Table 44.1 Global statistics

Global statistics:

Statistics based on the currently-selected data, omitting permanently and temporarily deleted, deselected and dropped items and persons

Active person, weighted

Persons currently active in this analysis. Weighted count only if active persons are weighted.

Active item, weighted

Items currently active in this analysis. Weighted count only if active items are weighted.

Active datapoints, weighted

Observations/responses currently active in this analysis (includes extreme scores).  Weighted count only if active items or persons are weighted.

% of Active+Missing datapoints

If any potentially active data are missing, then percent that are active.

Non-extreme datapoints, weighted

Observations/responses currently active in this analysis (excludes extreme scores). Weighted count if any active persons or items are weighted

Missing datapoints

Observations/responses not active in this analysis, usually because they do not have scored values

Standardized residuals N(0,1):

 mean: P.SD:

Standardized Residuals are modeled to have a unit normal distribution. Gross departures from mean of 0.0 and standard deviation of 1.0 indicate that the data do not conform to the basic Rasch model specification that randomness in the data be normally distributed. and standardized residuals to be close to mean 0.0, P.SD 1.0.

Log-likelihood chi-squared:

The chi-square value is approximately = -2 * log-likelihood of the active datapoints. It is based on the currently-reported estimates which may depart noticeably from the "true" maximum likelihood estimates for these datapoints.

with approximately .... d.f.,

the degrees of freedom are obtained by performing 100 simulations of Rasch-conforming data matching the active datapoints. The estimated d.f. will vary slightly with each output of Table 44. To keep the estimated d.f. constant, specify SISEED= a value 2 or greater.

probability  = ....

the probability that these data fit the Rasch model globally. There can be considerable local misfit in Tables 6 and 10.

Global (Weighted) Root-Mean-Square Residual (RMSR):

this is √(∑(X-E)²) where the sum is across X, each of the observations, and E, the expectation of each observation according to the Rasch model. Weighting is applied to the data if IWEIGHT= or PWEIGHT= are specified.

with expected value:

the expected value of the RMSR according to the Rasch model. RMSR values smaller than the expected value indicate better fit (or overfit) to the Rasch model.

Capped (Weighted) Binomial Deviance (CBD) = ... for ... dichotomies

this is the average of -[X*LOG10(E) + (1-X)*LOG10(1-E)] for all dichotomous observations where X=0,1 is the observation and E is its Rasch-model expectation. E is limited to the range 0.01 to 0.99. Weighting is applied to the data if IWEIGHT= or PWEIGHT= are specified.

Glickman, Mark E. "Parameter estimation in large dynamic paired comparison experiments." Journal of the Royal Statistical Society: Series C (Applied Statistics) 48.3 (1999): 377-394.

with expected value ...

the expected value of the CBD according to the Rasch model. CBD values smaller than the expected value indicate better fit (or overfit) to the Rasch model.