Objectives This study psychometrically evaluated GeneralSelf-Efficacy (GSE) Scale in patients planned for bariatricsurgery in Sweden.Design A cross-sectional psychometric study. Thepsychometric evaluation was guided by the COnsensus-based Standards for the selection of health statusMeasurement Instruments checklist for health-relatedreported-patient outcomes.Setting Three bariatric centres in Sweden.Participants Adult patients≥18 years old scheduled forprimary bariatric surgery (with sleeve gastrectomy orRoux-en-Y gastric bypass).Primary and secondary measures Psychometricproperties of the GSE.Results In total, 704 patients were included in theanalysis. Mean values for GSE items were 2.9–3.4 and themean GSE sum score was 31.4 (SD 4.7). There were nofloor or ceiling effects. Cronbach’s alpha was 0.89. Menreported a higher mean GSE than did women, that is, 31.2(SD 4.8) for women versus 32.1 (SD 4.3) for men, p=0.03.Correlation coefficients were weak or negligible: GSE andmental component summary score of 36-Item Short FormHealth Survey (SF-36)/RAND 36, r=0.18 (p<0.00); GSEand physical component summary score of SF-36/RAND36, r=0.07 (p=0.138); GSE and obesity- related problemscale r=−0.15 (p=0.001) and GSE and level of education,r=0.04 (p=0.35). Confirmatory factor analysis indicateda one-factor construct with a satisfactory goodness of fit,that is, Comparative Fit Index=0.927, root mean squareerror of approximation=0.092 and standardised root meansquare residual=0.045. The factor GSE explained almosthalf or over half of the variance of each item (0.45–0.75,p-values<0.001).Conclusions The GSE scale is a valid and reliable scalethat can be used to assess general self-efficacy in patientsundergoing bariatric surgery.

In this paper, we study a Kronecker structured model for covariance matrices when data are matrix-valued. Using the modified Cholesky decomposition for Kronecker structured covariance matrix, we propose a regularized covariance estimator by imposing shrinkage and smoothing penalties on the Cholesky factors. A regularized flip-flop (RFF) algorithm is developed to produce a statistically efficient estimator for a large covariance matrix of matrix-valued data. Asymptotic properties are investigated and the performance of the estimator is evaluated by simulations. The results presented are applied to real data example.

In this paper, we investigate the asymptotic distributions of two types of Mahalanobis distance (MD): leave-one-out MD and classical MD with both Gaussian- and non-Gaussian-distributed complex random vectors, when the sample size n and the dimension of variables p increase under a fixed ratio c=p/n→∞. We investigate the distributional properties of complex MD when the random samples are independent, but not necessarily identically distributed. Some results regarding the F-matrix F=S−12S1—the product of a sample covariance matrix S1 (from the independent variable array (be(Zi)1×n) with the inverse of another covariance matrix S2 (from the independent variable array (Zj≠i)p×n)—are used to develop the asymptotic distributions of MDs. We generalize the F-matrix results so that the independence between the two components S1 and S2 of the F-matrix is not required.

Estimating inverse covariance matrix is an essential part of many statistical methods. This paper proposes a regularized estimator for the inverse covariance matrix. Modified Cholesky decomposition (MCD) is utilized to construct positive definite estimators. Instead of directly regularizing the inverse covariance matrix itself, we impose regularization on the Cholesky factor. The estimated inverse covariance matrix is used to build Mahalanobis distance (MD). The proposed method is evaluated by detecting outliers through simulations and empirical studies.

A hypothesis related to the block structure of a covariance matrix under the doubly multivariate normal model is studied. It is assumed that the block structure of the covariance matrix belongs to a quadratic subspace, and under the null hypothesis, each block of the covariance matrix also has a structure belonging to some quadratic subspace. The Rao score and the likelihood ratio test statistics are derived, and the exact distribution of the likelihood ratio test is determined. Simulation studies show the advantage of the Rao score test over the likelihood ratio test in terms of speed of convergence to the limiting chi-square distribution, while both proposed tests are competitive in terms of their power. The results are applied to both simulated and real-life example data.

