Biomedical subjects

Guanzhong Luo

Publications and source records attributed to Guanzhong Luo.

4 recordsLinked to original sources

PubMed2005

Estimating parameters in the Rasch model in the presence of null categories.

A category with a frequency of zero is called a null category. When null categories are present in polytomous responses, then in the Rasch model for such responses, the thresholds that define the categories are inestimable with the commonly used joint maximum likelihood, marginal maximum likelihood, or standard conditional maximum likelihood estimation algorithms. The reason for this situation is that in principle, these estimation algorithms involve frequencies of each category. Andrich and Luo (2003) describe an algorithm in which the thresholds are reparameterized into their principal components and in which the estimate of any threshold is based on a function of the frequencies of all categories of the item rather than the frequency of a particular category. This algorithm works in the presence of null categories. However, in situations where the null categories are at the extremes of a set of categories, the estimates themselves can become too extreme. This paper describes a procedure in which the solution algorithm described by Andrich and Luo is further adapted in the presence of null categories by using their expected frequencies. The procedure is demonstrated with simulated and real data.

Algorithms↗

PubMed2005

The relationship between the Rating Scale and Partial Credit Models and the implication of disordered thresholds of the Rasch models for polytomous responses.

There is a perception in the literature that the Rating Scale Model (RSM) and Partial Credit Model (PCM) are two different types of Rasch models. This paper clarifies the relationship between the RSM and PCM from the perspectives of literature history and mathematical logic. It is shown that not only are the RSM and the PCM identical, but the two approaches used to introduce them are statistically equivalent. Then the implication of disordered thresholds is discussed. In addition, the difference between the structural thresholds and the Thurstone thresholds are clarified.

Data Interpretation, Statistical↗

PubMed2003

Conditional pairwise estimation in the Rasch model for ordered response categories using principal components.

In the Rasch model for items with more than two ordered response categories, the thresholds that define the successive categories are an integral part of the structure of each item in that the probability of the response in any category is a function of all thresholds, not just the thresholds between any two categories. This paper describes a method of estimation for the Rasch model that takes advantage of this structure. In particular, instead of estimating the thresholds directly, it estimates the principal components of the thresholds, from which threshold estimates are then recovered. The principal components are estimated using a pairwise maximum likelihood algorithm which specialises to the well known algorithm for dichotomous items. The method of estimation has three advantageous properties. First, by considering items in all possible pairs, sufficiency in the Rasch model is exploited with the person parameter conditioned out in estimating the item parameters, and by analogy to the pairwise algorithm for dichotomous items, the estimates appear to be consistent, though unlike for the dichotomous case, no formal proof has yet been provided. Second, the estimates of each item parameter is a function of frequencies in all categories of the item rather than just a function of frequencies of two adjacent categories. This stabilizes estimates in the presence of low frequency data. Third, the procedure accounts readily for missing data. All of these properties are important when the model is used for constructing variables from large scale data sets which must account for structurally missing data. A simulation study shows that the quality of the estimates is excellent.

Algorithms↗

PubMed2001

A Class of Probabilistic Unfolding Models for Polytomous Responses.

By revisiting the approaches used to present the Rasch model for polytomous response, this paper uses the principle of the rating formulation (Andrich, 1978) to construct a class of unfolding models for polytomous responses in terms of a set of latent dichotomous unfolding variables. By anchoring the dichotomous unfolding variables involved at the same location, this paper presents a formulation of a very general class of unfolding models for ordered polytomous responses, of which the unfolding models for ordered polytomous responses proposed hitherto are special cases. Within this class, the analytic and measurement properties of the probabilistic functions are well interpreted in terms of the latitudes of acceptance parameters of the dichotomous unfolding models. Based on the general form of this class of unfolding models, some new models are readily specified. Copyright 2001 Academic Press.

Journal Article↗