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The test of homogeneity for intraclass correlation coefficients has been one of the active topics in statistical research. Several chi-square tests have been proposed to test the homogeneity of intraclass correlations in the past few decades. The big concern for them is that these methods are seriously biased when sample sizes are not large. In this thesis, data driven approaches are proposed to testing the homogeneity of intraclass correlation coefficients of several populations. Through simulation study, data driven methods have been proved to be less biased and accurate than some commonly used chi-square tests.

This paper uses Maximum likelihood estimation method to estimate the common correlation coefficients for multivariate datasets. We discuss a graphical tool, Q-Q plot, to test equality of the common intraclass correlation coefficients. Kolmogorov-Smirnov test and Cramér-von Mises test are used to check if the intraclass correlation coefficients are the same among populations. Bootstrap and empirical likelihood methods are applied to construct the confidence interval of the common intraclass correlation coefficients.

Reliability measures have been well studied over many years, beginning with an entire chapter devoted to intraclass correlation in the first edition of Fisher (1925). Such measures have been thoroughly studied for two factor models. This dissertation, motivated by a medical research problem, extends point and confidence interval estimation of both intraclass correlation coefficient and interater reliability coefficient to models containing three crossed random factors -- subjects, raters and occasions. The intraclass correlation coefficient is used when decision is made on an absolute basis with rater's scores, while the interater reliability coefficient is defined for decisions made on a relative basis. The estimation is conducted using both ANOVA and MCMC methods. The results from the two methods are compared. The MCMC method is preferred for analyses of small data sets when ICC values are high. Besides, the bias of estimator of intraclass correlation coefficient in one-way random effects model is evaluated. / Statistics

The National health and nutrition examination survey (NHANES) is a respected nation-wide program in charge of assessing the health and nutritional status of adults and children in United States. Recent cal research found that folic acid play an important role in preventing baby birth defects. In this paper, we use the generalized estimating equation (GEE) method to study the generalized linear model (GLM) with compound symmetric correlation matrix for the NHANES data and investigate significant factors to ence the intake of food folic acid.

Multilevel datasets are commonly used and increasingly popular in research in the organizational and other social sciences. These models are complex and have many elements beyond those found in more traditional linear models. However, research on how multilevel models perform is lacking. The current paper examined the impact of common factors (average cluster size, cluster size distribution, average number of clusters, strength of the intraclass correlation coefficient, and effect sizes of individual and cluster level variables, and their interaction) in multilevel datasets. Monte Carlo data simulation was used across 6,144 factor-combination conditions. The results of study factors on observed intraclass correlation coefficients, calculated design effect, and empirical design effect are discussed. The results of this study have implications for both researchers in both academic and applied fields. The scale of the simulation variables allow it to be germane to datasets from across the social sciences. However, the nature of data simulation and analysis is such that there are still many elements that can and should be accounted for in future research.

Doctor of Philosophy / Department of Statistics / James Higgins / Many studies are performed on units that cannot be replicated due to cost or other restrictions. There often is an abundance of subsampling to estimate the within unit component of variance, but what is needed for statistical tests is an estimate of the between unit component of variance. There is evidence to suggest that the ratio of the between component of variance to the total variance will remain relatively constant over a range of studies of similar types. Moreover, in many cases this intraclass correlation, which is the ratio of the between unit variance to the total variance, will be relatively small, often 0.1 or less. Such situations exist in education, agriculture, and medicine to name a few. The present study discusses how to use such prior information on the intraclass correlation coefficient (ICC) to obtain inferences about differences among treatments in the face of no replication. Several strategies that use the ICC are recommended for different situations and various designs. Their properties are investigated. Work is extended to under-replicated experiments. The work has a Bayesian flavor but avoids the full Bayesian analysis, which has computational complexities and the potential for lack of acceptance among many applied researchers. This study compares the prior information ICC methods with traditional methods. Situations are suggested in which prior information ICC methods are preferable to traditional methods and those in which the traditional methods are preferable.

