Table 25.1 Item statistics in displacement order

(controlled by USCALE=, UMEAN=, UDECIM=, LOCAL=, TOTAL=, DISCRIMINATION=, ASYMPTOTE=, PVALUE=)

 

ITEM STATISTICS:  DISPLACEMENT ORDER

 PERSON: REAL SEP.: 1.55  REL.: .70 ... ITEM: REAL SEP.: 3.73  REL.: .93

 

Above the Table are shown the "real" separation coefficient and reliability (separation index) coefficients from Table 3.

 

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

|ENTRY   TOTAL  TOTAL           MODEL|   INFIT  |  OUTFIT  |PTMEASUR-AL|EXACT MATCH|ESTIM| ASYMPTOTE | P-  |     |     |        |                 |

|NUMBER  SCORE  COUNT  MEASURE  S.E. |MNSQ  ZSTD|MNSQ  ZSTD|CORR.  EXP.| OBS%  EXP%|DISCR|LOWER UPPER|VALUE| RMSR|WEIGH|DISPLACE| TAP           G |

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

|     1     35     35   -6.59A   1.85|1.00    .0|1.00    .0|A .00   .00|100.0 100.0| 1.00|  .00  1.00| 1.00| .000|  .50|    -.52| 1-4           1 |

|     5     31     35   -3.83     .70|1.04    .2| .52    .1|B .55   .55| 88.2  91.7| 1.01|  .05  1.00|  .89| .248| 1.00|    -.87| 2-1-4         2 |

|     6     30     35   -3.38     .64| MAXIMUM MEASURE     |  .53   .58|100.0 100.0|     |           |  .86| .289| 1.00|    -.64| 3-4-1         1 |

|     7     31     35   -3.83     .70| MINIMUM MEASURE     |  .40   .55|100.0 100.0|     |           |  .89| .281| 1.00|     .57| 1-4-3-2       2 |

|     8     27     35                | DROPPED             |           |           |     |           |     |     |     |        | 1-4-2-3       1 |

|    10      0     35                | INESTIMABLE: HIGH   |           |           |     |           |     |     |     |        | 2-4-3-1       3 |

|    11     35     35                | INESTIMABLE: LOW    |           |           |     |           |     |     |     |        | 1-3-1-2-4     4 |

|     9          DELETED             |          |          |           |           |     |           |     |     |     |        | 1-3-2-4       2 |

|    12          DESELECTED          |          |          |           |           |     |           |     |     |     |        | 1-3-2-4-3     1 |

....

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

| MEAN    18.5   35.0    -.59     .94| .96    .0| .68   -.1|           | 89.9  90.0|     |           |     |     |     |     .32|                 |

| P.SD    13.9     .0    4.21     .49| .28    .7| .58    .5|           |  6.3   5.3|     |           |     |     |     |     .27|                 |

--------------------------------------------------------------------------------------------------------------------------------+------------------

 

Column

Description

ENTRY NUMBER

the sequence number of the person, or item, in your data, and is the reference number used for deletion or anchoring.

TOTAL SCORE

TOTAL COUNT

 

Totalscore=Yes -. This is the score when reading in the data.

 

 

NON-EXTREME SCORE

NON-EXTREME COUNT

Totalscore=No -  the raw score and count of response by a person on the test, or the sum of the scored responses to an item by the persons, omitting responses in extreme and inestimable scores. This is the score when estimating person abilities and item difficulties.

MEASURE

the estimate (or calibration) of the person ability (theta, B, beta, etc.), or the item difficulty (b, D, delta, etc.). Values are reported in logits with two decimal places, unless rescaled by USCALE=, UIMEAN=, UPMEAN=, UDECIM=.

 

The difficulty of an item is defined to be the point on the latent variable at which its high and low categories are equally probable. SAFILE= can be used to alter this definition.

 
If unexpected results are reported, check whether TARGET= or CUTLO= or CUTHI= or ISGROUPS= are specified.

A after MEASURE, MAXIMUM, etc.

see STATUS Table below

MODEL S.E.

REAL S.E.

MODEL S.E. is the standard error of the estimate.  REAL S.E. is the misfit-inflated standard error. These are commonly referred to as conditional standard errors of measurement (CSEM).

INFIT

an information-weighted statistic, which is more sensitive to unexpected behavior affecting responses to items near the person's measure level.

OUTFIT

an unweighted statistic, more sensitive to unexpected behavior by persons on items far from the person's measure level.

MNSQ

a mean-square statistic. This is a chi-squared statistic divided by its degrees of freedom. Its expectation is 1.0.  Values substantially less than 1.0 indicate overfit = dependency in your data. Values values substantially greater than 1.0 indicate underfit = unmodeled noise.  See dichotomous and polytomous fit statistics.

 

Value

Meaning

>2.0

Off-variable noise is greater than useful information.  Degrades measurement. Always remedy the large misfits first.

>1.5

Noticeable off-variable noise.  Neither constructs nor degrades measurement

0.5 - 1.5

Productive of measurement

<0.5

Overly predictable. Misleads us into thinking we are measuring better than we really are. (Attenuation paradox.). Misfits <1.0 are only of concern when shortening a test

ZSTD

ZEMP

LOG

the INFIT or OUTFIT mean-square fit statistic t standardized to approximate a theoretical "unit normal", mean 0 and variance 1, distribution. ZSTD (standardized as a z-score) is used of a t-test result when either the t-test value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's t-statistic distribution value has been adjusted to a unit normal value. The standardization is shown on RSA, p.100-101. When LOCAL=Y, then ZEMP is shown, indicating a local {0,1} standardization.  When LOCAL=LOG, then LOG is shown, and the natural logarithms of the mean-squares are reported. More exact values are shown in the Output Files.
Ben Wright advises: "ZSTD is only useful to salvage non-significant MNSQ>1.5, when sample size is small or test length is short."

