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- Item Response Theory
- A Course in Rasch Measurement Theory
- Book: Introduction to Rasch Measurement: Theory, Models, and Applications

*The item response theory IRT , also known as the latent response theory refers to a family of mathematical models that attempt to explain the relationship between latent traits unobservable characteristic or attribute and their manifestations i.*

This essay describes Rasch analysis psychometric techniques and how such techniques can be used by life sciences education researchers to guide the development and use of surveys and tests. Specifically, Rasch techniques can be used to document and evaluate the measurement functioning of such instruments.

Rasch techniques provide a mechanism by which the quality of life sciences—related tests and surveys can be optimized and the techniques can be used to provide a context e. Rasch analysis allows researchers to construct alternative forms of measurement instruments, which opens the door to altering an instrument in light of student growth and change.

Rasch analysis also helps researchers think in more sophisticated ways with respect to the constructs variables they wish to measure. Some life sciences education researchers are already using Rasch techniques e. The purpose of this article is to provide a brief introduction to selected whys, whens, and hows of using Rasch techniques so that Rasch techniques become more widely used in the life sciences education research community.

I start by briefly introducing the importance of carefully measuring with a test or survey and outlining the mathematical errors common to test and survey analysis conducted using non-Rasch techniques, which can be avoided by using Rasch analysis. I then describe quality-control steps inherent to Rasch that can improve the quality of measurement instruments. I conclude by explaining how to use Rasch techniques to better communicate research findings and outlining the steps that should be taken to develop different forms of a test.

To appreciate the importance of Rasch techniques, we first need to think about what it means to measure a variable, such as the knowledge of a student or the attitude of a teacher. A researcher must begin by defining the single variable to be measured. Consider a concrete example of measuring the height of a flower, which can be measured along the continuum of a meter stick Figure 1. By focusing on measuring only one variable, a researcher can make comparisons with confidence.

For example, how do the heights of flowers A, B, and C in Figure 1 compare? Without a carefully developed measurement instrument that captures the parameters of one variable and one variable only, it is very difficult if not impossible to make meaningful comparisons.

Another strength of a meter stick is its linear scale. This means that, if the difference between the height of flower A and the height of flower B is 3 centimeters, and the difference between the height of flower A and the height of flower C is 6 centimeters, an observer can confidently state that the ratio of the differences in height is If the scale is not linear, then an observer could not make such an assertion. The concept of linearity is one of the most fundamental ideas for understanding why Rasch theory is an important tool for researchers.

Thinking about linear measurement. A meter stick being used to make linear measures and compare the height of three flowers. It is tempting to use raw survey and test data immediately, because there is so much linear data that researchers can immediately manipulate with simple mathematics. For example, the difference in running times between four runners can be confidently compared, the costs of six houses can be confidently compared, and so forth, because time and money are both linear.

Yet psychometricians agree that errors exist in analyses that make use of raw test scores to compare students. To understand this concern, let us think about an exam that is scored on a scale of 0—25 points. One problem of just adding up the number of correctly answered items and using that number to compare students is that it is highly unlikely that all test items are of equal difficulty.

Therefore, a sum of raw scores cannot be used to achieve accurate comparisons of student performance. Consider the results of a test in Figure 2. Twenty-five multiple-choice items were presented to ninth-grade students. Imagine that the test covered a single variable ninth-grade biology knowledge. Twenty of the items were well targeted to what ninth graders should know about the topic. However, the remaining five items were incredibly difficult, because they were at an introductory college level.

Example test scores. The raw test scores of four ninth-grade students who completed the same item test. Twenty items were appropriate for ninth-grade students, but five test items were at college level. However, this mathematical procedure contains a fundamental error, because the researcher ignores the differences in difficulty across the items.

Elizabeth was able to answer a number of the highly difficult test items. Henry, Pete, and Johnny were unlikely to have successfully answered any of the five highly difficult test items.