Thesis ((Ph.D. (Mathematics Education)) -- University of Limpopo, 2016 / The focus in this thesis was on the approaches that seek to compare two study arms in the absence of randomisation when the interclass correlation coefficient is greater than zero. Many reports on performance of learners in Grade 12 have used ordinary regression models (such as logistic regression model and linear regression models) which ignore clustering effect, and descriptive statistics (e.g., averages and standard deviations for continuous variables, and proportions expressed as percentages and frequencies). These models do not only bias point estimates but also give falsely narrow confidence intervals. The study was applied to two of the nine provinces of South Africa: Gauteng Province and Western Cape Province in 2008, 2009 and 2010 academic years. Causal models, and in particular, hierarchical models (or disaggregated approach), unlike descriptive analyses, are more powerful as they are able to adjust for individual covariates. For the analysis of continuous variables; Western Cape Province was expected to significantly score higher marks than Gauteng Province in 2008 (Crude estimate: 0.782) and 2009 (Crude estimate: 0.957 ) while Gauteng Province was expected to score higher marks than Western Cape Province in 2010 (Crude estimate: −0.302). Adjusted models indicate that Western Cape Province performed better than Gauteng Province in 2008 and 2009 but not in 2010 where Gauteng Province performed better than Western Cape Province after adjusting for gender. In case of binary outcome; the crude estimates favoured Western Cape Province than Gauteng Province in 2008 (Odds ratio = 1.16) and 2009 (Odds ratio = 1.19). Otherwise, the crude estimates favoured Gauteng Province in 2010 (Odds ratio = 0.11). The proportion of female learners in Gauteng Province ranged between 54.48% and 54.99%, while in Western Cape Province it ranged between 56.78% and 57.16%, in 2008 through 2010 academic years. Proportion of female learners in Western Cape Province were found to be higher than those in Gauteng during this period. At least 70.42% of learners in Gauteng and at least 73.96% of learners in Western Cape Province passed Grade 12 during the years 2008 to 2010. Through the application of causal model we have learned that although gender is not a significant predictor of the overall learner performance in Grade 12, the effect of gender gave the mixed findings depending on the nature of the outcome. The xi effect of gender on continuous endpoint (marks) suggests that a model of single-sex classrooms or single-sex schools may be adopted so as to mitigate the inherent perceptions and stereotype regarding learner-gender. However, the results based on binary endpoint (pass/not pass) suggest that coeducation system is the best bet. A school quintile is a significant predictor of the overall learner performance in the two provinces. The resourceful schools are more likely to produce learners with higher marks. Also, the resourced schools than the less or under resourced schools are more likely to produce the favourable results (higher marks (%) or/and pass) in the two provinces.

<p>Introduction</p> <p>The most common complication following invasive cardiac procedures is the development of vascular access site (VAS) bruising. The extent and impact of VAS bruising is poorly understood and minimally reported in the literature. Research into this common post-procedure complication is hindered by the lack of a reliable bruise measurement tool, and the concept that VAS bruising is a minor complication. This mixed methods study examined the inter-rater reliability of two methods to measure VAS bruise size. The embedded qualitative descriptive study explored patient perceptions of VAS bruising.</p> <p>Methods</p> <p>Participants having femoral or radial artery puncture for invasive cardiac procedures were included in this study. Participants reporting VAS bruising completed self measurement of bruise size using two methods, linear measurement and planimetry. The principal investigator and research assistant completed bruise measurements at the same time, and were blinded to participant and each others’ measurements. Following bruise measurement, the principal investigator conducted semi-structured interviews on a convenience sample of participants; including both sexes, a range of ages, and bruise sizes.</p> <p>Results</p> <p>Measurements were completed on 40 participants with VAS bruises. Analysis of inter-rater reliability was done using the intraclass correlation coefficient (ICC), two-way random effects model. The inter-rater reliability for both linear measurement and planimetry between all three measurers was high (.929; .914 respectively). Analysis of participant narratives uncovered three major themes concerns, impact and mediating factors, with several sub-themes.</p> <p>The findings of this study support the reliability of patient VAS bruise measurement using linear measurement and planimetry. The goals and available resources for VAS research may determine the choice of measurement approach. Qualitative descriptive results indicate that patients have concerns related to VAS bruising and that this bruising may impact activities of daily living. Future research examining VAS complications should include evaluation of VAS bruising as significant patient outcome.</p> / Doctor of Philosophy (PhD)

