Table 3 Iteration report for the main analysis

Convergence= and Iterations= control the number of iterations performed. Write=Yes writes the details reported on screen into Table 2. The number of iterations required depends on how difficult it is to obtain good estimates from the data. Many iterations may be required if

 

1) there is a poor fit of the data to the Rasch model.

2) the element parameter distribution is badly skewed or multi-modal.

3) there are rarely observed response categories.

4) exceedingly precise Convergence= criteria have been specified.

5) the data matrix is composed of disjoint subsets of observations, e.g., boys rated by Judge A, but girls by Judge B. When this is detected, a warning message is displayed.

 

 

Table 3. Iteration Report.

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

| Iteration      Max. Score Residual      Max. Logit Change |

|             Elements    %  Categories   Elements    Steps |

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

| PROX   1                                   .7405          |

| JMLE   2     26.6978  22.2    29.9588      .3374    .9902 |

| JMLE   3     22.4284  13.4    27.3399     -.1155   1.0049 |

| JMLE   4     11.0189   6.6    22.0935     -.0514    .9957 |

| JMLE   5     -3.5380  -2.9     9.5224     -.0304   -.7481 |

| JMLE   6     -5.7141  -4.8     2.6727     -.0620   -.2008 |

| JMLE   7     -4.5692  -3.4     1.8210      .0501   -.0892 |

| JMLE   8     -3.5327  -2.5     1.4746      .0393   -.0599 |

| JMLE   9     -2.7709  -1.9     1.2091      .0314   -.0529 |

| JMLE  10     -2.1980  -1.4      .9963      .0255   -.0446 |

| JMLE  11     -1.7600  -1.1      .8245      .0209   -.0371 |

| JMLE  12     -1.4209   -.9      .6847      .0172   -.0309 |

| JMLE  13     -1.1553   -.7      .5703      .0143   -.0258 |

| JMLE  14      -.9451   -.6      .4761      .0119   -.0215 |

| JMLE  15      -.7771   -.5      .3982      .0099   -.0180 |

| JMLE  16      -.6418   -.4      .3336      .0083   -.0151 |

| JMLE  17      -.5319   -.3      .2798      .0069   -.0127 |

| JMLE  18      -.4422   -.3      .2349      .0058   -.0106 |

| JMLE  19      -.3685   -.2      .1974      .0049   -.0089 |

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

Subset connection O.K.

 

Iteration counts the number of times the data has been read.

PROX is the "normal approximation algorithm" to obtain approximate estimates speedily. Steps are not estimated during PROX.

JMLE is joint (unconditional) maximum likelihood estimation to obtain precise estimates.

Facets generally produces its results with high precision. This precision is rarely needed in practice before the final runs. There are several ways to lower the precision of the results. Most immediately, Ctrl+F forces Facets to move into the reporting phase at the end of the current iteration through the data. Other specifications include Iterations= and Convergence=. Inspection of the iterations, Table 3 of the output, indicates when the changes per iteration are too small to have any important meaning at the current stage of your analysis. Here this happens after just 4 iterations.

 

Max. Score Residual

Elements: the largest difference (residual), in score points, between the observed and expected score corresponding to any element's parameter estimate. 1.0 is the smallest observable (i.e., in the data) difference with the standard model weighting of 1.

%: the largest residual as a percent of the (maximum possible score - minimum possible score) for any element.

Categories: the largest difference between the observed and expected counts of occurrence corresponding to any category of a rating scale (or partial credit). 1.0 is the smallest observable difference with the standard model weighting of 1.

 

Recount required

when this appears, it means that the scores corresponding to some element parameters had extreme values (either 0 or the maximum possible). These parameters are dropped from estimation, forcing a recount of the marginal scores of the other elements.

 

Max. Logit Change

Elements: the largest change, in logits, between any element parameter estimate this iteration and its estimate the previous iteration. Starting estimates are either 0.0 logits, or the values given in the specification file.

Categories: the largest change, in logits, between any step parameter estimate this iteration and its estimate the previous iteration. Starting estimates are either 0.0 logits, or the values given in the specification file.

 

After the first few iterations, both "Max. Score Residual" and "Max. Logit Change" should steadily reduce in absolute size, i.e., draw closer to zero. There may be occasional perturbations due to unusual data. If the iterative procedure seems to have reached a plateau, you may force termination by pressing the Ctrl+"S" keys simultaneously.

 

The more detailed iteration report, which appears on your screen, can be recorded in your output file with a "Write=Yes" specification

 

Subset connection O.K.

Facets has verified that all measures can be estimated in one, unambiguous frame of reference. Warning messages here require investigation.


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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
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Coming Winsteps & Facets Events
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