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

 

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 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

 


Help for Facets Rasch Measurement Software: www.winsteps.com Author: John Michael Linacre.
 

For more information, contact info@winsteps.com or use the Contact Form
 

Facets Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download
Winsteps Rasch measurement software. Buy for $149. & site licenses. Freeware student/evaluation download

State-of-the-art : single-user and site licenses : free student/evaluation versions : download immediately : instructional PDFs : user forum : assistance by email : bugs fixed fast : free update eligibility : backwards compatible : money back if not satisfied
 
Rasch, Winsteps, Facets online Tutorials

 

Forum Rasch Measurement Forum to discuss any Rasch-related topic

Click here to add your email address to the Winsteps and Facets email list for notifications.

Click here to ask a question or make a suggestion about Winsteps and Facets software.

Rasch Publications
Rasch Measurement Transactions (free, online) Rasch Measurement research papers (free, online) Probabilistic Models for Some Intelligence and Attainment Tests, Georg Rasch Applying the Rasch Model 3rd. Ed., Bond & Fox Best Test Design, Wright & Stone
Rating Scale Analysis, Wright & Masters Introduction to Rasch Measurement, E. Smith & R. Smith Introduction to Many-Facet Rasch Measurement, Thomas Eckes Invariant Measurement with Raters and Rating Scales: Rasch Models for Rater-Mediated Assessments, George Engelhard, Jr. & Stefanie Wind Statistical Analyses for Language Testers, Rita Green
Rasch Models: Foundations, Recent Developments, and Applications, Fischer & Molenaar Journal of Applied Measurement Rasch models for measurement, David Andrich Constructing Measures, Mark Wilson Rasch Analysis in the Human Sciences, Boone, Stave, Yale
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
Winsteps Tutorials Facets Tutorials Rasch Discussion Groups

 

Coming Rasch-related Events
Jan. 5 - Feb. 2, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
Jan. 10-16, 2018, Wed.-Tues. In-person workshop: Advanced Course in Rasch Measurement Theory and the application of RUMM2030, Perth, Australia (D. Andrich), Announcement
Jan. 17-19, 2018, Wed.-Fri. Rasch Conference: Seventh International Conference on Probabilistic Models for Measurement, Matilda Bay Club, Perth, Australia, Website
Jan. 22-24, 2018, Mon-Wed. In-person workshop: Rasch Measurement for Everybody en español (A. Tristan, Winsteps), San Luis Potosi, Mexico. www.ieia.com.mx
April 10-12, 2018, Tues.-Thurs. Rasch Conference: IOMW, New York, NY, www.iomw.org
April 13-17, 2018, Fri.-Tues. AERA, New York, NY, www.aera.net
May 22 - 24, 2018, Tues.-Thur. EALTA 2018 pre-conference workshop (Introduction to Rasch measurement using WINSTEPS and FACETS, Thomas Eckes & Frank Weiss-Motz), https://ealta2018.testdaf.de
May 25 - June 22, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com
June 27 - 29, 2018, Wed.-Fri. Measurement at the Crossroads: History, philosophy and sociology of measurement, Paris, France., https://measurement2018.sciencesconf.org
June 29 - July 27, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Further Topics (E. Smith, Winsteps), www.statistics.com
July 25 - July 27, 2018, Wed.-Fri. Pacific-Rim Objective Measurement Symposium (PROMS), (Preconference workshops July 23-24, 2018) Fudan University, Shanghai, China "Applying Rasch Measurement in Language Assessment and across the Human Sciences" www.promsociety.org
Aug. 10 - Sept. 7, 2018, Fri.-Fri. On-line workshop: Many-Facet Rasch Measurement (E. Smith, Facets), www.statistics.com
Sept. 3 - 6, 2018, Mon.-Thurs. IMEKO World Congress, Belfast, Northern Ireland www.imeko2018.org
Oct. 12 - Nov. 9, 2018, Fri.-Fri. On-line workshop: Practical Rasch Measurement - Core Topics (E. Smith, Winsteps), www.statistics.com

 

Our current URL is www.winsteps.com

Winsteps® is a registered trademark
 

Concerned about aches, pains, youthfulness? Mike and Jenny suggest Liquid Biocell