For each modelled scale code in Models= and Rating (or partial credit) scale= , found in the data, a table is produced. The heading describes which model the scale applies to. Only columns applicable to the type of scale are output.

 

Table 8.1  Category Statistics.

 

Model = ?,?,FACES

Rating (or partial credit) scale = FACES,R2,G,O

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|      DATA            |     FIT     |   STEP      |  EXPECTATION  |  MOST  |THURSTONE| Cat| Obsd-Expd|Response   |

| Category Counts  Cum.| Avge  OUTFIT|CALIBRATIONS |  Measure at   |PROBABLE|THRESHOLD|PEAK|Diagnostic|Category   |

|Score   Used   %    % |Measure  MnSq|Measure  S.E.|Category  -0.5 |  from  |    at   |Prob| Residual |  Name     |

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|  0      378  20%  20%|   -.87  1.2 |             |( -2.04)       |   low  |   low   |100%|      -.7 | dislike   |

|  1      620  34%  54%|    .13   .7 |  -.85    .07|    .00   -1.17|   -.85 |  -1.00  | 54%|          | don't know|

|  2      852  46% 100%|   2.23  1.5 |   .85    .06|(  2.05)   1.18|    .85 |    .99  |100%|          | like      |

------------------------------------------------------(Mean)---------(Modal)--(Median)-----------------------------

 

The column headings mean:

DATA =        Information relating to the data

Category Counts =        Observed use 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. % =        Percent of the Used responses in or below this category.

 

FIT =        Information relating to the validity of the categorization.        

Avge Measure =        The average of the measures that are modeled to generate the observations in this category. If Average Measure does not increase with each higher category, then the category average measure is flagged with a "*", and doubt is cast on the idea that higher categories correspond to "more" of the variable.

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. Extreme categories have greater opportunity for large mean-squares than central categories.

       The INFIT MnSq is not reported because it approximates the OUTFIT MnSq when the data are stratified by category.

 

SCALE CALIBRATIONS =

Measure =        calibration of the step up to this category. This is the Rasch model parameter. Use this for step anchor calibrations, or starting values.

S.E. =        standard error of the step calibration.

 

EXPECTATION Measure (Mean) =

       gives the details of the logit-to-expected score ogive.

at Category

       logit measure for the expected score corresponding to the value in the category score column. Calibrations corresponding to extreme responses, e.g., (-2.70), correspond to expected responses 0.25 score points from the extreme response, i.e., half way between the extreme response and 0.5 score points.

at -0.5

       logit measure for the expected score corresponding to the value in the category score column less 0.5 score points. These can be thought of as the transition points into one expected score from the one below.

 

MOST PROBABLE from (Mode) =

       lowest measure at which this category is the one most probable to be observed. It continues to be the most probable (modal) category until a numerically higher category becomes most probable.

       "low" indicates the most probable category at the low end of the scale.

       "no" indicates this category is never the most probable to be observed for any measure.

 

THURSTONE THRESHOLD at (Median) =

       measure at which the probability of being rated in this category or above equals that of being rated in any of the category below, i.e., is .5., i.e., the Rasch-Thurstone threshold.

 

Cat PEAK Prob (at Mean) =

       The largest percentage probability this category has of being observed at any measure. Extreme categories have a maximum probability of 100% at the extremes of the measurement continuum. Intermediate categories have their peak probabilities when the expected response value is numerically equal to the intermediate category's response value.

 

Obsd-Expd Diagnostic Residual =

       This column is produced only when the difference between the observed count of responses and the expected count, based on the calibrations, is greater than 0.5 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.

       iv) contradictory modeling, e.g., models = ?,?,#,#,R6 can imply contradictory estimates for elements.

 

Response Category Name =        name of category from Rating (or partial credit) scale= specification