In this paper we present the methodology of multidimensional scaling problems (MDS) solved by means of the majorization algorithm. The objective function to be minimized is known as stress and functions which majorize stress are elaborated. This strategy to solve MDS problems is called SMACOF and it is implemented in an R package of the same name which is presented in this article. We extend the basic SMACOF theory in terms of configuration constraints, three-way data, unfolding models, and projection of the resulting configurations onto spheres and other quadratic surfaces. Various examples are presented to show the possibilities of the SMACOF approach offered by the corresponding package.
Item response theory models (IRT) are increasingly becoming established in social science research, particularly in the analysis of performance or attitudinal data in psychology, education, medicine, marketing and other fields where testing is relevant. We propose the R package eRm (extended Rasch modeling) for computing Rasch models and several extensions. A main characteristic of some IRT models, the Rasch model being the most prominent, concerns the separation of two kinds of parameters, one that describes qualities of the subject under investigation, and the other relates to qualities of the situation under which the response of a subject is observed. Using conditional maximum likelihood (CML) estimation both types of parameters may be estimated independently from each other. IRT models are well suited to cope with dichotomous and polytomous responses, where the response categories may be unordered as well as ordered. The incorporation of linear structures allows for modeling the effects of covariates and enables the analysis of repeated categorical measurements. The eRm package fits the following models: the Rasch model, the rating scale model (RSM), and the partial credit model (PCM) as well as linear reparameterizations through covariate structures like the linear logistic test model (LLTM), the linear rating scale model (LRSM), and the linear partial credit model (LPCM). We use an unitary, efficient CML approach to estimate the item parameters and their standard errors. Graphical and numeric tools for assessing goodness-of-fit are provided.
Bayesian analysis can expand the repertoire of network analytic approaches to psychopathology. We discuss clinical implications and limitations of our findings.
In this paper we give a general framework for isotone optimization. First we discuss a generalized version of the pool-adjacent-violators algorithm (PAVA) to minimize a separable convex function with simple chain constraints. Besides of general convex functions we extend existing PAVA implementations in terms of observation weights, approaches for tie handling, and responses from repeated measurement designs. Since isotone optimization problems can be formulated as convex programming problems with linear constraints we then develop a primal active set method to solve such problem. This methodology is applied on specific loss functions relevant in statistics. Both approaches are implemented in the R package isotone.
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Networks have emerged as a popular method for studying mental disorders. Psychopathology networks consist of aspects (e.g., symptoms) of mental disorders (nodes) and the connections between those aspects (edges). Unfortunately, the visual presentation of networks can occasionally be misleading. For instance, researchers may be tempted to conclude that nodes that appear close together are highly related, and that nodes that are far apart are less related. Yet this is not always the case. In networks plotted with force-directed algorithms, the most popular approach, the spatial arrangement of nodes is not easily interpretable. However, other plotting approaches can render node positioning interpretable. We provide a brief tutorial on several methods including multidimensional scaling, principal components plotting, and eigenmodel networks. We compare the strengths and weaknesses of each method, noting how to properly interpret each type of plotting approach.
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