Agreement between raters on a categorical scale is not only a subject of scientific research but also a problem frequently encountered in practice. Whenever a new scale is developed to assess individuals or items in a certain context, inter-rater agreement is a prerequisite for the scale to be actually implemented in routine use. Cohen's kappa coeffcient is a landmark in the developments of rater agreement theory. This coeffcient, which operated a radical change in previously proposed indexes, opened a new field of research in the domain. In the first part of this work, after a brief review of agreement on a quantitative scale, the kappa-like family of agreement indexes is described in various instances: two raters, several raters, an isolated rater and a group of raters and two groups of raters. To quantify the agreement between two individual raters, Cohen's kappa coefficient (Cohen, 1960) and the intraclass kappa coefficient (Kraemer, 1979) are widely used for binary and nominal scales, while the weighted kappa coefficient (Cohen, 1968) is recommended for ordinal scales. An interpretation of the quadratic (Schuster, 2004) and the linear (Vanbelle and Albert, 2009c) weighting schemes is given. Cohen's kappa (Fleiss, 1971) and intraclass kappa (Landis and Koch, 1977c) coefficients were extended to the case where agreement is searched between several raters. Next, the kappa-like family of agreement coefficients is extended to the case of an isolated rater and a group of raters (Vanbelle and Albert, 2009a) and to the case of two groups of raters (Vanbelle and Albert, 2009b). These agreement coefficients are derived on a population-based model and reduce to the well-known Cohen's kappa coefficient in the case of two single raters. The proposed agreement indexes are also compared to existing methods, the consensus method and Schouten's agreement index (Schouten, 1982). The superiority of the new approach over the latter is shown. In the second part of the work, methods for hypothesis testing and data modeling are discussed. Firstly, the method proposed by Fleiss (1981) for comparing several independent agreement indexes is presented. Then, a bootstrap method initially developed by McKenzie et al. (1996) to compare two dependent agreement indexes, is extended to several dependent agreement indexes (Vanbelle and Albert, 2008). All these methods equally apply to the kappa coefficients introduced in the first part of the work. Next, regression methods for testing the effect of continuous and categorical covariates on the agreement between two or several raters are reviewed. This includes the weighted least-squares method allowing only for categorical covariates (Barnhart and Williamson, 2002) and a regression method based on two sets of generalized estimating equations. The latter method was developed for the intraclass kappa coefficient (Klar et al., 2000), Cohen's kappa coefficient (Williamson et al., 2000) and the weighted kappa coefficient (Gonin et al., 2000). Finally, a heuristic method, restricted to the case of independent observations, is presented (Lipsitz et al., 2001, 2003) which turns out to be equivalent to the generalized estimating equations approach. These regression methods are compared to the bootstrap method extended by Vanbelle and Albert (2008) but they were not generalized to agreement between a single rater and a group of raters nor between two groups of raters. / Sujet d'intenses recherches scientifiques, l'accord entre observateurs sur une échelle catégorisée est aussi un problème fréquemment rencontré en pratique. Lorsqu'une nouvelle échelle de mesure est développée pour évaluer des sujets ou des objets, l'étude de l'accord inter-observateurs est un prérequis indispensable pour son utilisation en routine. Le coefficient kappa de Cohen constitue un tournant dans les développements de la théorie sur l'accord entre observateurs. Ce coefficient, radicalement différent de ceux proposés auparavant, a ouvert de nouvelles voies de recherche dans le domaine. Dans la première partie de ce travail, après une brève revue des mesures d'accord sur une échelle quantitative, la famille des coefficients kappa est décrite dans différentes situations: deux