, as expected, somewhat low. On the other hand, the
correlation between the calibrations derived from the various
methods exceeded .98 in all cases. Given the large sample, all of
the correlations were significantly different than 0. By comparing
these correlations, it is clear that the difference between the
methods is minimal.
-------------------
Figure 2 about here
-------------------
-------------------
Table 1 about here
-------------------
Despite this high degree of similarity, there were still some
items that did not produce similar results across the two methods.
Figure 3 is a drop-line chart which displays all of the adjusted
operational or fresh pilot calibrations. The calibrations for a
single item are displayed along a vertical line with each point
representing a comparison calibration. The length of the line
relates to the disparity in the calibrations for the item. This
plot shows that, in general, the items that had extreme difficulty
estimates yielded larger differences between the results from the
two methods than the non-extreme items.
-------------------
Figure 3 about here
-------------------
The next series of analyses determined how many of the 152
displaced items showed significant differences between the fresh
calibrations and the adjusted operational calibration. In addition,
if the difference was statistically significant, the direction of
change was calculated (positive [more difficult] or negative
[easier]).
When items had shown significant displacement on only one
previous pool, the fresh calibration was compared to the original
value plus displacement. When items had shown significant
displacement on two or more consecutive pools, the weighted average
of displacement across the two pools and a pooled standard error
were used in order to make the comparison.
Table 2 displays the number of items that showed significant
differences and the direction of the differences for two different
levels of .The final column of the table shows the results after a
Bonferoni correction, which accounts for the family-wise error
associated with 152 t-tests.
-------------------
Table 2 about here
-------------------
Using strictly the results of the significance tests, one may
conclude that there is not much evidence to support the method of
adjusting the item calibration using the displacement statistic. In
the most favorable case, 41% of the adjusted operational
calibrations were either significantly higher or lower than the
pilot calibrations. One may conclude that it is advisable to
re-pilot the items that show drift and use the new calibration.
However, as in many studies, tests of statistical significance
may not tell the complete story. There is a practical component to
the comparisons that must be addressed as well. The majority of the
comparisons summarized in Table 1 involved confidence intervals
constructed using standard errors which were relatively small. (The
mean of the pooled variance was M = 0.09, SD = 0.06.) Accordingly,
the differences between the adjusted operational and fresh pilot
calibrations that were interpreted as statistically significant may
have amounted to little practical significance.
In order to investigate the practical meaning of the difference
in the calibrations, a subsequent analysis was conducted evaluating
the absolute magnitude of the difference between the adjusted
operational and the fresh pilot calibrations. Figure 4 is a
histogram of the absolute difference between the values arising
from the two recalibration methods. This distribution is skewed
with about half of the values being less than 0.27 logits. If we
apply the same rules that are used in this certification program to
flag items exhibiting parameter drift (the difference being
statistically significant and absolute difference greater than 0.5
logits), only 23 of the 152 items (15%) would have been
flagged.
-------------------
Figure 4 about here
-------------------
A substantial portion of the 23 items that yielded differences
between the two options were very difficult or very easy items.
Figure 5 is an X-Y plot comparing the absolute difference between
the adjusted operational and fresh pilot calibrations to the
original item difficulty estimate. This figure illustrates that
larger discrepancies between the two recalibration methods were
observed for items which had original calibrations at the extremes
of the difficulty continuum. Eight of the aforementioned 23 items
had original calibrations less than 0 logits, and five had
calibrations greater than 2 logits. Generally speaking, for this
exam, there are very few candidates with abilities less than 0
logits or more than 2 logits. Therefore, the error associated with
the adjusted calibrations was greatest for items less than 0 logits
or more than 2 logits. As can be seen in Figure 5, less than half
of the items would be flagged for drift in the “high traffic”
range.
-------------------
Figures 5 and 6 about here
-------------------
Discussion
This study demonstrated that there was a very strong correlation
between a displaced item’s adjusted operational calibration
(difficulty plus displacement) and the fresh pilot calibration. On
the other hand, through t-tests, this study showed that more than
40 percent of the adjusted operational calibrations were
significantly different than the fresh pilot calibration. Despite
the sizeable number of points that were significantly different,
the actual size of these differences was generally small. Moreover,
items within the “high-traffic” zone, tended to have less
discrepancy than more extreme items. Test makers interested in
implementing an adjusted calibration approach may consider using
the adjusted calibration for items within the “high traffic” range
and using fresh pilot calibrations for items outside the range. In
summary, the results provide support for recalibrating drifting
items by adjusting the anchored item difficulty estimate with the
displacement value obtained from a calibration with operational CAT
data.
