Multiple imputation for high-dimensional mixed incomplete continuous and binary data.

The natural performance of the location model is a potential tool for allocating an object into one of the two observed groups involving mixtures of continuous and binary variables. In constructing location model, continuous variable is used to estimate parameters while binary variable is utilized to create segmentation in each group. Such segmentation is called as multinomial cells. Basically, the multinomial cells will grow exponentially according to the number of the binary variable. These multinomial cells will become empty when there is no object can be assigned into some of them. Then the occurring of empty cells will lead to unreliable parameter estimation. Consequently, the construction of the discriminant rule based on location model is impossible. Therefore, this paper attempts to discuss how the location model based on maximum likelihood estimation can be constructed even dealing with many measured binary variables. In other word, how is location model able to deal with the issue of many empty ...

In this article, we illustrate ways in which generalizability theory (G-theory) can be used with continuous latent response variables (CLRVs) to address problems of scale coarseness resulting from categorization errors caused by representing ranges of continuous variables by discrete data points and transformation errors caused by unequal interval widths between those data points. The mechanism to address these problems is applying structural equation modeling (SEM) as a tool in deriving variance components needed to estimate indices of score consistency and validity. Illustrations include quantification of multiple sources of measurement error, use of non-nested and nested designs, derivation of indices of consistency for norm- and criterion-referenced interpretation of scores, estimation of effects when changing measurement procedures and designs, and disattenuation of correlation coefficients for measurement error. These illustrations underscore the effectiveness of G-theory with continuous latent response variables in providing stable indices of reliability and validity that are reasonably independent of the number of original scale points used, unevenness of scale intervals, and average degree of item skewness. We discuss general distinctions in reliability estimation within G-theory, SEM, and classical test theory; make specific recommendations for using G-theory on raw score and CLRV metrics; and provide computer code in an online supplement for doing all key analyses demonstrated in the article using R and Mplus. (PsycINFO Database Record (c) 2019 APA, all rights reserved).

A practical approach for hybrid distributed MPC

ABSTRACTConventional statistical process control tools target either continuous or categorical data but seldom both at the same time. However, mixed-type data consisting of both continuous and categorical observations are becoming more common in modern manufacturing processes and service management. However, they cannot be analyzed using traditional methods. By assuming that there is a latent continuous variable that determines the attribute levels of a categorical variable, the ordinal information among the attribute levels can be exploited. This enables us to simultaneously describe and monitor continuous and categorical data in a unified framework of standardized ranks, based on which a multivariate exponentially weighted moving average control chart is proposed. This control chart specializes in detecting location shifts in continuous data and in latent continuous distributions of categorical data. Numerical simulations show that our proposed chart can efficiently detect location shifts and is robust to various distributions.

Summary The primary purpose of this paper is to propose empirical measures of the structural differences between two communities of plants or animals composed of the same species. Structure is defined to consist of; 1) the species in the community, 2) the pattern of interactions as represented by the covariance or correlation matrix of successive observations on each species, and 3) the mean abundances of each species in each of the two communities. Statistical tests are proposed for testing whether the covariance matrices and the vectors of mean densities for each community are equal and empirical measures of the differences between the covariance matrices and mean vectors are proposed. Given unequal covariance or correlation matrices the factor analysis model is used to derive empirical measures of the degree to which each variable of the ecosystem is responsible for the observed defferences in the pattern of interactions in each community. These tests and measures were applied to data gathered by Hunter (1966) on the abundances of six species of Drosophila censused monthly over a period of approximately two and a half years in two adjacent, but different habitats near Bogota, colombia. The two covariance matrices were significantly different indicating different patterns of interactions in the two Drosophila communities.

Integrating Genetic Risk Factors with Age, Presenting White Cell Count and MRD Response As Continuous Variables to Predict Relapse in Paediatric Acute Lymphoblastic Leukemia (ALL)

Co-clustering is a data mining technique used to extract the underlying block structure between the rows and columns of a data matrix. Many approaches have been studied and have shown their capacity to extract such structures in continuous, binary or contingency tables. However, very little work has been done to perform co-clustering on mixed type data. In this article, we extend the latent block models based co-clustering to the case of mixed data (continuous and binary variables). We then evaluate the effectiveness of the proposed approach on simulated data and we discuss its advantages and potential limits.

