Journal of Data Science

Spatial probit generalized linear mixed models (spGLMM) with a linear fixed effect and a spatial random effect, endowed with a Gaussian Process prior, are widely used for analysis of binary spatial data. However, the canonical Bayesian implementation of this hierarchical mixed model can involve protracted Markov Chain Monte Carlo sampling. Alternate approaches have been proposed that circumvent this by directly representing the marginal likelihood from spGLMM in terms of multivariate normal cummulative distribution functions (cdf). We present a direct and fast rendition of this latter approach for predictions from a spatial probit linear mixed model. We show that the covariance matrix of the cdf characterizing the marginal cdf of binary spatial data from spGLMM is amenable to approximation using Nearest Neighbor Gaussian Processes (NNGP). This facilitates a scalable prediction algorithm for spGLMM using NNGP that only involves sparse or small matrix computations and can be deployed in an embarrassingly parallel manner. We demonstrate the accuracy and scalability of the algorithm via numerous simulation experiments and an analysis of species presence-absence data.

Abstract: Of interest in this paper is the development of a model that uses inverse sampling of binary data that is subject to false-positive misclassification in an effort to estimate a proportion. From this model, both the proportion of success and false positive misclassification rate may be estimated. Also, three first-order likelihood based confidence intervals for the proportion of success are mathematically derived and studied via a Monte Carlo simulation. The simulation results indicate that the score and likelihood ratio intervals are generally preferable over the Wald interval. Lastly, the model is applied to a medical data set.

Abstract: Different models are used in practice for describing a binary lon gitudinal data. In this paper we consider the joint probability models, the marginal models, and the combined models for describing such data the best. The combined model consists of a joint probability model and a marginal model at two different levels. We present some striking empirical observa tions on the closeness of the estimates and their standard errors for some parameters of the models considered in describing a data from Fitzmaurice and Laird (1993) and consequently giving new insight from this data. We present the data in a complete factorial arrangement with 4 factors at 2 levels. We introduce the concept of “data representing a model completely” and explain “data balance” as well as “chance balance”. We also consider the best model selection problem for describing this data and use the Search Linear Model concepts known in Fractional Factorial Design research (Sri vastava (1975)).

Abstract: Incomplete data are common phenomenon in research that adopts the longitudinal design approach. If incomplete observations are present in the longitudinal data structure, ignoring it could lead to bias in statistical inference and interpretation. We adopt the disposition model and extend it to the analysis of longitudinal binary outcomes in the presence of monotone incomplete data. The response variable is modeled using a conditional logistic regression model. The nonresponse mechanism is assumed ignorable and developed as a combination of Markov’s transition and logistic regression model. MLE method is used for parameter estimation. Application of our approach to rheumatoid arthritis clinical trials is presented.

Abstract: Fisher’s exact test (FET) is a conditional method that is frequently used to analyze data in a 2 × 2 table for small samples. This test is conservative and attempts have been made to modify the test to make it less conservative. For example, Crans and Shuster (2008) proposed adding more points in the rejection region to make the test more powerful. We provide another way to modify the test to make it less conservative by using two independent binomial distributions as the reference distribution for the test statistic. We compare our new test with several methods and show that our test has advantages over existing methods in terms of control of the type 1 and type 2 errors. We reanalyze results from an oncology trial using our proposed method and our software which is freely available to the reader.