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Asymmetric
Triangulation Scaling |
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For detailed information on asymmetric triangulation scaling
(ATRISCAL), please click here. As a type of
multidimensional scaling, ATRISCAL provides the global dependency
relationship between test items. In this method, each item is given
coordinates within a hemispherical dome as a result of analysis, and the
positional relationship of those coordinates are used to explore inter-item
dependency. |
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Model Overview |
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Stress Stress is the value of the target function of the estimated
model. There is no need, in particular, to investigate the magnitude of this
value. |
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Correct triangle ratio Given a perpendicular
dropped from origin O to the
segment joining the coordinates of two items, we consider that a correct
triangle is formed if the foot of that perpendicular lies on that segment and
that an incorrect triangle is formed if it does not. For n number of items, ATRISCAL adds an imaginary item so
that there are n+1 items in total.
As a result, the total number of item pairs is m=n(n+1)/2,
which means that the total number of triangles formed by connecting those
pairs to the origin is m. Now, the
ratio of correctly formed triangles among these m triangles is the correct triangle ratio. A ratio value near 1.0
indicates a good fit between the model and data. As the number of items
increases however, a value of 1.0 is difficult to approach.
Correct Triangle Incorrect
Triangle |
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Mean
Residual (MR) This index is also called Mean
Difference (MD). Among the item pairs used to form correct triangles,
this is the average error between actual conditional correct response rate
and estimated conditional correct response rate. A value of MD close to 0.0
indicates a good fit between model and data. |
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Standardized
Root Mean Squared Residual (SRMR) This index is also called Root Mean
Squared Difference (RMSD). This is the square root of the mean of the
square of the above error. A value of SRMR close to 0.0 indicates a good fit
between model and data. |
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Analysis
Setting |
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Estimation
model At the present, only binary data (correct/incorrect) can be
analyzed. |
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Output
Options |
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CCRR
coloring With this option, each
element making up the conditional correct response rate matrix is given a color
according to its magnitude. |
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Sorting
by correct response rate This option outputs items
according to correct response rate in order from highest to lowest. |
