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Table 8.1 Dichotomy, binomial trial and Poisson statistics |
Top Up Down
A A |
Scale codes in Models= and Rating (or partial credit) scale= control this Table of statistics for scale structures. For each modelled scale found in the data, a table is produced.
Dichotomies
This is generated by
Models=?,?,D
Table 8.1 Category Statistics.
Model = ?,?,D
--------------------------------------------
| DATA | QUALITY CONTROL |
| Category Counts Cum.| Avge Exp. OUTFIT|
|Score Used % % | Meas Meas MnSq |
--------------------------------------------
| 0 240 50% 50%| -3.36 -3.34 .8 |
| 1 236 50% 100%| 3.03 3.02 .6 |
--------------------------------------------
The column headings mean:
DATA = |
Information relating to the data |
Category Counts = |
Observed frequency of each category |
Score = |
Cardinal value assigned to each category, i.e., its rating. |
Used = |
Number of observations that participated in the estimation. |
% = |
Percent of the Used responses which are in this category. |
Cum. % = |
Cumulative percentage of responses in this category and lower. |
FIT = |
Information regarding validity of the data. |
Avge Meas = |
The average of the measures that are modeled to generate the observations in this category. If Avge Measure does not increase with category score, then the measure is flagged with a "*", and doubt is cast on the idea that larger response scores correspond to "more" of the variable. |
Exp. Meas = |
The expected value of the average measures. This provides guidance whether observations in a category are higher or lower than expected. |
OUTFIT MnSq = |
The unweighted mean-square for observations in this category. Mean-squares have expectation of 1.0. Values much larger than 1.0 indicate unexpected observations in this category. Central categories usually have smaller mean-squares than extreme categories. The INFIT MnSq is not reported because it approximates the OUTFIT MnSq when the data are stratified by category. |
Obsd-Expd Diagnostic Residual = |
score-point difference between the observed count of responses and the expected count, based on the Rasch measures. This is shown only when it is greater than 0.5 score-points for some category. This can be due to |
Response Category Name = |
name of category from Rating (or partial credit) scale= specification |
Binomial Trials with Fixed Discrimination
This is generated by
Models=?,?,B22 where 22 is the number of trials. This estimates a fixed binomial discrimination.
or
Models=?,?,Trials
Rating (or partial credit) scale=Trials,B22
0=0,1,A
*
Table 8.2 Category Statistics.
Model = 22,?,-?,B22
-------------------------------------------------------
| DATA | QUALITY CONTROL | Obsd-Expd|
| Category Counts Cum.| Avge Exp. OUTFIT|Diagnostic|
|Score Used % % | Meas Meas MnSq | Residual |
-------------------------------------------------------
| 4 .5 2% 2%| -.59 -1.31 1.2 | |
| 5 .5 2% 4%| -.91* -1.90 .2 | -.7 |
....
| 17 .5 2% 98%| .91 1.90 .2 | -.7 |
| 18 .5 2% 100%| .59* 1.31 1.2 | |
-------------------------------------------------------
Binomial trials discrimination: 1.00 Anchored
Binomial trials discrimination: 1.00 Anchored
reports the discrimination of the numerical observations for binomial trials and Poisson counts, either pre-set (anchored) or with its S.E.
Discrimination is anchored, unless scale type is specified using Rating (or partial credit) scale=
Binomial Trials with Estimated Discrimination
Specify
Models=?,?,Trials
Rating (or partial credit) scale=Trials,B22
The Binomial trials discrimination parameterizes the binomial rating scale term in the model. The separate Rating Scale= specifies a scale discrimination. ai in the following model:
log (Pnik/Pnik-1) = Bn - Di - ai log (k/(m-k+1))
Table 8.2 Category Statistics.
Model = 22,?,-?,BB22
Rating (or partial credit) scale = BB22,B22,G,O
-------------------------------------------------------
| DATA | QUALITY CONTROL | Obsd-Expd|
| Category Counts Cum.| Avge Exp. OUTFIT|Diagnostic|
|Score Used % % | Meas Meas MnSq | Residual |
-------------------------------------------------------
| 4 .5 2% 2%| -.60 -1.32 1.3 | |
| 5 .5 2% 4%| -.93* -1.95 .2 | -.7 |
| 6 3.5 14% 18%| -.81 -.33 1.6 | 2.0 |
....
| 15 1.5 6% 82%| .76 .77 .3 | |
| 16 3.5 14% 96%| .81 .33 1.6 | 2.0 |
| 17 .5 2% 98%| .93 1.95 .2 | -.7 |
| 18 .5 2% 100%| .60* 1.32 1.3 | |
-------------------------------------------------------
Binomial trials discrimination: 1.03 S.E. .07
Poisson Counts with Fixed Discrimination
Specify
Models=?,?,Poisson
Rating (or partial credit) scale=Poisson,P
0=0,1,A
*
The separate Rating Scale= specifies a fixed Poisson scale discrimination.
log(Pnik/Pnik-1) = Bn - Di - log(k)
Table 8.1 Category Statistics.
Model = ?B,?B,?,P
-------------------------------------------------------
| DATA | QUALITY CONTROL | Obsd-Expd|
| Category Counts Cum.| Avge Exp. OUTFIT|Diagnostic|
|Score Used % % | Meas Meas MnSq | Residual |
-------------------------------------------------------
| 40 1 4% 4%| 3.64 .63 .8 | .8 |
| 41 0 0% 4%| | |
| 42 0 0% 4%| | |
| 43 1 4% 8%| 3.77 .72 .0 | .8 |
|.....
|133 0 0% 96%| | |
|134 1 4% 100%| 4.81 .37 9.9 | .9 |
-------------------------------------------------------
Poisson discrimination: 1.00 Anchored
Poisson Counts with Estimated Discrimination
Specify
Models=?,?,Poisson
Rating (or partial credit) scale=Poisson,P
The separate Rating Scale= specifies a scale discrimination, ai, is to be estimated.
log(Pnik/Pnik-1) = Bn - Di - ai log(k)
Table 8.1 Category Statistics.
Model = ?B,?B,?,CHOPS
Rating (or partial credit) scale = CHOPS,P,G,O
-------------------------------------------------------
| DATA | QUALITY CONTROL | Obsd-Expd|
| Category Counts Cum.| Avge Exp. OUTFIT|Diagnostic|
|Score Used % % | Meas Meas MnSq | Residual |
-------------------------------------------------------
| 40 1 4% 4%| .77 .14 .1 | .8 |
| 41 0 0% 4%| | |
| 42 0 0% 4%| | |
| 43 1 4% 8%| .79 .16 .0 | .8 |
...
|133 0 0% 96%| | |
|134 1 4% 100%| 1.02 .08 2.1 | .9 |
-------------------------------------------------------
Poisson discrimination: .21 S.E. .00
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