The monitoring and diagnosis of multivariate categorical processes (MCPs) have drawn increasing attention lately, as categorical variables have been frequently involved in modern quality control applications. In these applications, there may exist causal relationships among multiple categorical variables, where the attribute level of a cause variable influences that of its effect variable. In such a case, shifts occurring in a cause variable will propagate to its effect variable based on the causal structure. Furthermore, there usually exists natural order among the attribute levels of some categorical variables such as good, neutral, and bad for measuring the product quality. By assuming a latent continuous variable, the attribute levels of an ordinal categorical variable can be determined by classifying the value of the latent variable based on thresholds. In this paper, we leverage Bayesian networks (BNs) to characterize MCPs with a causal structure, where the categorical variables can be either nominal, ordinal or a combination of both. We develop one general control chart and one directional control chart, both of which fully exploit the causal relationships and the ordinal information for better process monitoring and diagnosis. Numerical simulations have demonstrated the superiority and robustness of our method in detecting and diagnosing the conditional probability shifts of nominal factors as well as the conditional latent location shifts of ordinal factors. Note to Practitioners-This paper aims at addressing the challenges in monitoring and diagnosing MCPs when there are causal relationships among the categorical variables. The developed method is greatly beneficial, especially when there are nominal and ordinal variables involved in the MCP. Specifically, a BN is employed to characterize the dependence structure of the variables involved in the process, and a latent continuous variable is utilized to model the orders of attribute levels of the ordinal variables. Then, a novel method is proposed to detect the probability shift in the nominal factors and the location shift on the latent variables of the ordinal variables based on the likelihood ratio test. A general monitoring control chart as well as a directional version which also facilitates diagnosis is proposed. In this paper, although our method is based on the assumption that the latent continuous variables of the ordinal variables follow logistic distributions, the proposed charts are demonstrated to perform efficiently and robustly in various cases as shown in the simulations and case studies.

ABSTRACTIn Rheumatoid Arthritis studies, scientists usually need to focus on multiple endpoints simultaneously. Regulatory agencies require ACR20 as the primary endpoint for approval and making decisions. However, the proportional measurement for a binary variable is less reliable with a small sample size. DAS28 is an increasingly popular co-primary or key secondary endpoint for decision making in interim analyses because it is a continuous variable as well as a linear combination of multiple measurements that are also contained in ACR20. In a group sequential (GS) design, one of the most important parts is to compute the correlation among test statistics in interim and final analyses. We perform a logistic regression to link DAS28 and ACR20 and compute the correlation numerically. We also prove that the covariance matrix between binary and continuous variables with underlying logistic regression is a consistent estimator. Three methods including “GS design with univariate variable (ACR20),” “GS design with change of endpoints (DAS28 and ACR20),” and “Bonferroni tests with change of endpoints” are compared in three cases—“early stopping for efficacy,” “early stopping for futility,” and “early stopping for both” through simulation. The results show that in the first and third cases, the power of tests with a change of endpoint is much higher than tests that only use ACR20. In the case of “early stopping for futility,” the methods with a change of endpoint also provide a higher probability of correctly stopping early for futility.

Traditionally quantum information research has centred on discrete quantum variables, particularly binary variables (qubits). However, recently much attention has focused on quantum information manipulations with continuous variables such as the amplitude and phase of the electromagnetic field. As well as offering the possibility of high data rates, continuous variables also exhibit greater versatility in realizing certain operations. For example teleportation, in which quantum information is passed intact through a classical channel with the assistance of shared entanglement, can be achieved more efficiently using continuous variable techniques. I review recent work on the characterization of teleportation and entanglement swapping and present new work on interferometric tests of teleportation. These interferometric tests are important because they allow the efficacy of teleportation to be checked without knowledge of the input quantum state. They can be applied equally to the cases of discrete and continuous variable inputs and in so doing highlight unexpected similarities. I contrast the various classical limits which emerge from the different ways of assessing teleportation. An obvious omission from the list of continuous variable quantum information manipulations is any proposal for direct analogues of 2 photon interference effects, especially those that lead to Bell inequality type tests of local realism. Bell-type correlations are the defining feature of discrete variable entanglement experimentally. I discuss new work that shows how entanglement of the Bell-type can be observed in continuous variable, homodyne measurement schemes.

