The Juran Report

The Rasch Model - An Advanced Tool for Dealing with Human Variation

This is an introduction to Rasch modeling and analysis. It is an advanced statistical topic for social and human data rather than economic data. The Rasch Model is also a topic covered in The Scientific Leader mentioned above.

Suppose a research group wanted to know how well a workplace survey measured the work environment in several call centers. They also wanted to be sure that the measure worked equally well in different sized call centers. The researchers administered five questions and obtained responses from 123 call center professionals. How might the researchers determine the quality of their measure?

Problems like this confound many experts. Measures of every kind surround us every day. We check the time and weather when we wake up in the morning, the news reports on the latest election polls, or popularity ratings of television shows. We use measuring cups to prepare our food and take the temperature of our children when they show signs of illness. We measure our speed as we drive to work and measure out a good size cup of coffee before we begin to work. On some days we receive the latest test results from our doctor when we’ve checked on our health.

In the workplace there are many measures that are captured, tracked, and reported. Measures of productivity, product quality, customer satisfaction, and financial performance are all very familiar to us. For many of these measures we never question the accuracy, but for others we may sometimes wonder. Measures can be inaccurate and imprecise for many reasons. The instrument being used to measure may not be calibrated properly, the person taking the measure might do it inaccurately, the sample being measured may not be representative of other samples, and for some types of measurement, the object being measured is difficult to observe (e.g., charm quarks in particle physics and cognitive states in psychology).

Most Black Belts are trained on measurement systems analysis tools to deal with these types of problems. Unfortunately, these tools do not deal effectively or accurately with many types of human variation. There is however another tool, a more advanced tool, called the Rasch Model.

Rasch models are used for analyzing data from assessments to measure such human centric things as abilities, attitudes, and personality traits. For example, they may be used to estimate a student's reading ability from answers to questions on a reading assessment or an individual’s opinion relative to capital punishment from responses on a questionnaire. Many high school competency exams and college entrance exams are based on the Rasch model.

Georg Rasch (1901-1980) was a mathematician and statistician at the University of Copenhagen. Rasch first published his work about the models that bear his name in 1961. The models were useful and popular in the study of psychometrics. Psychometrics is the psychological theory or technique of mental measurement.

Early applications in psychometrics, for example, concerned the probability of an individual’s response to a series of test questions given the individual’s subject knowledge and the difficulty of a given question. This was referred to as an Item-Response Model using Item-Response Theory (IRT). When the equation of the probability of an event is written in “logit” form it is referred to as a Rasch model. Logit forms are a subject unto themselves but are used extensively in logistic regression. For now, remember a “logit” is the logarithm of the odds ratio. The odds ratio, as every gambler knows, is the probability for an event occurring divided by the probability against the event. Many of these models had parameters for the individual subject and the characteristic of interest concerning the individual.

Some of Rasch’s early work concerned analysis of dyslexic children, intelligence of military recruits and a new intelligence test. Rasch modeling and analysis are also used in analysis of medical diagnosis choice in health care and customer preferences in marketing.

Rasch analysis today is often used on data measurements using a Likert scale. The Likert scale is commonly used on surveys to solicit the strength of opinion on a topic or evaluation of an instructor or training course on various factors related to satisfaction with the course, etc.

Likert scales are one-dimensional, linear rating scales. You have used them many times on opinion surveys. For example, a Likert scale for a questionnaire might be:

Rate all the questions in the survey on a “1” through “5” scale where

= strongly disagree
= disagree
= neither agree nor disagree
= agree
= strongly agree

Since Rasch originally proposed his models, two other types of Rasch models have been developed. They are the dichotomous and polytomous models. Dichotomous models have two choices such as “yes” or “no”; “0” or “1”. Polytomous models are a generalization from dichotomous models where the choices for responses are more than two choices, e.g. multiple choice “a., b., c., d.”

Rasch himself did not like to write about his own work and theories in contrast to most academicians. However, many other mathematicians and writers have filled in the gaps. Rasch modeling and analysis is an advanced topic. Once you have mastered basic descriptive statistics, inferential statistics, and hypothesis testing, consider looking into Rasch models; especially if you find yourself using or analyzing Likert scale data frequently.

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