Worksheet Functions
Real Statistics Functions: The Real Statistics Resource Pack contains the following functions:
UCON(R1, head): returns output similar to that shown in Figure 5 of Building a Polytomous Model based on the data in R1.
UCONFIT(R1, head): returns output similar to that shown in Figure 2 of Polytomous Model Fit based on the data in R1.
UCON_SUBJ(R1, head): returns an array with three columns consisting of the subject labels, and corresponding ability parameters and standard errors based on the data in R1.
UCON_ITEM(R1, head): returns an array with three columns consisting of the item labels, and corresponding difficulty parameters and standard errors based on the data in R1.
UCON_THRESH(R1, head): returns an array with two columns consisting of the category labels (0, 1, …, m), and corresponding threshold parameters based on the data in R1
iter = the maximum number of iterations, but when the precision value is less than prec (default .001) then the iterations stop prior to iter. If head = TRUE (default) then R1 contains row/column headings, more specifically R1 is formatted as in range A4:K23 of Figure 5 of Building a Polytomous Model when head = TRUE and as range B5:K23 when head = FALSE.
Examples
The output from =UCON(A4:K23) is as shown in Figure 5 of Building a Polytomous Model and the output from =UCONFIT(A4:K23) is as shown in Figure 2 of Polytomous Model Fit. In addition to the output shown in these figures, the output also includes the number of iterations actually made and the precision at that point.
The first column of the output from =UCON_SUBJ(A4:K23) consists of the values in range AR8:AR16 in Figure 5 of Building a Polytomous Model, while the other two columns consist of the values in BC8:BC16 in that figure. The first column of the output from =UCON_ITEM(A4:K23) consists of the values in AS7:BB7, while the other two columns contain the values in AS17:BB18 of that figure.
The output from =UCON_THRESH(A4:K23) consists of a 3 × 2 range, the first column of which contains the values 0, 1, 2, and the second column of which contains the values 0, -1.13, 1.13. The output from =UCON_THRESH(A4:K13,,1) is as shown in range AN41:AO43 in Figure 5 of Building a Polytomous Model.
Data Analysis Tool
Real Statistics Data Analysis Tool: We can use Real Statistics’ Item Analysis data analysis tool to create a polytomous Rasch model.
To use this data analysis tool for Example 1 of Building a Polytomous Model, press Ctrl-m and select Reliability from the menu that is displayed and then choose the Rasch Item Response Analysis option (or press Ctrl-m and select Rasch Item Response Analysis from the Corr tab if using the Multipage user interface). Next, fill in the dialog box that appears as shown in Figure 1 of Rasch Analysis Support, except that this time choose the UCON method (polytomous scoring) and set the Highest score to 2.
The output is similar to that shown in Figure 5 of Building a Polytomous Model and Figure 2 of Polytomous Model Fit.
Observation
As noted previously, before starting the analysis you must remove any subject who recorded a 0 for every item or an m (where m is the highest score) for every item. Similarly, you must remove any item for which every subject scored a 0 or every subject scored an m. Note too that after removing such subjects/items, additional subjects/items may now qualify for elimination, and so this can be an iterative process. The Real Statistics functions and data analysis tool described above assumes that this has already been done.
As previously described, you can accomplish this via the Eliminate zero and perfect scores option on the dialog box shown in Figure 1 of Rasch Analysis Support, or by using the RASCH_INIT function.
Examples Workbook
Click here to download the Excel workbook with the examples described on this webpage.
References
Wright, B.D. & Masters, G.N. (1982) Rating scale analysis. Chicago: MESA Press
https://research.acer.edu.au/measurement/2/
Ataei, S.and Mahmud, Z. (2015) Rasch-Andrich thresholds in engineering students’ attitudes towards learning mathematics
https://www.semanticscholar.org/paper/Rasch-Andrich-Thresholds-in-Engineering-Students%E2%80%99-Ataei-Mahmud/1b60dc7d5a3be98db220d29b957de55e4550d2e2
Linacre J.M. (2002) What do Infit and Outfit, Mean-square and Standardized mean? Rasch Measurement Transactions, 2002, 16:2 p.878
https://www.rasch.org/rmt/rmt162f.htm#:~:text=Polytomous%20fit%20statistics.,sensitive%20or%20information%2Dweighted%20fit.&text=Outfit%20means%20outlier%2Dsensitive%20fit,person%2C%20and%20vice%2Dversa.
Winsteps (2020) Fit diagnosis: infit outfit mean-square standardized
https://www.winsteps.com/winman/misfitdiagnosis.htm