Table 8.1 Rating scale statistics

For each modeled 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.

+------------------------------------------------------------------------------------------------------------------------+

|----------------------+-------------------+-------------+---------------+--------+----------+----+----------+-----------|

| 0 378 20% 20%| -.87 -1.03 1.2 | |( -2.04) | low | low |100%| -.9 | dislike |

| 1 620 34% 54%| .13 .33 .7 | -.85 .07| .00 -1.17| -.85 | -1.00 | 54%| | don't know|

| 2 852 46% 100%| 2.23 2.15 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. If two Scores are shown, the second score is after structural zeroes have been removed
Used	Number of observations that participated in the estimation.
%	Percent of the Used responses which are in this category. The observed probability is the "Category Counts %" divided by 100. The probability of paired agreement by chance is sum (probability of each category2) across all the categories. In the Table above, Probabilities = .20, .34, .46 (they sum to 1.0) Probability2 = Probability * Probability = .04, .13, .21 Sum (Probability**2) = .04 + .13 + .21 = .38 = Agreement by chance
Cum. %	Percent of the Used responses in or below this category.
QUALITY CONTROL	Information relating to the validity of the categorization.
Avge Meas	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.
Exp. Meas	The expected value of the average measure if these data fit the Rasch model.
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.
RASCH-ANDRICH THRESHOLDS	Step calibrations, rating scale structure
Measure	value of the Rasch-Andrich threshold, the location on the latent variable (relative to the center of the rating scale) where adjacent categories are equally probable. This is the Rasch model parameter. Use this for anchoring rating scale, or for estimation starting-values.
S.E.	standard error of the Rasch-Andrich threshold (step calibration).
EXPECTATION Measure at	gives the details of the logit-to-expected-score ogive. This is the expected (mean) value of the observations for measures at this point on the latent variable relative to the rating scale.
at Category	logit measure for the expected score on the rating scale corresponding to the value in the category score column. Measures 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	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.
RASCH-THURSTONE Thresholds	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 50% (median) cumulative probability threshold.
Cat PEAK Prob	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, the "at Category" 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 Rasch measures, is greater than 0.5 for some category. This can be due to i) lack of convergence: set smaller values in 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

Unobserved Categories: Structural Zeroes or Incidental (Sampling) Zeroes

Structural zero: A category cannot be observed, and is omitted from qualitative levels. (The default.)

"Category" shows the category number. "Score" shows the value used for analysis.

Model = ?,?,R3

+----------------------------------------------------------------------------------------------------------------+

|--------------------------+-------------------+-------------+---------------+--------+----------+----+----------|

| 0 0 378 20% 20%| -.87 -1.03 1.2 | |( -2.04) | low | low |100%| -.9 |

| 1 1 620 34% 54%| .13 .33 .7 | -.85 .07| .00 -1.17| -.85 | -1.00 | 54%| |

| 2 | | | | | | | |

| 3 2 852 46% 100%| 2.23 2.15 1.5 | .85 .06|( 2.05) 1.18| .85 | .99 |100%| |

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

Incidental (Sampling) zero: A category can be observed (but not in this dataset). It is included in the qualitative levels. (Keep.) The "Category Score" is the value used for analysis.

Model = ?,?,R3K <= K means "Keep unobserved intermediate categories"

+------------------------------------------------------------------------------------------------------------+

|----------------------+-------------------+-------------+---------------+--------+----------+----+----------|

| 0 378 20% 20%| -.68 -.74 1.2 | |( -1.99) | low | low |100%| 1.0 |

| 1 620 34% 54%| -.11 -.06 .6 | -.90 .07| -.23 -1.09| -.90 | -.95 | 56%| -.7 |

| 2 0 0% 54%| | | .63 .24| | .55 | 0%| |

| 3 852 46% 100%| 1.35 1.34 1.7 | .90 .07|( 1.50) 1.10| .90 | .55 |100%| |

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

Equivalence with Winsteps output:

Winsteps:

-------------------------------------------------------------------

|CATEGORY OBSERVED|OBSVD SAMPLE|INFIT OUTFIT||STRUCTURE|CATEGORY|

|LABEL SCORE COUNT %|AVRGE EXPECT| MNSQ MNSQ||CALIBRATN| MEASURE|

|-------------------+------------+------------++---------+--------|

| 0 0 378 20| -.87 -1.03| 1.08 1.19|| NONE |( -2.07)| 0 Dislike

| 1 1 620 34| .13 .33| .85 .69|| -.86 | .00 | 1 Neutral

| 2 2 852 46| 2.24 2.16| 1.00 1.47|| .86 |( 2.07)| 2 Like

-------------------------------------------------------------------

---------------------------------------------------------------------------

| LABEL MEASURE S.E. | AT CAT. ----ZONE----|PROBABLTY| M->C C->M|DISCR|

|------------------------+---------------------+---------+----------+-----|

| 0 NONE |( -2.07) -INF -1.19| | 62% 42%| | 0 Dislike

| 1 -.86 .07 | .00 -1.19 1.19| -1.00 | 54% 71%| .73| 1 Neutral

| 2 .86 .06 |( 2.07) 1.19 +INF | 1.00 | 85% 78%| 1.19| 2 Like