Development of a Microsoft Excel tool for one-parameter Rasch model of continuous items: an application to a safety attitude survey

A great deal of work has been devoted to the probabilistic modeling of Likert-type responses in the past 50 years [1]. Questionnaires built and tested using item response theory (IRT) are common in educational assessment, and they are being used more frequently in health assessment [2]. However, collecting continuous responses is more often and prevalent in healthcare settings than is collecting categorically ordered data such as questionnaire surveys.

Many researchers have proposed IRT-based models of continuous item responses to deal with those multivariate behavioral research in real world [3–9], no one has provided user-friendly healthcare software for assessing, for example, pain intensity [10] or personality [4, 11]. We were, therefore, interested in developing a Microsoft Excel-based computer module that executes continuous observations similar to easily deal with binary and polytomous scores based on IRT modeling [12, 13].

Samejima [6] developed a unidimensional latent trait model for continuous responses, but it did not aim at “specifically objective” comparisons of persons and items, which is a key and unique feature of Rasch models [14]. Behar [11] applied the normal ogive (logistic curve) case of the continuous response model to items from a personality inventory. Muller [3] proposed a continuous rating scale model, based on Andrich’s [15] rating scale model (RSM) for categorical responses, which belongs to the Rasch family and so has the interesting specific objectivity property. Although Muller’s model is limited to an “integer” response format, observations can be presented for Rasch analysis in the form of a range of percentages (0–100) without decimal values. Ferrando [4] proposed a similar idea of a truncation mechanism using R language software: extending the linear response model to a nonlinear congeneric model that takes the bounded nature of the data into account rather than rescaling a latent response to fit the response format. This study creates a model in MS Excel that will take the bounded nature of the data into account and rescale a latent response to fit the response format. A unidimensional latent trait model for continuous responses that is easy and friendly use for ordinary practitioners is thus required.

There are two forms for continuous and percentage observations [16]: (i) they are very rarely exist in additive, such as continuous form (e.g., weight and height) and allow us using standard statistical techniques to make direct comparisons between groups; and (ii) they are frequently seen in the real world and might not be directly additive (e.g., time to perform a task and weight lifted with the left hand) or follow a logistic distribution. Their implications in the specific context are unlikely to be additive until they have been transformed to a linear interval score, for instance, using Rasch modeling technique.

IRT-based Rasch probabilistic modeling is a way to transform ordinal scores into interval Rasch measures [2, 3, 9, 12–16], but this type of transformation applies only to discretely ordered category scores. A computer module that is required to deal with continuous item responses (CIRs) that are often seen in healthcare settings. Accordingly, we are interested in rescaling CIRs in a percentage range from 0 to 1 using Rasch probability theory to program a Microsoft Excel-based computer module.

The first section of this article presents the designed response mechanism using the Newton-Raphson method, from which the parameters of items and persons can be estimated and well calibrated. Some resulting estimations yielded by the author-made computer module are verified with the professional Rasch Winsteps software [17] on two discretely ordered category scales [12, 13]. The second applies the model to real healthcare data and shows CIR analysis is more advantageous than is classic test theory (CTT) because the CIR uses probabilistic modeling to deal with continuous and percentage observations.

Based on the study motivation provided, this study aims to accomplish the following:

1. i.

   to verify the CIR that can be a tool used in healthcare settings.

2. ii.

   to apply the CIR to a safety attitude survey using the model’s fit statistics.

3. iii.

   to demonstrate an online computer adaptive testing (CAT) of safety attitudes for collecting data from hospital employees.