Under a model having a Kronecker product covariance structure with compound symmetry, hypothesis testing for a correlation is investigated. Several tests are suggested and practical recommendations are made based on their type I error probabilities and powers.

Centers and vertices principal component analyses are common methods to explain variations within multivariate interval data. We introduce multivariate equicorrelated structures to vertices’ covariance. Assuming the structure, we show equivalence between centers and vertices methods by proving their eigensystems proportional.

OBJECTIVES: The aim was to psychometrically test and evaluate the Swedish functional health literacy scale and the Swedish communicative and critical health literacy scale in patients undergoing bariatric surgery.

DESIGN: A prospective cross-sectional psychometric study.

SETTING: Patients from three bariatric centres in Sweden were consecutively included in this study.

PARTICIPANTS: A total of 704 patients undergoing bariatric surgery filled in the questionnaires preoperatively. Inclusion criteria were scheduled for primary bariatric surgery (Roux-en-Y gastric bypass or sleeve gastrectomy) and greater than 17 years, proficiency in Swedish.

PRIMARY AND SECONDARY MEASURES: Psychometric outcomes of the Swedish Functional Health Literacy scale and the Swedish Communicative and Critical Health Literacy scale.

RESULTS: There was a higher proportion of females (74.4%, n=523) to males (25.6%, n=180). The mean age was 42 years (SD 11.5). Limited functional health literacy and limited communicative and critical health literacy (including both inadequate and problematic health literacy) was reported in 55% (n=390) and 40% (n=285), respectively. Cronbach alpha for the Swedish Functional Health Literacy scale was α=0.86 and for the Swedish Communicative and Critical Health Literacy scale, α=0.87. Construct validity showed weak to negative correlations between the Swedish Functional Health Literacy scale and income, education and SF-36/RAND36 summary scores. Confirmatory factor analysis showed a one-factor solution for the Swedish Functional Health Literacy scale and a two-factor solution for the Swedish Communicative and Critical Health Literacy scale.

CONCLUSIONS: The Swedish Functional Health Literacy scale and the Swedish Communicative and Critical Health Literacy scale are valid and reliable to use for patients undergoing bariatric surgery in a Swedish context. Measuring dimensions of health literacy can be used as a guide for the development of health literacy friendly patient information in patients undergoing bariatric surgery.

This thesis concerns the study of multilevel models with specific patterned covariance structures and addresses the issues of maximum likelihoodestimation. In particular, circular symmetric hierarchical datastructures are considered.

In the first paper (Paper I), we consider so-called dihedral block symmetrymodels and extend them to models which covariance structures reflects both circularity and exchangeability present in the data. The main contribution of Paper I are two derived patterns of the covariancematrices which characterizes models under consideration. The relationship between these two patterned covariance matrices was investigatedand it has been verified they are similar matrices. New expressions for the eigenvalues of block circular symmetric matrices are obtained which take into account the block structure. Paper II deals with estimation ofbalanced multilevel models with block circular symmetric covariance matrices. The spectral properties of such patterned covariance matrices are established. Maximum likelihood estimation is considered through the spectral decomposition of the patterned covariance matrix. The main results of Paper II concern the spectrum of the covariance matrix inthe model of interest and the existence of explicit maximum likelihood estimators for the covariance parameters.

This thesis concerns inference problems in balanced random effects models with a so-called block circular Toeplitz covariance structure. This class of covariance structures describes the dependency of some specific multivariate two-level data when both compound symmetry and circular symmetry appear simultaneously.

We derive two covariance structures under two different invariance restrictions. The obtained covariance structures reflect both circularity and exchangeability present in the data. In particular, estimation in the balanced random effects with block circular covariance matrices is considered. The spectral properties of such patterned covariance matrices are provided. Maximum likelihood estimation is performed through the spectral decomposition of the patterned covariance matrices. Existence of the explicit maximum likelihood estimators is discussed and sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and the corresponding maximum likelihood estimators are presented.

