﻿ IWEIGHT= item (variable) weighting

# IWEIGHT= item (variable) weighting

IWEIGHT= allows for differential weighting of items. The standard weights are 1 for all items. To change the weighting of persons, specify PWEIGHT=.

IWEIGHT of 2 has the same effect on person estimation as putting the item and its responses into the analysis twice. It does not change an item scored 0-1 into an item scored 0-2. When IWEIGHT is 0 for an item, the measure and fit statistics are reported for the item, but the item does not influence the measures or fit statistics of the other items or persons. IWEIGHT= applies to everything except the dimensionality computations (Tables 23, 24) where PWEIGHT= is set to 1 and IWEIGHT= is set to 1 for all persons and items.

 IWEIGHT= file name file containing details IWEIGHT = * in-line list IWEIGHT = \$S1W1 field in item label

Raw score, count, and standard error of measurement reflect the absolute size of weights as well as their relative sizes. Measure, infit and outfit and correlations are sensitive only to relative weights.

Weighting is treated for estimation as that many independent observations. So, if you weight all items by two, you will divide the S.E. by the square-root of 2, but will not change the measures or fit statistics.

If you want to do different weighting at different stages of an analysis, one approach is to use weighting to estimate all the measures. Then anchor them all (IFILE= and IAFILE= etc.) and adjust the weighting to meet your "independent observation" S.E. and reporting requirements.

If you want the standard error of the final weight-based measure to approximate the S.E. of the unweighted measure, then ratio-adjust case weights so that the total of the weights is equal to the total number of independent observations.

Formats are:

IWEIGHT=file name the weights are in a file of format:

item number weight

IWEIGHT=*

item number weight

....

*

IWEIGHT=\$S...\$W... or \$S...\$E... weights are in the item labels using the column selection rules, e.g.,starting in column S... with a width of W... or starting in column S and ending in column E. This can be expanded, e.g.,

IWEIGHT = \$S23W1+"."+\$S25W2
places the columns next to each other (not added to each other)

Example 1: In a 20-item test, item 1 is to be given a weight of 2.5, all other items have a weight of 1.

IWEIGHT=*

1 2.5

2-20 1

*

A better weighting, which would make the reported person standard errors more realistic by maintaining the original total sum of weights at 20 , is:

IWEIGHT=*

1 2.33 ; 2.5 * 0.93

2-20 0.93 ; the sum of all weights is 20.0

*

or adjust the weights to keep the sample-based "test" separation and reliability about the same - so that the reported statistics are still reasonable:

e.g., original sample "test" reliability (person separation index) = .9, separation coefficient = 3, but separation coefficient with weighting = 4

Multiply all weights by (3/4)² to return separation coefficient to about 3.

Example 2: The item labels contain the weights in columns 16-18.

IWEIGHT= \$S16W3 ; or \$S16E18

&END

Item 1 Hello   0.5

Item 2 Goodbye 0.7

......

END NAMES

Example 3: Item 4 is a pilot or variant item, to be given weight 0, so that item statistics are computed, but this item does not affect person measurement.

IWEIGHT=*

4 0 ; Item 4 has weight 0, other items have standard weight of 1.

*

Example 4: We have 24 0/1 items and 5 0/1/2/3 items. We want them to weight equally. There are several concerns here. These may require different weights for different purposes, i.e., several runs.

(a) Raw score reporting. For 24 items of 0/1 and 5 items of 0/0.33/0.67/1. Then

IWEIGHT=*

1-24 1

25-29 0.333

*

This will give the reportable raw scores you want, 0-29, but incorrect reliabilities (too small).

(b) Statistical information. The total amount of overall statistical information can be maintained approximately by maintaining the total raw score. So original ordinal unweighted raw score range = 0 - (24x1 +5x3) = 39. New raw score in (a) = 29. So we need to up the weights by 39/29 = 1.345. This will give peculiar-looking raw scores, but a better estimate of fit.

IWEIGHT=*

1-24 1.345

25-29 0.448

*

The Rasch measures for (a) and (b) will be the same, but the standard errors, reliabilities and fit statistics will differ.

(c) Reliability maintenance. If you want to maintain the same person "test" reliability (i.e., measure reproducibility), then

approximate weighting factor = (1 - weighted person model reliability) / (1 - unweighted person model reliability)

IWEIGHT=*

1-24 3 * weighting factor

25-29 1 * weighting factor

*

(d) recoding the 0/1 data into 0/3 to give equal weighting with 0/1/2/3 is not recommended because of the two unobserved categories, 1, 2, which change the slope of the model ICC, so distorting the measures, altering the fit and creating artificially high reliabilities.

Example 5: The items are to be weighted in accordance with Jian Tao, Ning-Zhong Shi and Hua-Hua Chang (2012). Item-Weighted Likelihood Method for Ability Estimation in Tests Composed of Both Dichotomous and Polytomous Items. Journal of Educational and Behavioral Statistics, 2012, 37, 2, 298-315.

In their empirical example, items 1-50 are dichotomies. Item 51 is a 0-4 polytomy. Their weighting is:

IWEIGHT=*

1-50 0.9924  ; this is the weighting for the 50 dichotomous items

51 1.3795 ; this is the weighting for the 1 polytomous (0-4) item

*

Example 6: A demonstration:

1. Analyze exam1.txt in the Winsteps Examples folder. Save the person measures. Table 17.
-----------------------------------------------------------------------------------------------
|ENTRY   TOTAL  TOTAL           MODEL|   INFIT  |  OUTFIT  |PT-MEASURE |EXACT MATCH|          |
|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.  EXP.| OBS%  EXP%| KID      |
|------------------------------------+----------+----------+-----------+-----------+----------|
|     7     14     18    3.73     .94| .95    .1| .39   -.1|  .69   .69| 85.7  88.8| Susan   F|

2. Add these lines to the exam1.txt control file:

IWEIGHT=*

13 2   ; weight item 13 double

*

3. Analyze exam1.txt in the Winsteps Examples folder. Compare the person measures. Table 17, with Table 17 from 1.

-----------------------------------------------------------------------------------------------

|ENTRY   TOTAL  TOTAL           MODEL|   INFIT  |  OUTFIT  |PT-MEASURE |EXACT MATCH|          |

|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.  EXP.| OBS%  EXP%| KID      |

|------------------------------------+----------+----------+-----------+-----------+----------|

|     7     15     19    3.85     .91| .92    .0| .37   -.1|  .67   .66| 86.7  89.2| Susan   F|

There are also differences in the item Table 14:

---------------------------------------------------------------------------------------------------------

|ENTRY   TOTAL  TOTAL           MODEL|   INFIT  |  OUTFIT  |PT-MEASURE |EXACT MATCH|     |              |

|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.  EXP.| OBS%  EXP%|WEIGH| TAP          |

|------------------------------------+----------+----------+-----------+-----------+-----+--------------|

|    13      7     35    1.87     .54| .49  -1.9| .24   -.6|  .67   .42| 94.1  86.4| 2.00| 1-4-3-2-4    |

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