For a general introduction, see Diagnosing Misfit, also Polytomous mean-square fit statistics.
Person Responses to Items: Easy--Items--Hard |
Diagnosis of Pattern |
Person OUTFIT MnSq |
Person INFIT MnSq |
Point-Measure Correlation |
|---|---|---|---|---|
111¦0110110100¦000 |
Modeled/Ideal |
1.0 |
1.1 |
0.62 |
111¦1111100000¦000 |
Guttman/Deterministic |
0.3 |
0.5 |
0.87 |
000¦0000011111¦111 |
Miscoded |
12.6 |
4.3 |
-0.87 |
011¦1111110000¦000 |
Carelessness/Sleeping |
3.8 |
1.0 |
0.65 |
111¦1111000000¦001 |
Lucky Guessing |
3.8 |
1.0 |
0.65 |
101¦0101010101¦010 |
Response set/Miskey |
4.0 |
2.3 |
0.11 |
111¦1000011110¦000 |
Special knowledge |
0.9 |
1.3 |
0.43 |
111¦1010110010¦000 |
Imputed outliers * |
0.6 |
1.0 |
0.62 |
Right¦Transition¦Wrong |
|
|
|
|
high - low - high |
OUTFIT sensitive to outlying observations |
>>1.0 unexpected outliers |
>>1.0 disturbed pattern |
|
low - high - low |
INFIT sensitive to pattern of inlying observations |
<<1.0 overly predictable outliers |
<<1.0 Guttman pattern |
|
* as when a tailored test (such as a Binet intelligence test) is scored by imputing all "right" responses to un administered easier items and all "wrong" responses to un administered harder items. The imputed responses are indicated by italics |
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The exact details of these computations have been lost, but the items appear to be uniformly distributed about 0.4 logits apart, extracted from Linacre, Wright (1994) Rasch Measurement Transactions 8:2 p. 360
The ZSTD Z-score standardized Student's t-statistic report, as unit normal deviates, how likely it is to observe the reported mean-square values, when the data fit the model. The term 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 value has been adjusted to a unit normal value.
When there is guessing by a person, we expect
(1) the person to be on the less-able side
(2) the Outfit Mean-square to be large (much greater than 1.0)
(3) the point-measure correlation to be much less than expected
(4) the estimated lower asymptote for the person to be away from 0.0
(5) individual responses to be among the worst fitting.
Item Responses by Persons: High-Person-Ability-Low |
Diagnosis of Pattern |
Item OUTFIT MnSq |
Item INFIT MnSq |
Point-Measure Correlation |
|---|---|---|---|---|
111¦0110110100¦000 |
Modeled/Ideal |
1.0 |
1.1 |
0.62 |
111¦1111100000¦000 |
Guttman/Deterministic |
0.3 |
0.5 |
0.87 |
000¦0000011111¦111 |
Miscoded |
12.6 |
4.3 |
-0.87 |
011¦1111110000¦000 |
Carelessness/Sleeping |
3.8 |
1.0 |
0.65 |
111¦1111000000¦001 |
Lucky Guessing Response set |
3.8 |
1.0 |
0.65 |
000¦0010010001¦110 |
Miskey |
4.0 |
2.3 |
0.11 |
111¦1010110010¦000 |
Imputed outliers * |
0.6 |
1.0 |
0.62 |
111¦0101010101¦000 |
Low discrimination |
1.5 |
1.6 |
0.46 |
111¦1110101000¦000 |
High discrimination |
0.5 |
0.7 |
0.79 |
111¦1111010000¦000 |
Very high discrimination |
0.3 |
0.5 |
0.84 |
Right¦Transition¦Wrong |
|
|
|
|
high - low - high |
OUTFIT sensitive to outlying observations |
>>1.0 unexpected outliers |
>>1.0 disturbed pattern |
|
low - high - low |
INFIT sensitive to pattern of inlying observations |
<<1.0 overly predictable outliers |
<<1.0 Guttman pattern |
|
* as when a tailored test (such as a Binet intelligence test) is scored by imputing all "right" responses to un administered easier items and all "wrong" responses to un administered harder items. The imputed responses are indicated by italics |
||||
When there is guessing on an item, we expect
(1) the item to be on the difficult side
(2) the Outfit Mean-square to be large (much greater than 1.0)
(3) the point-measure correlation to be much less than expected
(4) the estimated lower asymptote to be away from 0.0
(5) the empirical ICC/IRF to have noticeably high lower tail. One glance at this, and we know we are in trouble!
