Table 8.1 Dichotomy, binomial trial and Poisson statistics |
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.
Dichotomies
This is generated by
Models=?,?,D
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 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 |
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)))
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
*
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)
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)
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