Winsteps is Windows-based software which assists with many applications of the Rasch model, particularly in the areas of educational testing, attitude surveys and rating scale analysis. There is more information at: www.winsteps.com

 

Winsteps started from "Rating Scale Analysis" (Wright & Masters, 1982), available by free download at

www.rasch.org (green book).

 

Rasch analysis is a method for obtaining objective, fundamental, additive measures (qualified by standard errors and quality-control fit statistics) from stochastic observations of ordered category responses. Georg Rasch, a Danish mathematician, formulated this approach in 1953 to analyze responses to a series of reading tests (Rasch G, Probabilistic Models for Some Intelligence and Attainment Tests, Chicago: MESA Press, 1992, with instructive Foreword and Afterword by B.D. Wright). Rasch is pronounced like the English word rash in Danish, and like the English sound raa-sch in German. The German pronunciation, raa-sch, is used to avoid misunderstandings.

 

The person and item total raw scores are used to estimate additive measures. Under Rasch model conditions, these measures are item-free (item-distribution-free) and person-free (person-distribution-free). So that the measures are statistically equivalent for the items regardless of which persons (from the same population) are analyzed, and for the items regardless of which items (from the same population) are analyzed. Analysis of the data at the response-level indicates to what extent these ideals are realized within any particular data set. Rasch analysis is "conjoint measurement". The person abilities and item difficulties are measured on the same scale. If you add something to the item difficulties then you add the same amount to the person abilities (thetas) in order to keep the relationship between the person and items the same.

 

The Rasch models implemented in Winsteps include the Georg Rasch dichotomous, Andrich "rating scale", Masters "partial credit", Bradley-Terry "paired comparison", Glas "success model", Linacre "failure model",  Bradley-Massof "consecutive dichotomization" and most combinations of these models. Other models such as binomial trials and Poisson can also be analyzed by anchoring (fixing) the response structure to accord with the response model. (If you have a particular need, please let us know as Winsteps is continually being enhanced.)

 

The estimation methods are JMLE, "Joint Maximum Likelihood Estimation" and CMLE "Conditional Maximum Likelihod Estimation", with initial starting values provided by PROX, "Normal Approximation Algorithm".

 

Rasch Models implemented in Winsteps

 

The necessary and sufficient transformation of ordered qualitative observations into additive measures is a Rasch model. Rasch models are logit-linear models, which can also be expressed as log-linear models. Typical Rasch models operationalized with Winsteps are:

 

The dichotomous model:

loge(Pni1 / Pni0 ) = Bn - Di

 

The polytomous "Rating Scale" model:

log(Pnij/ Pni(j-1) ) = Bn - Di - Fj

 

The polytomous "Partial Credit" model: ISGROUPS=0

log(Pnij/ Pni(j-1) ) = Bn - Di - Fij = Bn - Dij

 

The polytomous "Grouped response-structure" model: ISGROUPS=11122333

log(Pnij/ Pni(j-1) ) = Bn - Dig - Fgj

 

where

Pnij is the probability that person n encountering item i is observed in category j,

Bn is the "ability" (theta) measure of person n,

Di is the "difficulty" (delta) measure of item i, the point where the highest and lowest categories of the item are equally probable.

Fj is the "calibration" measure of category j relative to category j-1, the point where categories j-1 and j are equally probable relative to the measure of the item. No constraints are placed on the possible values of Fj.

 

Other Rasch models can be implemented by using anchored thresholds, SAFILE=. These include the Rasch Binomial Trials model and the Rasch Poisson Counts model.

 

Another useful model that can be implemented is the Rasch Paired Comparison (Bradley-Terry) model. Also a useful approximation to the Rasch Rank-Order model.

 

Also models with the form of "Continuation Ratio" models, such as the "Success" model and the "Failure" model.

 

For methods of estimation, see RSA, pp. 72-77.

 

---

Work-flow with Winsteps

 

Control + Data file or Control file and Data file(s)

↓

User-interaction → Winsteps ← Anchor Files

↓

Report Output File + Output Tables + Graphs + Output Files

↓

Word Processor, Spreadsheet, Statistical Package

↓

Actions

 

---

Winsteps is designed to construct Rasch measurement from the responses of a set of persons to a set of items. Responses may be recorded as letters or integers and each recorded response may be of one or two characters. Alphanumeric characters, not designated as legitimate responses, are treated as missing data. This causes these observations, but not the corresponding persons or items, to be omitted from the analysis. The responses to an item may be dichotomous ("right"/"wrong", "yes"/"no"), or may be on a rating scale ("good"/ "better"/"best", "disagree"/"neutral"/"agree"), or may have "partial credit" or other hierarchical structures. The items may all be grouped together as sharing the one response structure, or may be sub-groups of one or more items which share the same response structure.

 

Winsteps begins with a central estimate for each person measure, item calibration and response-structure calibration, unless pre-determined, "anchor" values are provided by the analyst. An iterative version of the PROX algorithm is used reach a rough convergence to the observed data pattern. The JMLE method is then iterated to obtain more exact estimates, standard errors and fit statistics.

 

Output consists of a variety of useful plots, graphs and tables suitable for import into written reports. The statistics can also be written to data files for import into other software. Measures are reported in Logits (log-odds units) unless user-rescaled. Fit statistics are reported as mean-square residuals, which have approximate chi-square distributions. These are also reported t standardized, N(0,1).

 

As computer speeds and available memory (and dataset sizes) increase, I improve the numerical precision and other aspects of the software. Winsteps recently moved to native 64-bit computations. It is now advancing from double-precision floating point to quad-precision. An interesting example: a large dataset that Winsteps needed one week to analyze in 2006 required only 2.5 hours in late 2021!