References
Bock, R. D., Muraki, E., & Pfeiffenberger, W. (2005). Item
pool maintenance in the presence of item parameter drift. Journal
of Educational Measurement, 25, 275-285.
DeMars, C. E. (2004). Detection of item parameter drift over
multiple test administrations. Applied Measurement in Education,
17, 265-300.
Do, B. R., Chuah, S. C., & Drasgow, F. (2005). Effects of
Range Restriction on Item Parameter Recovery with Multistage
Adaptive Tests. Manuscript submitted for publication.
Donoghue, J. R., & Isham, S. P. (1998). A comparison of
procedures to detect item parameter drift. Applied Psychological
Measurement, 22, 33-51.
Goldstein, H. (1983). Measuring Change in Educational Attainment
Over Time: Problems and Possibilities. Journal of Educational
Measurement, 20, 369-377.
Ito, K., & Sykes, R. C. (1994). The effect of restricting
ability distributions in the estimation of item difficulties:
Implications for a CAT implementation. Paper presented at the
annual meeting of the National Council on Measurement in Education,
New Orleans, LA.
Linacre, J. M. (2009). Winsteps 3.68.1 [Computer Software].
Chicago: Mesa Press.
Sykes, R. C., & Ito, K. (1993). Item parameter drift in
IRT-based licensure examinations. Paper presented at the Annual
Meeting of the National Council on Measurement in Education,
Atlanta, GA.
Wells, C. S., Subkoviak, M. J., & Serlin, R. C. (2002). The
effect of item parameter drift on examinee ability estimates.
Applied Psychological Measurement, 26, 77-87.
Wright, B. & Stone, M. (1999). Measurement Essentials, 2nd
Edition, Wilmington, DE, Wide Range, Inc.
Figure 1. Scatter plot of item recalibrations plotted against
the initial anchor calibration for the item.
Figure 2. Scatter plot of adjusted operational calibrations
plotted against the fresh pilot calibration.
Figure 3. Drop-line chart displaying the difference between
adjusted operational and fresh pilot calibrations.
Figure 4. Histogram of absolute difference between adjusted
operational and fresh pilot calibrations.
Figure 5. Scatter plot of original item calibration vs. absolute
difference between adjusted operational and fresh pilot
calibrations.
Figure 6. Scatter plot of original item calibration vs. standard
error of measurement.
Figure 1. Scatter plot of item recalibrations plotted against
the initial anchor calibration for the item.
Figure 2. Scatter plot of adjusted operational calibrations
plotted against the fresh pilot calibration.
Figure 3. Drop-line chart displaying the difference between
adjusted operational and fresh pilot calibrations.
Figure 4. Histogram of absolute difference between adjusted
operational and fresh pilot calibrations.
Figure 5. Scatter plot of original item calibration vs. absolute
difference between adjusted operational and fresh pilot
calibrations.
Figure 6. Scatter plot of original item calibration vs. standard
error of measurement.
Table 1
Correlations between Item Calibrations at Different Time
Points
Calibration
Original (Pilot)
Adjusted Op 1
Adjusted Op 2
Adjusted Op 3
‘Fresh’ Pilot Calibration
Original (Pilot)
---
.425**
.762**
.404**
.408**
Adjusted Op 1
---
.993**
.988**
.985**
Adjusted Op 2
---
.995**
.983**
Adjusted Op 3
---
.984**
‘Fresh’ Pilot Calibration
---
Table 2
Summary of Comparison of Fresh Pilot and Displacement-Adjusted
Calibration, by t-test Level
Comparison between
Pilot and Adjusted Calibration
Level
0.05
0.01
0.05/152
Positive Difference
34
31
22
No Significant Difference
56
68
89
Negative Difference
62
53
41
Adj Op
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Op
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Initial Anchor Calibration
Recalibrations
Adj Op
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Op
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Op
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Adjusted Operational Calibrations
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Original Calibration (logits)
Standard Error of Measurement
0
d
p
d
0
SE
p
SE
0
22
0
0
p
opp
p
nSEnSE
nn
¶-¶
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