Scale codes in Models= and Rating (or partial credit) scale= control this Table of statistics for scale structures. For each modeled scale found in the data, a table is produced.
To see the Average Measure for the categories of each item for the Rating Scale model: ?,?,?,...
1. do the rating scale analysis
2. output the anchor file: Anchorfile=
3. leave everything anchored, but change the Models= to put # for the facet you want the ability mean measures.
4. analyze the anchor file
Dichotomies
This is generated by
Models=?,?,D
Table 8.1 Category Statistics.
Model = ?,?,D
+----------------------------------------------------+
| DATA | QUALITY CONTROL |
| Category Counts Cum.| Avge Exp. OUTFIT|
|Score Total Used % % | Meas Meas MnSq |
|--------------------------------+-------------------|
| 0 289 240 50% 50%| -3.39 -3.38 .8 |
| 1 341 236 50% 100%| 3.06 3.05 .6 |
+----------------------------------------------------+
The column headings mean:
DATA =
|
Information relating to the data
|
Score =
|
Cardinal value assigned to each category, i.e., its rating.
|
Category Counts
Total =
Used =
|
Number of observations of this category in the analysis
Number of observations that participated in the estimation (excludes observations in extreme scores)
|
% =
|
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
i) lack of convergence
ii) anchor values incompatible with the data
iii) responses do not match the specified scale structure, e.g., Poisson counts.
|
Response Category Name =
|
name of category from Rating (or partial credit) scale= specification
|
Dichotomies with anchored thresholds are reported as Table 8.1 Rating Scales
+----------------------------------------------------------------------------------------------------------+
| DATA | QUALITY CONTROL |RASCH-ANDRICH| EXPECTATION | MOST | RASCH- | Cat|Response|
| Category Counts Cum.| Avge Exp. OUTFIT| Thresholds | Measure at |PROBABLE| THURSTONE|PEAK|Category|
|Score Used % % | Meas Meas MnSq |Measure S.E.|Category -0.5 | from |Thresholds|Prob| Name |
|----------------------+-------------------+-------------+---------------+--------+----------+----+--------|
| 0 27 79% 79%| -.79 -.67 .6 | |( .87) | low | low |100%| 0 |
| 1 7 21% 100%| 2.34 1.87 .3 | 2.00A |( 3.07) 1.99| 2.00 | 1.99 |100%| 1 |
+----------------------------------------------------------------------------------------------------------+
Binomial Trials with Estimated Discrimination
This is generated by
Models=?,?,B22 where 22 is the number of trials. This estimates the binomial discrimination.
or
Models=?,?,Trials
Rating (or partial credit) scale=Trials,B22
0=Lowest category
*
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
Binomial Trials with Fixed Discrimination
This is generated by
Models=?,?,Trials
Rating (or partial credit) scale=Trials,B22
0=0,1.0,A ; 1.0 is the anchored (pre-set, fixed) discrimination of the binomial scale
*
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=
Poisson Counts with Estimated Discrimination
Specify
Models=?,?,P
or
Models=?,?,Poisson
Rating (or partial credit) scale=Poisson,P
0 = Lowest
*
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
Poisson Counts with Fixed Discrimination
Specify
Models=?,?,Poisson
Rating (or partial credit) scale=Poisson,P
0=0,1.0,A ; 1.0 is the anchored (pre-set, fixed) discrimination of the Poisson scale
*
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
