Bond & Fox (2001) Applying the Rasch Model ...

Chapter 3: Developmental Pathway

You will need to read the text of the book to understand these examples. Official authors' website: Bond & Fox
Winsteps numerical results may differ somewhat from those in Bond & Fox due to differences in estimation procedures.

EXCEL Bubble Plot

B&F Figure 3.1 paralleled p. 12

No dataset is provided for this, so we will perform a parallel analysis using the Knox Cube Test data.

Start Ministep.
"Control File Name?" Press the Enter key.
In the File dialog box, select and open Exam1.txt
"Report output file name ..." Press the Enter key
"Extra specifications ..." Press the Enter key

Ministep runs.
Ministep reports "Measures constructed"

To produce a plot like Fig. 3.1, go to the "Plots" pull-down menu, and select "Bubble chart".

Up the Fig. 3.1 pathway

Click on the "Output Tables" pull-down menu
Click on "1. Variable Maps" - top of middle column.
The Variable Map displays.

This map has the vertical direction of the Developmental Pathway. At the left are the people. Ric(k) and Sus(an)are the most developed. Don and Hel(en) are the least developed.

On the right are the items, shown by their labels. In the Knox Cube Test, children are asked to tap on 4 wooden blocks in particular orders. The item labels indicate the order. The most difficulty item is at the top, 4-1-3(-4-2-1-4). The easiest items are at the bottom, 1-2-4, 1-2 and 2-3.

People are aligned with the items, e.g., Ber(t) with 1-4-3(-2-4), on which they have a 50% chance of success.

Across the Fig. 3.1 pathway

Fig. 3.1 uses a t fit statistic for its x-axis. This is probably a transformation of the information-weighted chi-square statistic, so it would be the "standardized infit statistic" reported by Ministep.

Comment: Since it is the size, rather than the statistical significance, of misfit which distorts measurement, Ministep users are encouraged to focus on the mean-square rather than the standardized forms of the misfit statistics.

To produce a picture of the fit, to parallel the x-axis in Fig. 3.1, we need to tell Ministep to produce a non-standard sub-table.
Click on the "Specification" pull-down menu.
In the box, type Chart=Yes - You can use capitals or lower case letters.
Click OK
The control instruction is repeated back to you on the screen.
Now do the same for Mnsq=No

These instructions, Chart=Yes and Mnsq=No, could have been put in your control file, just as we did with Pdfile=*

If, at any time, you wonder what is the setting of a control instruction,
click on the "Output Files" pull-down menu
click on "Control variable file="
a list of all control variables, and their settings, is displayed.

"Output Tables" pull-down menu, "17. KID measure"
Scroll down to Table 17.2
This is subtable is only produced if "Chart=Yes"
Look at the column headings, "STANDARDIZED" is produced by "Mnsq=No". If "MEAN-SQUARE" displays, then download the current version of MINISTEP.
This Table shows the person measures on the left, and the Infit Standardized statistic, the B&F t statistic in the center.
The vertical colons match the edge of the shaded area in Fig. 3.1
The person names on the far right correspond to the person names in the squares in Fig. 3.1

"Output Tables" pull-down menu, "13. TAP measure"
Scroll down to Table 13.2
This Table shows the item measures on the left, and the Infit Standardized statistic, the B&F t statistic in the center.
The item labels on the far right correspond to the item letters in the circles in Fig. 3.1

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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
in Spanish: Análisis de Rasch para todos, Agustín Tristán Mediciones, Posicionamientos y Diagnósticos Competitivos, Juan Ramón Oreja Rodríguez
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