124 research outputs found
Modelling Ordinal Responses with Uncertainty: a Hierarchical Marginal Model with Latent Uncertainty components
In responding to rating questions, an individual may give answers either
according to his/her knowledge/awareness or to his/her level of
indecision/uncertainty, typically driven by a response style. As ignoring this
dual behaviour may lead to misleading results, we define a multivariate model
for ordinal rating responses, by introducing, for every item, a binary latent
variable that discriminates aware from uncertain responses. Some independence
assumptions among latent and observable variables characterize the uncertain
behaviour and make the model easier to interpret. Uncertain responses are
modelled by specifying probability distributions that can depict different
response styles characterizing the uncertain raters. A marginal parametrization
allows a simple and direct interpretation of the parameters in terms of
association among aware responses and their dependence on explanatory factors.
The effectiveness of the proposed model is attested through an application to
real data and supported by a Monte Carlo study
Qualitative and quantitative models for ordinal data analysis
EnIn this paper, we explore and compare classical regression and ordinal data models when quantitative data are related to a qualitative assessment. Specifically, we test the approach on a data set of graduated students and we check the relative performance and the interpretative content of the models. Some further comments end the paper
A hybrid approach for the analysis of complex categorical data structures: assessment of latent distance learning perception in higher education
A long tradition of analysing ordinal response data deals with parametric models, which started with the seminal approach of cumulative models. When data are collected by means of Likert scale survey questions in which several scored items measure one or more latent traits, one of the sore topics is how to deal with the ordered categories. A stacked ensemble (or hybrid) model is introduced in the proposal to tackle the limitations of summing up the items. In particular, multiple items responses are synthesised into a single meta-item, defined via a joint data reduction approach; the meta-item is then modelled according to regression approaches for ordered polytomous variables accounting for potential scaling effects. Finally, a recursive partitioning method yielding trees provides automatic variable selection. The performance of the method is evaluated empirically by using a survey on Distance Learning perception
Mixture Models for Ordinal Responses to Account for Uncertainty of Choice
In CUB models the uncertainty of choice is explicitly modelled as a Combination of discrete Uniform and shifted Binomial random variables. The basic concept to model the response as a mixture of a deliberate choice of a response category and an uncertainty component that is represented by a uniform distribution on the response categories is extended to a much wider class of models. The deliberate choice can in particular be determined by classical ordinal response models as the cumulative and adjacent categories model. Then one obtains the traditional and flexible models as special cases when the uncertainty component is irrelevant. It is shown that the effect of explanatory variables is underestimated if the uncertainty component is neglected in a cumulative type mixture model. Visualization tools for the effects of variables are proposed and the modelling strategies are evaluated by use of real data sets. It is demonstrated that the extended class of models frequently yields better fit than classical ordinal response models without an uncertainty component
Mixture Models for Ordinal Responses to Account for Uncertainty of Choice
In CUB models the uncertainty of choice is explicitly modelled as a Combination of discrete Uniform and shifted Binomial random variables. The basic concept to model the response as a mixture of a deliberate choice of a response category and an uncertainty component that is represented by a uniform distribution on the response categories is extended to a much wider class of models. The deliberate choice can in particular be determined by classical ordinal response models as the cumulative and adjacent categories model. Then one obtains the traditional and flexible models as special cases when the uncertainty component is irrelevant. It is shown that the effect of explanatory variables is underestimated if the uncertainty component is neglected in a cumulative type mixture model. Visualization tools for the effects of variables are proposed and the modelling strategies are evaluated by use of real data sets. It is demonstrated that the extended class of models frequently yields better fit than classical ordinal response models without an uncertainty component
Methodological issues for a clustered ordinal response framework
In this paper, we present alternative frameworks for clustered ordinal data concerning a specific class of models denoted as CUB. Specifically, we analyze models that contain variables measured at different levels of the hierarchy by integrating them in a multi-context or multilevel structure. After a brief review on CUB models, we describe the two approaches and introduce the methodological issues for interpreting and discussing of the results
- …