INTRODUCTION: Despite an excellent prognosis and survival rate, quality of life (QOL) in thyroid cancer is lower than expected. QOL in thyroid cancer survivors is similar to persons with colon and gynecologic cancers, but worse than breast cancer.1 The SF-36 QOL questionnaire has shown to be a valid tool for assessing QOL in thyroid cancer subjects.2 We evaluated QOL in both thyroid nodule and thyroid cancer patients in an institutional cancer registry. METHODS: The Short Form-36 data version 2 (SF-36) QOL data was obtained from single institution prospective bioinformatics thyroid cancer and benign nodule registry. Physical and mental health scores from the SF-36 questionnaire were obtained from both thyroid cancer and nodule patients. Physical and mental QOL responses were scored on a scale from 20-80 and categorized as either “the same or better than the average population,”; “below average,”; or “well below average.” A two sample Wilcoxon rank sum test and a chi-squared test were used to compare QOL between thyroid cancer and nodule subjects, using QOL as a continuous or categorical variable. Univariate descriptive statistics and bivariate analyses were performed using a Wilcoxon Rank Sum and Chi-squared test for categorical QOL data and Kruskal-Wallis for continuous QOL data. RESULTS: We analyzed 321 thyroid cancer and 32 nodule subjects who completed the SF-36 at a single point in time after diagnosis. There was no difference between the groups with regard to sex, age or QOL scores overall. Average age was 43 and 48 years in cancer and nodule groups respectively. Average Physical QOL score was 50.8 (standard deviation SD + 8.8) and 29.6 (SD+ 12.1), respectively (p=0.42). Average Mental QOL score was 48.9 (SD + 9.9) and 48.3 (SD + 8.1) respectively, p=0.16. Physical QOL score was significantly decreased as cancer stage increased when evaluating results as a continuous variable: Stage 1: 51.8 + 8.7; Stage 2: 50.6 +9.5; Stage 3: 48.7 + 7.2; Stage 4: 47.4 + 9.2. Results for mental QOL as a continuous variable by cancer stage showed improvement in reported QOL with increasing cancer stage: Stage 1: 48 (SD+ 9.9); Stage 2: 50.6 (SD + 11.1); Stage 3: 51.1 (SD + 9.13); Stage 4: 53 (SD+ 6.4), p=0.03. CONCLUSIONS: We found no overall difference in physical nor mental QOL between patients with thyroid cancer or benign thyroid nodules. Overall, QOL was in the “same or better than average” for all respondents, but low cancer stage was associated with higher physical and lower mental QOL scores.REFERENCES:1. Barbus, Elena & Peştean, Claudiu & Iulia Larg, Maria & Piciu, Doina. (2016). Quality of life in thyroid cancer patients: A literature review. Clujul Medical. 90. 10.15386/cjmed-7032. Lubitz CC, De Gregorio L, Fingeret AL, et al. Measurement and Variation in Estimation of Quality of Life Effects of Patients Undergoing Treatment for Papillary Thyroid Carcinoma. Thyroid. 2017;27(2):197-206. doi:10.1089/thy.2016.0260

Recently, analysis of structural equation models with polytomous and continuous variables has received a lot of attention. However, contributions to the selection of good models are limited. The main objective of this article is to investigate the maximum likelihood estimation of unknown parameters in a general LISREL-type model with mixed polytomous and continuous data and propose a model selection procedure for obtaining good models for the underlying substantive theory. The maximum likelihood estimate is obtained by a Monte Carlo Expectation Maximization algorithm, in which the E step is evaluated via the Gibbs sampler and the M step is completed via the method of conditional maximization. The convergence of the Monte Carlo Expectation Maximization algorithm is monitored by the bridge sampling. A model selection procedure based on Bayes factor and Occam's window search strategy is proposed. The effectiveness of the procedure in accounting for the model uncertainty and in picking good models is discussed. The proposed methodology is illustrated with a real example.

Linear models in social science, psychlology, economics, and epidemiology are often formullated in latent continuous variables, which can be measured only with error or through two or more observed indicators. Henice, the latent variables are connected with the observed variables by a measurement model. If the observed indicators are metric, the covariance matrix of the observed variables is analyzed by using covariance structure models. Covariance structure models have been extended by MuthMn (1984) to deal with indicators that are metric and ordered categorical rather than metric alone. By abandoning the analysis of covariance structures and returning to some of the original ideas of latent structure analysis, we can extend the class of variables that may serve as indicators for latent variables utsed in a simultaneous equation system to include variables on any level of measurement. This class comprises observed variables that may be metric, censored metric, counts, ordered, or unordered categorical. A limited marginal maximum likelihood approach is used to estimate the model. Numerical procedures necessary to implement such an estimation are discussed.

Estimating large covariance and precision (inverse covariance) matrices has become increasingly important in high dimensional statistics because of its wide applications. The estimation problem is challenging not only theoretically due to the constraint of its positive definiteness, but also computationally because of the curse of dimensionality. Many types of estimators have been proposed such as thresholding under the sparsity assumption of the target matrix, banding and tapering the sample covariance matrix. However, these estimators are not always guaranteed to be positive-definite, especially, for finite samples, and the sparsity assumption is rather restrictive. We propose a novel two-stage adaptive method based on the Cholesky decomposition of a general covariance matrix. By banding the precision matrix in the first stage and adapting the estimates to the second stage estimation, we develop a computationally efficient and statistically accurate method for estimating high dimensional precision matrices. We demonstrate the finite-sample performance of the proposed method by simulations from autoregressive, moving average, and long-range dependent processes. We illustrate its wide applicability by analyzing financial data such S&P 500 index and IBM stock returns, and electric power consumption of individual households. The theoretical properties of the proposed method are also investigated within a large class of covariance matrices.

Discrimination and allocation using a mixture of discrete and continuous variables with some empty states