﻿ Model statement examples

Model statement examples

Model statements are best understood through examples. Here are a number of model statements which could be used in an analysis where

Persons comprise facet 1,

Items comprise facet 2,

Judges comprise facet 3.

Model= 23,?,?,M

When person 23 ("23" for facet 1) is rated on any item ("?" for facet 2) by any judge ("?" for facet 3), treat the datum as missing ("M"). This has the effect of deleting person 23.

Model= ?,1,?,D

For any person ("?") rated on item 1 ("1") by any judge ("?"), treat the "0" and "1" data as dichotomous ("D"), i.e.,
log() = Bn - D1 - Cj for item i=1

Model= ?,2,?,D3

For any person ("?") rated on item 2 ("2") by any judge ("?") dichotomize the data ("D3"), treating 0,1,2 as 0, and 3 and above as 1, i.e.,
log() = Bn - D2 - Cj with data recoding for item i=2

Model= ?,2,?,R

For any person ("?") rated on item 2 ("2) by any judge ("?") use a common rating scale (or partial credit) ("R"). Valid ratings are in the range 0 through 9, i.e.,
log() = Bn - D2 - Cj - Fk for i=2, k=1,9

Model= ?,2,?,R2

For any person ("?") rated on item 2 ("2) by any judge ("?") use a common rating scale (or partial credit) ("R"). Valid ratings are in the range 0 through 2, i.e.,
log() = Bn - D2 - Cj - Fk for i=2, k=1,2

Model= ?,3,#,R

Let each judge ("#") apply his own version of the rating scale ("R"), i.e., a partial credit scale, to every person ("?") on item 3 ("3"), i.e.,
log() = Bn - D3 - Cj - Fjk for i=3, k=1,9

Model= ?, ,?,B2

For each person ("?"), ignore the item number (", ,") and let every rating by each judge ("?") be considered two binomial trials ("B2") scored 0 or 1 or 2, i.e.,
log() = Bn - Di - log(k/(3-k)) for k=1,2

Model= ?,?,0,P

For each person ("?") observed on each item ("?") which is not judged ("0"), the data are Poisson counts of successes. These are in the theoretical range of 0 to infinity, but in the empirically observed range of 0 to 255, i.e.,
log() = Bn - Di - log(k) for k=1,...

Model= ?,?,?,R,2

For any person ("?") rated on any ("?") by any judge ("?") use a common rating scale ("R"), but give each datum a double weight in the estimation, i.e.,
log() = Bn - Di - Cj - Fk for k=1,9

Model= ?B,?,?B,D

For any person ("?B") rated on any item ("?") by any judge ("?B"), the data are on a dichotomous scale ("D"), i.e.,
log() = Bn - Di - Cj

Then, after that estimation has been completed and all measures and rating-scale structures have been anchored, estimate bias measures for the bias interactions between each person ("?B") and each judge ("?B") across the whole data set for all models specified, i.e.,

log() = {Bn,Di,Cj,Fk,...} + Cnj
where {...} are the final estimates of the previous stage used as anchors and only the Cnj bias terms are now estimated. Cnj terms are appended to all model statements. The modeled expectation of Cnj is zero, but the mean of all estimated Cnj will not be zero due to the non-linear conversions between accumulated raw score residuals and bias measures in logits. Each bias term is a diagnostic specialization which turns a systematic misfit into a measure.

Model= ?,-?,?,D

For any person ("?") rated on any item ("-?") by any judge ("?"), the outcome is a dichotomy ("D"). The orientation of the second, item facet is reversed ("-") for data matching this model only, i.e.,
log() = Bn - (-Di) - Cj = Bn + Di - Cj

Model= ?, ,?,R

For any person ("?"), irrespective of the item (" "), rated by any judge ("?"), the outcome is a rating ("R"). The item facet is ignored, except that, if the item element number for a matching datum is not specified after Labels=, the datum is treated as missing.

Model= ?,X,?,R

For any person ("?"), irrespective of the item ("X"), rated by any judge ("?"), the outcome is a rating ("R"). The item facet is entirely ignored, so that, even if the item element number for a matching datum is not specified after Labels=, the datum is still treated as valid. If a facet is never referenced anywhere, then it may be more convenient to use Entry= rather than "X".

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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
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