Generalized linear modeling of a panel mobility index with correlated multivariate categorical responses

Data with multivariate, longitudual categorical responses often occur in applications. It can be difficult to analyze and model such data while simultaneously taking into account explanatory variables and correlations between the responses over time. We take a generalized linear model approach to this problem in analyzing panel data from the Health and Retirement Survey (HRS) that includes older Americans’ mobility over several years as a response. We provide a general formula for the likelihood of such data and apply it to the case when there are three binary responses. This approach can be taken, with computational limits, for data with multivariate, categorical responses with any number of categories. We consider, simultaneously, interpretations of coefficients, dependence of responses and goodness-of-fit in reduced models for parsimony while taking into account explanatory data. The gradient of the objective function is provided for use in gradient descent and the coded optimization algorithm is tested with a Monte Carlo simulation. Dependence of responses in mobility is shown before taking explanatory variables into account, and dependence is shown in a Markov logistic regression model and in the generalized linear model taking into account race, age, gender and interactions between them.

The symptom-syndrome analysis of multivariate categorical data based on Zhegalkin polynomials

In this article, we study the distribution, entropy and other informational properties of finite projective subspaces (syndromes) parameterized by impulse sequences with basic elements in the form of symptoms - polynomials over the field F2 which are known as Zhegalkin polynomials. It has been proven that the super syndrome, which is a linear syndrome with basic elements in the form of a multiplicative syndrome, is closed. If in the multiplication of two symptoms one is neutral, then we are talking about its majorization. The ordered by majorization symptoms form a majorized syndrome. Is proved that the majorized syndrome is closed and coincides with the super syndrome. The statements formulated in the first part of the paper are used to justify the convergence of the iterative procedure (PI), in which the most informative symptoms selected from partial super syndromes are again used in the next step. The stationary state of PI is obtained if all elements of the input set belong to either the same partial super syndrome or to the majorized syndrome. Thanks IP it is possible to quickly find the optimal syndrome from a large set of variables. An example from phthisiology shows how the specificity of classification can be improved using symptom analysis.

Sequentially additive nonignorable missing data modelling using auxiliary marginal information

Summary We study a class of missingness mechanisms, referred to as sequentially additive nonignorable, for modelling multivariate data with item nonresponse. These mechanisms explicitly allow the probability of nonresponse for each variable to depend on the value of that variable, thereby representing nonignorable missingness mechanisms. These missing data models are identified by making use of auxiliary information on marginal distributions, such as marginal probabilities for multivariate categorical variables or moments for numeric variables. We prove identification results and illustrate the use of these mechanisms in an application.