# Measuring what Matters: Introduction to Rasch Analysis in R

*Last edit 2021-03-05*

# Chapter 1 Introduction

This is meant to be a general introduction for using the Rasch model via R for constructing measures. The book is meant to get you started but is by no means where you should stop. Please see, Wilson (2005) and Bond & Fox (2015) for more.

The Rasch model is based on a theory of measurement. Whereas one may typically fine-tune a model to fit the data, in the Rasch paradigm, one compares the data to the Rasch model. Under this view, when the data does not fit the Rasch model, it is believed that the data may not be suitable for measurement.

Sometimes it is said that Rasch is difficult or unrealistic to work with because of its assumptions about the underlying data structure. However, these are not assumptions like the assumptions of ordinary least squares (OLS or linear regression). Instead, these “assumptions” - that the data fit the Rasch model - are the very things we are interested in testing to see if our data is suitable for measurement. Even if we are not constructing an instrument, this information is useful for understanding the extent to which we can trust results. If we deem that the data is suitable for measurement, we may proceed to use the results. If we deem that it the data is not suitable for measurement, all is not lost. We can take that information to alter our items, theory, or model.

There are often two lines of objections to the Rasch model. One line says that data conforming to the Rasch model does not guarantee measurement. That is, data fitting the Rasch model itself is not sufficient for claiming measurement. For more on this view, see the work of Joel Michell. Another objection says that the form of additive measurement for which the users of Rasch measurement advocate is not the only form of measurement that’s acceptable, especially in the realm of using Item Response Theory models. For instance, some might advocate for the claim that estimates derived from other IRT models such as 2PL, 3PL, or 4PL models can be considered measurement results. For a wider view on Item Response Theory (IRT), including more on this latter view, see Embretson & Reise (2013). For more on the different traditions and this debate generally, see Andrich (2004) or Wilson (2003)

## 1.1 Basic Use of the Book

For understanding the basics, Chapters 3 discusses the basics of the Rasch model - using dichotomous data to help solidify the workflow. Chapters 4 and 5 discuss working with polytomous item-types, or items with multiple response options (for instance, Likert scales). Chapter 6 shows you how to work with multidimensional Rasch models.

## 1.2 Packages

All models are run using the package, `TAM`

, - see (Robitzsch, Kiefer, & Wu, 2020). We make some use of the `eRm`

package, (Mair & Hatzinger, 2007). Additionally, we make use of the `WrightMap`

package in R (Irribarra & Freund, 2014). For data cleaning and visualizing, we make extensive use of the `tidyverse`

(Wickham, 2019) suite of packages. However, no knowledge of any of these is required.

For questions, comments, and feedback, please contact:

Danny Katz - dkatz@ucsb.edu