Table 8.1 Dichotomy, binomial trial and Poisson statistics

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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
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

 

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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