Calculating estimates

Initial estimates are obtained by the PROX algorithm, and then more refined ones by the JMLE (UCON) algorithm (or by the Facets implementation of PMLE). Check that convergence is occurring by reviewing the "Residual" and "Change" columns for smaller values each iteration. The iterative process can be terminated by pressing Ctrl+S simultaneously.


With T3onscreen= No, so that detailed output is displayed:


Table 3. Iteration Report

Iteration 1   Largest Residuals  |----------Score------------|   logit Measure

Facet     Name          No./Cat   Raw  Expected Residual Resd%  Value    Change


Junior Sc Betty               2     79                            .740     .740

Iteration    1  PROX                                               max.=   .740


PROX - "normal approximation algorithm" is used to make initial estimates.

If "PROX Recount required" is displayed, some elements or categories had a 0 or perfect score. Measure for these can not be estimated directly, so their estimation is deferred and all marginal scores recounted without them. PROX ceases when the maximum change is less than 0.1 logits


Iteration 2   Largest Residuals  |----------Score------------|   logit Measure

Facet     Name          No./Cat   Raw  Expected Residual Resd%  Value    Change

Checking subset connection..


Scale:    ?B,?B,?,CREATIVI    4     31      6.3     24.7  79.8   -.948    -.948

Scale:    ?B,?B,?,CREATIVI    5      6      6.5      -.5  -8.7    .961     .961

Junior Sc Fred                6     39     18.0     21.0  17.5   -.409     .237

Iteration    2  JMLE                       max.=    21.0  17.5     max.=   .237


JMLE= "joint maximum likelihood estimation" makes more precise estimates. The least-converged elements or rating-scale categories are shown (largest residual, largest residual percent, largest logit change). We want max.= to approach 0.


Subset connection O.K.


Facets confirms that all elements can be measured unambiguously in one frame of reference.



more JMLE iterations


Iteration 15  Largest Residuals  |----------Score------------|   logit Measure

Facet     Name          No./Cat   Raw  Expected Residual Resd%  Value    Change


Scale:    ?B,?B,?,CREATIVI    4     31     30.8       .2    .6  -1.477    -.001

Scale:    ?B,?B,?,CREATIVI    1      4      4.0       .0   -.7   -.644    -.009

Traits    Enthusiasm          5     58     58.4      -.4   -.2    .498     .004

Junior Sc Betty               2     79     78.7       .3    .2    .638     .005

Junior Sc Fred                6     39     39.3      -.3   -.2   -.562    -.004

Iteration   15  JMLE                       max.=     -.4   -.2     max.=   .005


JMLE ceases when the max.= values are small, and the convergence criteria are met. If the maximum residual does not decrease noticeably per iteration, then Estimation menu, "Bigger".. If the maximum residual oscillates between large positive and negative values, then Estimation menu "Reduce". See also "My analysis does not converge."


Column headings have the following meanings:

Facet = Name of the facet, as given in specifications or "Scale:" if details apply to a category of a rating scale (or partial credit).

Name = Name of element within Facet or model statement of a rating scale (or partial credit)

No./Cat = Number of element within facet or category number of a rating scale (or partial credit)



Raw = Raw score (= sum of categories, after renumbering if necessary), or count of responses in category, an integer

Expected = Score or count expected based on current estimates, in tenths

Residual = Difference between observed Score and Expected score, in tenths

Resd% = Residual/(Maximum score - minimum score)%.


Logit Measure

Value = Revised estimate of parameter in log-odds units (logits) as a result of this iteration.

Change = Change in logit estimate from logit estimate of the previous iteration.


max.= is the maximum change or residual corresponding to any element, used to determine convergence.


Iteration = The number of times PROX or JMLE has been applied to the data.



Analysis fails after recounting


Table 3. Iteration Report


| Iteration      Max. Score Residual      Max. Logit Change |

|             Elements    %  Categories   Elements    Steps |


Validating subset connection... (Subsets=No to bypass)


| PROX   1     Recount required             3.6889          |

Consolidating 2 subsets


Subset connection O.K.


| PROX   2     Recount required             2.3615          |


| PROX   3     Recount required             3.6142          |




| PROX  20     Recount required           -20.4497          |


| PROX  21     Recount required            -5.2877          |

Error F36: All data eliminated as extreme.


This report suggests that Models= does not match the data or that there are not enough observations to estimate the rating-scale structure.

Suggestion: specify a predefined rating-scale structure, such as Binomial Trials. For instance:

Models = ?, ?, B6  ; instead of R6

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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
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