The seminal introduction to Rasch analysis, Best Test Design Wright and Stone, , discusses these issues in detail. Now let us consider an example that illustrates a related problem with survey data. Figure 3 presents a commonly used rating scale of strongly agree SA , agree A , disagree D , and strongly disagree SD.

A code of 4, 3, 2, and 1 is used as shorthand in a spreadsheet to indicate which response was selected for each survey item e. Figure 3 highlights one problem with immediately conducting statistical analysis with numerically coded respondent rating-scale answers. If a researcher conducts an immediate mathematical procedure with the rating-scale data, the researcher is assuming that the size of the jump from a strongly agree to agree is the same as the size of the jump from agree to disagree.

The researcher can indeed argue that strongly agree represents more agreement than agree, and that agree represents more agreement than disagree, and so on. However, the researcher cannot immediately assume that the size of the jump between rating categories is equal. Example survey rating scale. Furthermore, the way the rating scale functions across the items is not identical. Figure 3 also presents an additional issue with rating scales. Not only may the steps between adjacent rating categories be unequal, but the pattern of steps may differ from item to item.

When the numerical answers to survey items are coded e. The only certainty is that, given a specific survey item, a rating of strongly agree means more agreement than a rating of agree, and so on through disagree to strongly disagree. Figure 3 shows the potential unequal spacing of rating-scale categories for three survey items.

Just as all test items cannot be assumed to exhibit the same difficulty, all survey items should not be assumed to be equally agreeable.

For example, a 4 strongly agree in response to item 8 of a survey should not be assumed to indicate the same level of agreement as answering a 4 strongly agree to item 10 of a survey. This instrument includes 13 survey items that define a self-efficacy scale for preservice elementary teachers. Rasch techniques involve corrections for a number of psychometric issues e. Figure 4 is a commonly used schematic that summarizes the core mathematical and theoretical concepts of the Rasch model, which were first developed by the Danish mathematician Georg Rasch ; see Appendix A in the Supplemental Material for a summary of selected Rasch terms.

The single vertical line represents the construct to be evaluated by a test. Along this vertical line is a notation regarding the ability level of a student Oli along the variable. Also, three test items are plotted along the variable. Each item is located in a position that indicates the level of difficulty or ease of each item with regard to the variable.

Of the greatest importance is that each item along the variable exhibits a probability of the respondent with a specific ability level correctly answering each item. An item exhibiting difficulty higher than the ability level of the respondent will have a lower probability of being correctly answered than an item of difficulty below the ability level of the respondent.

Rasch measurement schematic. To measure, an analyst must 1 consider a single construct represented by the vertical line ; 2 consider the parts of the variable marked by different test items; 3 understand that a test taker will be located at some point along the variable; and 4 understand that the probability of a respondent answering a test item correctly can be expressed.

Figure 5 depicts the Rasch mathematical model for dichotomous test items. The dichotomous Rasch model. Rasch analysis is both mathematics and theory.

To understand how Rasch theory can guide instrument development, let us consider a biology education research project in which a researcher plans to administer a question multiple-choice biology knowledge test to students. Some items will exhibit a low level of difficulty, and these items will mark the easier end of the meter stick.

Other items will exhibit a middle level of difficulty, marking the middle of the meter stick. Still other items will exhibit a high level of difficulty, marking the high end of the meter stick. This idea is similar to a meter stick for measuring the height of the flowers Figure 1. Practically speaking, we can make only a limited number of marks on the meter stick. Thus, if we do not know the length of what we are meanning an equal distribution of marks along the meter stick provides optimal measurement opportunity.

The next step in applying Rasch theory is for our researcher to predict the location of marks item difficulty along the meter stick for specific test items.

This means that the professor must use his or her understanding of what is being measured and, ideally, research on student biology knowledge to make predictions of item difficulty where items fall on the meter stick.

This use of theory to make predictions is central to measurement and Rasch analysis. If test developers cannot make the predictions, then the test developers do not understand what is being measured and cannot discern the meaning of one student performing better or worse than another student.

