|
Polytomous mean-square fit statistics |
Top Up Down
A A |
Response String Easy............Hard |
INFIT |
OUTFIT |
Point-measure correlation |
Diagnosis |
|
|
|
|
|
I. modeled: |
|
|
|
|
33333132210000001011 |
0.98 |
0.99 |
0.78 |
Stochastically |
31332332321220000000 |
0.98 |
1.04 |
0.81 |
monotonic in form |
33333331122300000000 |
1.06 |
0.97 |
0.87 |
strictly monotonic |
33333331110010200001 |
1.03 |
1 |
0.81 |
in meaning |
|
|
|
|
|
II. overfitting (muted): |
|
|
|
|
33222222221111111100 |
0.18 |
0.22 |
0.92 |
Guttman pattern |
33333222221111100000 |
0.31 |
0.35 |
0.97 |
high discrimination |
32222222221111111110 |
0.21 |
0.26 |
0.89 |
low discrimination |
32323232121212101010 |
0.52 |
0.54 |
0.82 |
tight progression |
|
|
|
|
|
III. limited categories: |
|
|
|
|
33333333332222222222 |
0.24 |
0.24 |
0.87 |
high (low) categories |
22222222221111111111 |
0.24 |
0.34 |
0.87 |
central categories |
33333322222222211111 |
0.16 |
0.2 |
0.93 |
only 3 categories |
|
|
|
|
|
IV. informative-noisy: |
|
|
|
|
32222222201111111130 |
0.94 |
1.22 |
0.55 |
noisy outliers |
33233332212333000000 |
1.25 |
1.09 |
0.77 |
erratic transitions |
33133330232300101000 |
1.49 |
1.4 |
0.72 |
noisy progression |
33333333330000000000 |
1.37 |
1.2 |
0.87 |
extreme categories |
|
|
|
|
|
V. non-informative: |
|
|
|
|
22222222222222222222 |
0.85 |
1.21 |
0 |
one category |
12121212121212121212 |
1.5 |
1.96 |
-0.09 |
central flip-flop |
01230123012301230123 |
3.62 |
4.61 |
-0.19 |
rotate categories |
03030303030303030303 |
5.14 |
6.07 |
-0.09 |
extreme flip-flop |
03202002101113311002 |
2.99 |
3.59 |
-0.01 |
random responses |
|
|
|
|
|
VI. contradictory: |
|
|
|
|
11111122233222111111 |
1.75 |
2.02 |
0 |
folded pattern * |
11111111112222222222 |
2.56 |
3.2 |
-0.87 |
central reversal |
22222222223333333333 |
2.11 |
4.13 |
-0.87 |
high reversal |
00111111112222222233 |
4 |
5.58 |
-0.92 |
Guttman reversal |
00000000003333333333 |
8.3 |
9.79 |
-0.87 |
extreme reversal |
from Smith R.M. (1996) Rasch Measurement Transactions 10:3 p. 516
The z-score standardized statistics 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.
* "folded data" can often be rescued by imposing a theory of "not reached" and "already passed" on to the observations. For instance, in archaeological analysis, the absence of bronze implements can mean a "stone age" or an "iron age" society. A useful recoding would be "1" = "stone age", "2" = "early bronze", "3" = "bronze", "2=>4" = "late bronze", "1=>5" = "iron age". This can be done iteratively to obtain the most self-consistent set of 4's and 5's. (Folding is discussed in Clive Coombes' "A Theory of Data".)