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

Chapter 6: Computer Opinion Survey

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.

B&F Figure 6.1 p. 69

No data is available for this Figure.

B&F Computer Opinion Survey data p. 75

The entire dataset is obtained from www.facebook.com/ApplyingTheRaschModelBondFox.

The original data set contains 26 items and 273 children. This exceeds the MINISTEP maximum of 25 items and 75 persons, so the 26th item and last 198 persons are not analyzed.

Highlight with your mouse from here >

Title = "B&F CAIN Computer Anxiety Index: 26 items"
Item1 = 3        ; Response to first item is in column 3
NI    = 26       ; 26 items used.
Name1 = 1        ; Person identifier starts in column 1
Xwide = 1        ; Each observation is 1 columns wide
IREFER= FFFFRFRFRFRRFRFFFRRRRRRRRF ; two types of item: F = Forward, R = Reverse
Codes = 123456   ; valid codes 1-6.
IVALUEF=123456   ; Forward (positive) items
IVALUER=654321   ; Reversed (negative) items
cfile=*         ; label the scored rating scale categories
1 Strongly Agree
2 Agree
3 Slightly Agree
4 Slightly Disagree
5 Disagree
6 Strongly Disagree
*
Total = Yes      ; show total raw scores
Chart = Yes      ; produce across-pathway picture
Mnsq  = No       ; use Standardized fit statistics
Uimean= 0        ; Item mean difficulty at 0.
Stbias= Yes      ; Adjust for estimation bias
&End
01  Available    ; Item labels are original CAIN item numbers
02  Time-saver   ; Please use item text, where possible!
03  Conceptualize
04  Better
05R Not enjoy    ; R="reversed" - to remind ourselves!
06  Easier
07R Negative
08  Fun
09R Dump
10  Anticipate
11R Not use
12R Avoid
13  Enjoy
14R Excessive
15  Important
16  Learning
17  Satisfy
18R Trouble
19R Uncomfortable
20R Nervous
21R Unlearnable
22R Complicated
23R Unhappy
24R Intimidated
25R Overwhelming
26  Useful
END NAMES
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< to here. Then Copy.

Start Ministep.
Do not answer the "Control File Name?" question.
Go immediately to "Edit" pull-down menu.
Click on "Edit/Create File with WordPad"
WordPad screen opens.
"Paste Special" as "Unformatted Text" what you just copied above.

It should look exactly like the block above.

"Save as"
Go to the C:\WINSTEPS directory
File Name: CAIN.txt
Save as type: Text document
"Save"
"You are about to save the document in a Text-Only format ..."
Click "Yes"

Click on Ministep or Winsteps on the bottom of your screen
"Control File Name?" displays.
Press the Enter key
Find CAIN.txt in the file list.
Click on it.
Click "Open"

"Report output file name ..."
Press the Enter key

"Extra specifications ..."
Press the Enter key

Ministep runs.
Ministep reports "Measures constructed"

B&F Figure 6.2 paralled p. 76

Click on the "Output Tables" pull-down menu
Click on "13. ITEM Measure". The Table displays.
Scroll down to Table 13.2. This approximates Fig. 6.2, which obtained from a larger sample.
Thresholds are not shown in Table 13.2.

To see the thresholds,
Click on the "Output Tables" pull-down menu
Click on "2.0 Measure forms (all)". The Table displays.
Scroll down to Table 2.3 to see the B&F Thresholds.
This Table shows the measurement system horizontally, with each item on a separate line.
The "thresholds", sometimes called "Thurstone Thresholds" (though not estimated according to Thurstone's method) are the points at which there is a 50% probability of being observed in categories below and 50% being observed in categories above the category transition point.
In this plot, each thresholds is identified by the category to its right (i.e., higher up the measurement scale.)

B&F Table 6.2 p. 77-8

In Table 6.2, the "Taus", i.e., the Rasch rating scale structure parameters, are the same for every item. To see them,
Click on the "Output Tables" pull-down menu
Click on "3.2 Rating Scale Structure". The Table displays.
In the second panel there is the "STRUCTURE". The "Measure" column corresponds to the first row of the "Taus", and the "S.E." column to the "Error" row.

Now for the item-level statistics:
Click on the "Output Tables" pull-down menu
Click on "13 Item measure". The Table displays.
The item measures, errors, and fit statistics are shown. The order is slightly different to B&F because the last 73 people were not included in the anaysis.

B&F Fig. 6.3 p. 80

Click on "02"on your Task bar or
Click on the "Output Tables" pull-down menu
Click on "2 Measure forms (all)". The Table displays.
Scroll down to Table 2.4
In Fig. 6.3, each item is a column. In Table 2.4 each item is a row.
In Table 2.4 the person distribution is shown beneath the Table, with the frequencies displayed vertically so that
32
734
means 37, then 23, then 4

In Fig. 6.3, the "Thresholds" are now the rating scale structure parameters or "Taus." (This ambiguous use of the word "Threshold" is common in the literature.) These parameters are not usually pictured in this way, because they have a pairwise, rather than global meaning. When put in a picture like this, we automatically interpret them globally, and start to be concerned that the category numbers are "disordered".
To verify that the categories themselves are order,
Click on the "Output Tables" pull-down menu
Click on "3.2 Rating scale structure". The Table displays.
Look at the "Obsvd Avrge", Observed Average Measure, column. These report the average (person ability-item difficulty) measures of those who chose each category. They are in order except for a slight wrinkle between categories 5 and 6.
Click on "02" on your Taskbar, and investigate this further by looking at Table 2.6. "OBSERVED AVERAGE MEASURES BY OBSERVED CATEGORY FOR PERSONS"
We expected to see "123456" for the forward items, and "654321" for the reversed items. The itemes with "R" in their labels are indeed reversed.
Some items, such as item 13, have their categories in order, but most don't. Why?

Click on the "Output Tables" pull-down menu
Click on "23. ITEM: principal components". The Table displays.
This Table looks for stucture in the items that is not explained by one underlying dimension.
Scroll down to Table 23.3.
Above the dividing line, only one item has an "R". Below the dividing line nearly all items have an "R". There is something different about the reversed items. Perhaps some responded failed to notice they were reversed. Perhaps the the forward items correspond to acceptance and the reversed items to rejection, and they are not exact opposites. Here is a fruitful area to launch a qualititative analysis of the items and the respondents. But note that
"Yardstick (variance explained by measures)-to-This Factor ratio: 7.0:1"
This means that the forward-reverse item effect is only 1/7th the size of the main dimension - not usually enough to motivate two separate instruments. But we can always analyze the forward and reverse items separately, to see what happens.

B&F Fig. 6.4 p. 81

Scroll up to Table 12.1 or
Click on the "Output Tables" pull-down menu
Click on "12 ITEM Map". The Table displays.

B&F Table 6.3 p. 83

Click on the "Output Tables" pull-down menu
Click on "18 PERSON Entry". The Table displays.

Note: The Winsteps instructions on p. 80-81 are conceptual.

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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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John "Mike" L.'s Wellness Report: I'm 72, take no medications and, March 2018, my doctor is annoyed with me - I'm too healthy!
According to Wikipedia, the human body requires about 30 minerals, maybe more. There are 60 naturally-occurring minerals in the liquid Mineral Supplement which I take daily.