CMLE is considered statistically superior to other estimation methods, such as JMLE, MMLE, PMLE and Minimum Chi-square. CMLE has advantages, but also practical drawbacks.
Option
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Supported / Allowed
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Not Supported / Not allowed
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MODELS= model types
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"R" (the default) - dichotomies and rating scales
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CMLE analysis is not performed with "S", "F" - Success and Failure models
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ISGROUPS= rating scale models
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Dichotomous, Rating Scale Model, Partial Credit Model and Grouped Rating Scale Model
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All = ISGROUPS= options are supported
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Data structure, DATA= and EDFILE=
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Complete and Incomplete (missing data) datasets (rectangles)
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All Winsteps data structures supported
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Anchoring: PAFILE=, IAFILE=, SAFILE=
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Item anchoring IAFILE= and threshold (step) anchoring SAFILE= and person anchoring PAFILE= allowed.
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Weighting: IWEIGHT=, PWEIGHT=
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Person (row) weighting with PWEIGHT= supported for item and person estimation.
CMLE item and threshold estimation analysis is done ignoring IWEIGHT=, except for computing the item mean difficulty. Person estimates are made with IWEIGHT=
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Extreme scores (maximum and minimum possible)
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Allowed for persons (rows)
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Items with extreme scores are omitted from CMLE, but included in JMLE.
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Targeting (information weighting) : TARGET=
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No
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Not allowed
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Analysis of transposed data: TRPOFILE=
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Persons become columns ("items"), and items become rows ("persons"). ISGROUPS= applies to the columns (persons), not the rows (items). Andrich (2010)
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(supported)
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Unobserved intermediate categories in a rating scale
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Allowed with STKEEP=Yes. Reported as "NULL" in Table 3.2 and adjusted values in SFILE=
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Option
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What happens
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Notes
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CMLE=Yes
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CMLE estimation is performed along with JMLE estimation.
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Exact CMLE is performed using the Summation algorithm (Gustafsson, 1980).
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CMLE output is displayed in the measure tables (Tables 14, 18, etc.)
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CMLE WMLE controlled by WMLE=
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CMLE output is included in the measure output files, IFILE=, PFILE= SFILE=
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Choose the CMLE fields to include in IFILE= and PFILE= using the IFILE=/PFILE= field selection dialog box.
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CMLE item statistics estimated from the data
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item measures, standard errors, infit and outfit statistics, Warm MLE measures
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AMLE person measures are estimated from the items anchored at their CMLE measures and the data
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AMLE person measures, standard errors, Warm MLE measures.
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CMLE person infit and outfit statistics,
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Person fit statistics are computed from the CMLE item response probabilities, not from the AMLE person response probabilities
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CMLE Andrich thresholds for polytomous (rating scale) items
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Thresholds output in SFILE= and Table3.2
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JMLE estimation and output are unchanged
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Most of the Winsteps output continues to be based on the JMLE estimates.
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Suggestion: from the CMLE analysis, output SFILE=, IFILE= PFILE=. These contain both JMLE and CMLE values. Remove the JMLE values and use SAFILE= etc. to anchor the step estimates at the CMLE values. Then rerun Winsteps. The fit statistics will not make sense, but the graphical output will match CMLE.
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CMLE=No
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CMLE estimation is not done.
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There is no CMLE output.
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Technical notes:
1. The "Summation algorithm" CMLE estimation accommodates missing data and ISGROUPS=, but is slow for large datasets. It loses precision with large numbers of items, usually about 200.
2. CMLE estimation builds a table of response probabilities matching the observed data. These probabilities are used to obtain:
(a) the item estimates, their standard errors, and their Warm Mean Likelihood estimates
(b) the item INFIT and OUTFIT statistics
(c) the person INFIT and OUTFIT statistics.
3. The CMLE item estimates (anchored) and the data are used to obtain:
(a) the person AMLE (Anchored Maximum Likelihood Estimates) and their standard errors.
(b) AMLE response probabilities. These are not used because they are biased relative to the CMLE response probabilities.
4. CMLE estimates are "consistent" and "unbiased' under most conditions. AMLE estimates are slightly biased. Absolute distances between person and item estimates change slightly when the dataset is transposed. (They are not changed under transposition with JMLE).
Andrich, D. (2010) Sufficiency and conditional estimation of person parameters in the polytomous Rasch model. Psychometrika. 75, 2, 292–308.
Gustafsson, J.-E. (1980). A solution of the conditional estimation problem for long tests in the Rasch model for dichotomous items. Educational and Psychological Measurement, 40(2), 377–385.
