﻿ Multidimensional Model - Multidimensionality

# Multidimensional Model - Multidimensionality

Winsteps estimates unidimensional Rasch models, but many of the benefits of multidimensional modeling can be obtained through a Winsteps analysis. The Winsteps results are often easier to understand an use than those of a multidimensional analysis.

1. Identifying dimensions among the items.

This can be done by inspecting the content of the items or through Table 23.

1. Do a standard unidimensional Rasch analysis

2. Use Winsteps Table 23.1 and other information to identify each item's "dimension"

3. Enter a code for the item's dimension into column 1 of the item label

4. Do the standard Rasch analysis

5. Winsteps Table 31, Differential Person Functioning, will give a measure for each person on each "dimension", all in the same frame-of-reference.

Example: I always have a problem in unidimensionality. How can I solve this problem in this data and others?

Unexplned variance in 1st contrast = 4.6 so that the eigenvalue of first contrast is noticeably greater than 2.0

(1) is it truly a problem? There are many reasons for dependency in the data. For instance, if your items are groups using ISGROUPS=, then items in the same group (and so with the same rating scale) are slightly more dependent with each other than with other items.

(2) Look at Table 23.1.

Look at the content (wording) of the items at the top of the plot, and compare them with the items at the bottom of the plot.

What is in the top items that contrasts with what is in the bottom item? Are they on different dimensions (for instance, geography and history) or is the difference only superficial (for instance, response format or position on page)?

(3) Please look at the disattenuated correlations of the person measures at the bottom of Table 23.1:

Approximate relationships between the KID measures

PCA      ACT       Pearson       Disattenuated Pearson+Extr  Disattenuated+Extr

Contrast  Clusters  Correlation   Correlation   Correlation   Correlation

1        1 - 3      0.1404        0.2175        0.1951        0.2923  < far from 1.0

If the correlations are near 1.0, then the person measures for the different "dimensions" are statistically the same. No action is needed.

(4) If the items really are on different dimensions and the person measures have a low correlation, then split the items into two subsets .

Dimensionality: contrasts & variances

Dimensionality investigation - an example

Dimensionality: when is a test multidimensional?

in Table 23 Identifies structure and dimensionality in response residuals

Table 23.0 Variance components scree plot for items

Table 23.2, 23.12 Item Principal components analysis/contrast of residuals

Table 23.3, 23.13 Item contrast by persons

Table 23.6, 23.16 Person measures for item clusters in contrast. Cluster Measure Plot for Table 23.6.

Table 23.99 Largest residual correlations for items

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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
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