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The R package multgee implements the local odds ratios generalized estimating equations (GEE) approach proposed by Touloumis et al. (2013), a GEE approach for correlated multinomial responses that circumvents theoretical and practical limitations of the GEE method. A main strength of multgee is that it provides GEE routines for both ordinal (ordLORgee) and nominal (nomLORgee) responses, while relevant softwares in R and SAS are restricted to ordinal responses under a marginal cumulative link model specification. In addition, multgee offers a marginal adjacent categories logit model for ordinal responses and a marginal baseline category logit model for nominal. Further, utility functions are available to ease the local odds ratios structure selection (intrinsic.pars) and to perform a Wald type goodness-of-fit test between two nested GEE models (waldts). We demonstrate the application of multgee through a clinical trial with clustered ordinal multinomial responses., Comment: To appear in Journal of Statistical Software

Estimating a covariance matrix is an important task in applications where the number of variables is larger than the number of observations. Shrinkage approaches for estimating a high-dimensional covariance matrix are often employed to circumvent the limitations of the sample covariance matrix. A new family of nonparametric Stein-type shrinkage covariance estimators is proposed whose members are written as a convex linear combination of the sample covariance matrix and of a predefined invertible target matrix. Under the Frobenius norm criterion, the optimal shrinkage intensity that defines the best convex linear combination depends on the unobserved covariance matrix and it must be estimated from the data. A simple but effective estimation process that produces nonparametric and consistent estimators of the optimal shrinkage intensity for three popular target matrices is introduced. In simulations, the proposed Stein-type shrinkage covariance matrix estimator based on a scaled identity matrix appeared to be up to 80% more efficient than existing ones in extreme high-dimensional settings. A colon cancer dataset was analyzed to demonstrate the utility of the proposed estimators. A rule of thumb for adhoc selection among the three commonly used target matrices is recommended., Comment: To appear in Computational Statistics and Data Analysis

The matrix-variate normal distribution is a popular model for high-dimensional transposable data because it decomposes the dependence structure of the random matrix into the Kronecker product of two covariance matrices: one for each of the row and column variables. We develop tests for assessing the form of the row (column) covariance matrix in high-dimensional settings while treating the column (row) dependence structure as a nuisance. Our tests are robust to normality departures provided that the Kronecker product dependence structure holds. In simulations, we observe that the proposed tests maintain the nominal level and are powerful against the alternative hypotheses tested. We illustrate the utility of our approach by examining whether genes associated with a given signalling network show correlated patterns of expression in different tissues and by studying correlation patterns within measurements of brain activity collected using electroencephalography.

The structural information in high-dimensional transposable data allows us to write the data recorded for each subject in a matrix such that both the rows and the columns correspond to variables of interest. One important problem is to test the null hypothesis that the mean matrix has a particular structure without ignoring the potential dependence structure among and/or between the row and column variables. To address this, we develop a simple and computationally efficient nonparametric testing procedure to assess the hypothesis that, in each predefined subset of columns (rows), the column (row) mean vector remains constant. In simulation studies, the proposed testing procedure seems to have good performance and unlike traditional approaches, it is powerful without leading to inflated nominal sizes. Finally, we illustrate the use of the proposed methodology via two empirical examples from gene expression microarrays., Comment: in Biometrics, 2015