For example, studies of student understanding of evolutionary change support a theory that students will have 1 more difficulty explaining evolutionary change of plants in comparison to animals; 2 more difficulty understanding between-species change in comparison to within-species change; and 3 more difficulty understanding loss of variables in comparison to gain of variables Nehm et al.

This information can be used to formulate test items that span the meter stick of student understanding of evolutionary change. The same Rasch techniques can be applied when developing a survey instrument.

Items should be included that would be agreeable even to teachers with low levels of confidence e. Following the thoughtful construction of the measurement instrument, our researcher should collect pilot data, conduct a Rasch analysis of the pilot data, and then refine the instrument, for instance, by adding or removing items or changing the rating scale to have more or fewer rating-scale steps.

Two exemplary steps taken in a Rasch analysis to evaluate the functioning of an instrument are outlined below. Many Rasch software programs can be used.

Winsteps Linacre, , the most widely used Rasch software, is user-friendly, and the author of the program provides guidance and assistance to users. In the case of a test, a Wright map allows researchers to evaluate how well the test items are defining a variable. A Wright map also allows researchers to compare the predicted order of item difficulty with the actual order of item difficulty in a data set. Such comparisons facilitate an assessment of construct validity by providing evidence that the instrument is measuring in a way that matches what a theory would predict.

Wright maps open, multiple avenues for researchers to evaluate the inferences that can be confidently made through use of an instrument. I will provide an overview of selected Rasch analysis techniques, which are described in detail in Rasch Analysis in the Human Sciences Boone et al.

Figure 6 depicts a Wright map that plots the items in an instrument according to their order of difficulty. On the right side of the Wright map, the 25 items of the test are presented from easiest item 2, bottom to most difficult item 30, top.

The items are plotted in terms of item difficulty computed using Winsteps and the Rasch model formula. Example Wright map. A Wright map can allow researchers to quickly identify strengths and weaknesses of an instrument.

This essay describes Rasch analysis psychometric techniques and how such techniques can be used by life sciences education researchers to guide the development and use of surveys and tests. Specifically, Rasch techniques can be used to document and evaluate the measurement functioning of such instruments. Rasch techniques provide a mechanism by which the quality of life sciences—related tests and surveys can be optimized and the techniques can be used to provide a context e. Rasch analysis allows researchers to construct alternative forms of measurement instruments, which opens the door to altering an instrument in light of student growth and change. Rasch analysis also helps researchers think in more sophisticated ways with respect to the constructs variables they wish to measure. Some life sciences education researchers are already using Rasch techniques e. The purpose of this article is to provide a brief introduction to selected whys, whens, and hows of using Rasch techniques so that Rasch techniques become more widely used in the life sciences education research community.

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The purpose of this book is to illustrate techniques for conducting Rasch measurement theory analyses using existing R packages. The book includes some background information about Rasch models, but the primary objective is to demonstrate how to apply the models to data using R packages and interpret the results. The primary audience for this book is graduate students or professionals who are familiar with Rasch measurement theory at a basic level, and who want to use open-source software to conduct their Rasch analyses. We provide a brief overview of several key features of Rasch measurement theory in this chapter, and we provide descriptions of basic characteristics of the models and analytic techniques in each of the following chapters. Accordingly, we encourage readers who are new to Rasch measurement theory to use this book as a supplement to other excellent introductory texts on the subject that include a detailed theoretical and statistical introduction to Rasch measurement. For example, interested readers may find the following texts useful to begin learning about Rasch measurement theory:.

Course "Rasch models in the social and tehavicral sciences" test-theory and other item-response mcdeis. In relaticn to a Possible areas of application of the Pasch model are discussed. (Author/DWH) INTRODUCTION. It is often the.

*The Rasch model , named after Georg Rasch , is a psychometric model for analyzing categorical data , such as answers to questions on a reading assessment or questionnaire responses, as a function of the trade-off between a the respondent's abilities, attitudes, or personality traits and b the item difficulty.*

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