# Rasch Analysis

Rasch analysis can be applied to assessments in a wide range of disciplines, including health studies, education, psychology, marketing, economics and social sciences.

Many assessments in these disciplines involve a well defined group of people responding to a set of items for assessment. Generally, the responses to the items are scored 0, 1 (for two ordered categories); or 0, 1, 2 (for three ordered categories); or 0, 1, 2, 3 (for four ordered categories) and so on, to indicate increasing levels of a response on some variable such as health status or academic achievement. These responses are then added across items to give each person a total score. This total score summarise the responses to all the items, and a person with a higher total score than another one is deemed to show more of the variable assessed. Summing the scores of the items to give a single score for a person implies that the items are intended to measure a single variable, often referred to as a unidimensional variable.

The Rasch model is the only item response theory (IRT) model in which the total score across items characterizes a person totally. It is also the simplest of such models having the minimum of parameters for the person (just one), and just one parameter corresponding to each category of an item. This item parameter is generically referred to as a threshold. There is just one in the case of a dichotomous item, two in the case of three ordered categories, and so on.

## 1. What is Rasch Analysis?

What is a Rasch Analysis? The Rasch model, where the total score summarizes completely a person's standing on a variable, arises from a more fundamental requirement: that the comparison of two people is independent of which items may be used within the set of items assessing the same variable. Thus the Rasch model is taken as a criterion for the structure of the responses, rather than a mere statistical description of the responses. For example, the comparison of the performance of two students' work marked by different graders should be independent of the graders.

In this case it is considered that the researcher is deliberately developing items that are valid for the purpose and that meet the Rasch requirements of invariance of comparisons.

Analyzing data according to the Rasch model, that is, conducting a Rasch analysis, gives a range of details for checking whether or not adding the scores is justified in the data. This is called the test of fit between the data and the model. If the invariance of responses across different groups of people does not hold, then taking the total score to characterize a person is not justified. Of course, data never fit the model perfectly, and it is important to consider the fit of data to the model with respect to the uses to be made of the total scores. If the data do fit the model adequately for the purpose, then the Rasch analysis also linearises the total score, which is bounded by 0 and the maximum score on the items, into measurements. The linearised value is the location of the person on the unidimensional continuum - the value is called a parameter in the model and there can be only one number in a unidimensional framework. This parameter can then be used in analysis of variance and regression more readily than the raw total score which has floor and ceiling effects.

Many assessments in these disciplines involve a well defined group of people responding to a set of items for assessment. Generally, the responses to the items are scored 0, 1 (for two ordered categories); or 0, 1, 2 (for three ordered categories); or 0, 1,2, 3 (for four ordered categories) and so on, to indicate increasing levels of a response on some variable such as health status or academic achievement. These responses are then added across items to give each person a total score. This total score summarise the responses to all the items, and a person with a higher total score than another one is deemed to show more of the variable assessed. Summing the scores of the items to give a single score for a person implies that the items are intended to measure a single variable, often referred to as a unidimensional variable.

The Rasch model is the only item response theory (IRT) model in which the total score across items characterizes a person totally. It is also the simplest of such models having the minimum of parameters for the person (just one), and just one parameter corresponding to each category of an item. This item parameter is generically referred to as a threshold. There is just one in the case of a dichotomous item, two in the case of three ordered categories, and so on.

2.   Why undertake a Rasch analysis?

3.   The research paradigm and the Rasch model

4.   Is there more than one Rasch model?

5.   Different Rasch Model Specifications

6.   Thresholds and Steps

7.   Disordered Thresholds as an Anomaly

8.   Who should use a Rasch analysis?

9.   An ideal approach to a Rasch analysis?

10. Recommended Rasch Software

11. The RUMM approach to Rasch Analysis

12. What courses and workshops are available on Rasch analysis?

13. What cloud analysis engines and API's are available?

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