Geofferey N. Masters

The Partial Credit Model

The Partial Credit Model (PCM) is a unidimensional model for the analysis of responses recorded in two or more ordered categories. In this sense, the model is designed for the same purpose as several other models in this book, including Samejima’s graded response model (Samejima, 1969). The PCM differs from the graded response model, however, in that it belongs to the Rasch family of models and so shares the distinguishing characteristics of that family: separable person and item parameters, sufficient statistics, and, hence, conjoint additivity. These features enable “specifically objective” comparisons of persons and items (Rasch, 1977) and allow each set of model parameters to be conditioned out of the estimation procedure for the other.

The essential process in a family of measurement models

Five members of the Rasch family of latent trait models which have appeared more or less independently in the literature are brought together and identified as one model. In addition to sharing the distinguishing characteristic of the dichotomous Rasch model—separable person and item parameters and hence sufficient statistics—all five models share a common algebraic form and have as their basic element the fundamental process defined by Raschs simple logistic expression. In these models, the sufficient statistics for person and item parameters are counts of events constructed to be indicative of the variable being measured, and the measures they enable are ‘fundamental’.

A comparison of latent trait and latent class analyses of Likert-type data

This paper brings together and compares two developments in the analysis of Likert attitude scales. The first is the generalization of latent class models to ordered response categories. The second is the introduction of latent trait models with multiplicative parameter structures for the analysis of rating scales. Key similarities and differences between these two methods are described and illustrated by applying a latent trait model and a latent class model to the analysis of a set of “life satisfaction” data. The way in which the latent trait model defines a unit of measurement, takes into account the order of the response categories, and scales the latent classes, is discussed. While the latent class model provides better fit to these data, this is achieved at the cost of a logically inconsistent assignment of individuals to latent classes.

Measurement Models for Ordered Response Categories

Quantitative educational research depends on the availability of carefully constructed variables. The construction and use of a variable begin with the idea of a single dimension or line on which students can be compared and along which progress can be monitored. This idea is operationalized by inventing items intended as indicators of this latent variable and using these items to elicit observations from which students’ positions on the variable might be inferred.

Common-Person Equating with the Rasch Model

Two procedures, one based on item difficulties, the other based on person abilities, were used to equate 14 forms of a reading comprehension test using the Rasch model. These forms had no items in common. For practical purposes, the two procedures produced equivalent results. An advantage of common-person equating for testing the unidimensionality assumption is pointed out, and the need for caution in interpreting tests of common-item invariance is stressed.

Measuring attitude to school with a latent trait model

A latent trait model for rating scales is used to ana lyze responses to an attitude-to-school questionnaire as part of an evaluation of projects operating in 10 West ern Australian schools under the Australian Priority Schools Program. The invariance of item parameter estimates over the 10 schools is examined, and varia tions in item estimates from school to school are stud ied in the light of the different projects operating in these schools. Results show how the investigation of items that do not retain their difficulties from group to group can provide valuable insight into the ways in which calibration groups differ.

Reforming the Assessment of Student Achievement in the Senior Secondary School

The challenge that confronts agencies responsible for assessment and reporting in the senior secondary school is to extend systematic assessment procedures to a broader range of learning outcomes than those currently assessed by public examinations, to develop methods of reporting which are more descriptive of individual achievement and which provide a better basis for describing and maintaining standards, and to provide results which are sufficiently comparable across schools to enable fair comparisons of applicants for tertiary study. Some recent developments in assessment and reporting practice are considered with a view to identifying methods and approaches capable of satisfying this diverse set of demands. An approach which is particularly appealing because of its potential to provide simultaneously more descriptive reports of student achievement and adequate levels of comparability is the use of a set of common assessment tasks attempted by all students enrolled in each Year 12 course of study.

DICOT: Analyzing Classroom Tests with the Rasch Model

A computer program (DICOT) for the Rasch analysis of classroom tests is described. Results are presented in a simple, self-explanatory form, and person ability and item difficulty estimates are expressed in a metric like the one with which teachers and parents are already familiar. Person and item fit statistics provide an opportunity to diagnose strengths and weaknesses of individual children and to identify items which are problematic.