PTMEASUR-AL CORR.

PTMEASUR-AL EXP.

an observed point-correlation: PTBISERL-AL, PTBISERL-EX, PTMEASURE-A, PTMEASUR-EX, see Correlations.  Negative reported correlations suggest that the orientation of the scoring on the item, or by the person, may be opposite to the orientation of the latent variable. This may be caused by item miskeying, reverse scoring, person special knowledge, guessing, data entry errors, or the expected randomness in the data.

 

In FIT ORDER Tables 6.1 and 10.1, letters A, B, ... indicating the identity of persons or items appearing on the Infit and Outfit plots, Tables 4, 5, 8, 9,  precede the correlations. If the point-correlation is inestimable because items have different numbers of categories, this column does not appear, or only the FIT letters display.

 

EXP. is the expected value of the point-correlation when the data fit the Rasch model with the estimated measures. See Correlations.

EXACT MATCH OBS%

EXACT MATCH EXP%

OBServed% is the percent of data points that are within 0.5 score points of their expected values, i.e., that match predictions.

EXPected% is the percent of data points that are predicted to be within 0.5 score points of their expected values.

ESTIM DISCRIM

an estimate of the item discrimination, see DISCRIM=

ASYMPTOTE LOWER

ASYMPTOTE UPPER

estimates of the upper and lower asymptotes for dichotomous items, see ASYMPTOTE=

P-VALUE

the observed proportion-correct (p-value) for 0/1 dichotomies, or observed average rating on the item, see PVALUE=.

RMSR

root-mean-square-residual of observations not in extreme scores, see RMSR=.

WEIGH

the weight assigned by IWEIGHT= or PWEIGHT=. When WEIGHT = 0.0, the item or person is estimated, but does not influence the estimate of any other item or person.

DISPLACE

the displacement of the reported MEASURE from its data-derived value. This should only be shown with anchored measures. The displacement values can be see in IFILE= and PFILE= output files.

The displacement is an estimate of the amount to add to the MEASURE to make it conform with the data.
+ logit displacement for a person ability indicates that the observed person score is higher (higher ability) than the expected person score based on the reported measure (anchor value).
+ logit displacement for an item difficulty indicates that the observed item score is lower (harder item) than the expected item score based on the reported measure (anchor value).
Unanchored measures: If small displacements are shown, tighten the convergence criteria, CONVERGE=, LCONV=, RCONV=
Anchored measures: we expect half the displacements to be negative and half to be positive, and for them to be normally distributed according to the standard errors of the measures.

PERSON

ITEM

the name of the list of persons (data rows) or items (data columns) reported here

G

the grouping code assigned with ISGROUPS=. Table 3.2, 3.3, etc. show the details of rating scales, etc., for each grouping code.

M

model code assigned with MODELS=

SUBSET:

the person or items are in incomparable subsets, see Subsets.

 

Reported

STATUS

PFILE=, IFILE=

Measured?

Reason

A (after Measure)

2

Yes

Anchored (fixed) measure. The reported S.E. is that which would have been obtained if the value had been estimated. Values are reported in logits with two decimal places, unless rescaled by USCALE=, UDECIM=

(MEASURE)

1

Yes

Estimated measure

MINIMUM

0

Yes

Extreme minimum score. Measure estimated using EXTRSC=

MINIMUM and MAXIMUM measures may occur because other MINIMUM and MAXIMUM measures have been dropped from the estimation. Inspect with TOTALSCORE=No.

MAXIMUM

-1

Yes

Extreme maximum score. Measure estimated using EXTRSC=

MINIMUM and MAXIMUM measures may occur because other MINIMUM and MAXIMUM measures have been dropped from the estimation.  Inspect with TOTALSCORE=No.

DROPPED

-2

No

No responses available for measurement. Perhaps due to CUTLO=, CUTHI=, CODES=, or deletion of other persons or items.

DELETED

-3

No

Deleted by user. PDELETE=, PDFILE=, IDELETE=, IDFILE=, PSELECT=, ISELECT=

INESTIMABLE: HIGH

-4

No

Inestimable: high (all responses in the same category with ISGROUPS=0 or CUTHI=). The measure probably has a high value. For an item, this can be resolved using SAFILE= or grouping this item with a similar estimable item:

SAFILE=*

23 0 0 ; item-number bottom-category 0

23 1 0 ; item-number top-category 0

*

INESTIMABLE: LOW

-5

No

Inestimable: low (all responses in the same category with ISGROUPS=0 or CUTLO=).  The measure probably has a low value. For an item, this can be resolved using SAFILE=  or grouping this item with a similar estimable item:

SAFILE=*

23 0 0 ; item-number bottom-category 0

23 1 0 ; item-number top-category 0

*

DROPPED

A (after Measure)

-6

Yes

Anchored (fixed) measure with no observed raw score

DESELECTED

-7 to -16

No

Temporarily deselected by Specification box with iSELECT= , etc. (usual STATUS - 10)

OMITTED

-17 to -26

No

Temporarily deleted by Specification box with iDELETE=, etc. (usual STATUS - 20)

REMOVED

-27 to -36

No

Temporarily deselected and deleted by Specification box with iSELECT= , etc., and iDELETE=, etc. (usual STATUS - 30)


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Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
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Coming Rasch-related Events
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