This thesis also deals with hypothesis testing of block covariance structures, especially block circular Toeplitz covariance matrices. We consider both so-called external tests and internal tests. In the external tests, various hypotheses about testing block covariance structures, as well as mean structures, are considered, and the internal tests are concerned with testing specific covariance parameters given the block circular Toeplitz structure. Likelihood ratio tests are constructed, and the null distributions of the corresponding test statistics are derived.

In this article, we address the problem of simultaneous testing hypothesis about mean and covariance matrix for repeated measures data when both the mean vector and covariance matrix are patterned. In particular, tests about the mean vector under block circular and doubly exchangeable covariance structures have been considered. The null distributions are established for the corresponding likelihood ratio test statistics, and expressions for the exact or near-exact probability density and cumulative distribution functions are obtained. The application of the results is illustrated by both a simulation study and a real-life data example.

Estimation of mean parameters in the growth curve model, when the covariance matrix has a block circular Toeplitz structure, is considered. The purpose of this article is to find the appropriate design matrices so that explicit mean estimators can be obtained.

We extend the existing family of flexible survival models by assembling models scattered across the literature into a more knit form and under the same umbrella. New special cases are obtained not only by constraining the shape and scale parameters of the extended generalized gamma (EGG) model to fixed constants, but also by imposing relationships (such as equality, reciprocal, and negative reciprocal) between them. Apart from common parametric distributions such as exponential, Weibull, gamma, and log normal, the further extended family includes Rayleigh, inverse Rayleigh, ammag, inverse ammag, and half-normal distributions. The models are applied, in a Bayesian framework, on time to entry into first marriage among Eritrean men and women based on data from the 2010 Population and Health Survey. The application demonstrates that the further extended family of distributions provides a wide range of alternatives for a baseline distribution in the analysis of survival data. The empirical results reveal that the inverse gamma model fits best the data for men. It also performs closely as good as the EGG model in the data for women as well as in the combined sample.

Under a model having a Kronecker product covariance structure with compound symmetry or circular symmetry, two-sample hypothesis testing for the equality of two correlation parameters is considered. Different tests are proposed by using the ratio of independent F distributions. Several tests are compared with the proposed ones and practical recommendations are made based on their type I error probabilities and powers. Finally, all mentioned tests are applied to a real data example.

Under a model having a Kronecker product covariance structure with compound symmetry or circular symmetry, two-sample hypothesis testing for the equality of two correlation parameters is considered. Different tests are proposed by using the ratio of independent F distributions. Several tests are compared with the proposed ones and practical recommendationsare made based on their type I error probabilities and powers. Finally, all mentioned tests areapplied to a real data example.

Hierarchical linear models with a block circular covariance structure are considered. Sufficient conditions for obtaining explicit and unique estimators for the variance-covariance components are derived. Different restricted models are discussed and maximum likelihood estimators are presented. The theory is illustrated through covariance matrices of small sizes and a real-life example.

Models that capture symmetries present in the data have been widely used in different applications, with early examples from psychometric and medical research. The aim of this article is to study a random effects model focusing on the covariance structure that is block circular symmetric. Useful results are obtained for the spectra of these structured matrices.

In this article we consider a multilevel model with block circular symmetric covariance structure. Maximum likelihood estimation of the parameters of this model is discussed. We show that explicit maximum likelihood estimators of variance components exist under certain restrictions on the parameter space.

The aim of the paper is to determine maximum-likelihood estimation equations. Observations follow a multivariate normal distribution, X-i similar to N-p,N-q (mu, Psi, Sigma), where D[X-i] = Sigma circle times Psi, Psi and Sigma describe the unknown covariance structure between rows and columns of X-i, respectively. Imposing restrictions on Psi and Sigma four types of covariance structures will be considered.