observateurs, plusieurs observateurs, un observateur isolé et un groupe d'observateurs, et enfin deux groupes d'observateurs. Pour quantifier l'accord entre deux observateurs, le coefficient kappa de Cohen (Cohen, 1960) et le coefficient kappa intraclasse (Kraemer, 1979) sont largement utilisés pour les échelles binaires et nominales. Par contre, le coefficient kappa pondéré (Cohen, 1968) est recommandé pour les échelles ordinales. Schuster (2004) a donné une interprétation des poids quadratiques tandis que Vanbelle and Albert (2009c) se sont interessés aux poids linéaires. Les coefficients d'accord correspondant au coefficient kappa de Cohen (Fleiss, 1971) et au coefficient kappa intraclasse (Landis and Koch, 1977c) sont aussi donnés dans le cas de plusieurs observateurs. La famille des coefficients kappa est ensuite étendue au cas d'un observateur isolé et d'un groupe d'observateurs (Vanbelle and Albert, 2009a) et au cas de deux groupes d'observateurs (Vanbelle and Albert, 2009b). Les coefficients d'accord sont élaborés à partir d'un modèle de population et se réduisent au coefficient kappa de Cohen dans le cas de deux observateurs isolés. Les coefficients d'accord proposés sont aussi comparés aux méthodes existantes, la méthode du consensus et le coefficient d'accord de Schouten (Schouten, 1982). La supériorité de la nouvelle approche sur ces dernières est démontrée. Des méthodes qui permettent de tester des hypothèses et modéliser des coefficients d'accord sont abordées dans la seconde partie du travail. Une méthode permettant la comparaison de plusieurs coefficients d'accord indépendants (Fleiss, 1981) est d'abord présentée. Puis, une méthode basée sur le bootstrap, initialement développée par McKenzie et al. (1996) pour comparer deux coefficients d'accord dépendants, est étendue au cas de plusieurs coefficients dépendants par Vanbelle and Albert (2008). Pour finir, des méthodes de régression permettant de tester l'effet de covariables continues et catégorisées sur l'accord entre deux observateurs sont exposées. Ceci comprend la méthode des moindres carrés pondérés (Barnhart and Williamson, 2002), admettant seulement des covariables catégorisées, et une méthode de régression basée sur deux équations d'estimation généralisées. Cette dernière méthode a été développée dans le cas du coefficient kappa intraclasse (Klar et al., 2000), du coefficient kappa de Cohen (Williamson et al., 2000) et du coefficient kappa pondéré (Gonin et al., 2000). Enfin, une méthode heuristique, limitée au cas d'observations indépendantes, est présentée (Lipsitz et al., 2001, 2003). Elle est équivalente à l'approche par les équations d'estimation généralisées. Ces méthodes de régression sont comparées à l'approche par le bootstrap (Vanbelle and Albert, 2008) mais elles n'ont pas encore été généralisées au cas d'un observateur isolé et d'un groupe d'observateurs ni au cas de deux groupes d'observateurs. / Het bepalen van overeenstemming tussen beoordelaars voor categorische gegevens is niet alleen een kwestie van wetenschappelijk onderzoek, maar ook een probleem dat men veelvuldig in de praktijk tegenkomt. Telkens wanneer een nieuwe schaal wordt ontwikkeld om individuele personen of zaken te evalueren in een bepaalde context, is interbeoordelaarsovereenstemming een noodzakelijke voorwaarde vooraleer de schaal in de praktijk kan worden toegepast. Cohen's kappa coëfficiënt is een mijlpaal in de ontwikkeling van de theorie van interbeoordelaarsovereenstemming. Deze coëfficiënt, die een radicale verandering met de voorgaande indices inhield, opende een nieuw onderzoeksspoor in het domein. In het eerste deel van dit werk wordt, na een kort overzicht van overeenstemming voor kwantitatieve gegevens, de kappa-achtige familie van overeenstemmingsindices beschreven in verschillende gevallen: twee beoordelaars, verschillende beoordelaars, één geïsoleerde beoordelaar en een groep van beoordelaars, en twee groepen van beoordelaars. Om de overeenstemming tussen twee individuele beoordelaars te kwantificeren worden Cohen's kappa coëfficiënt (Cohen, 1960) en de intraklasse kappa coëfficiënt (Kraemer, 1979) veelvuldig gebruikt voor binaire en nominale gegevens, terwijl de gewogen Kappa coëfficiënt (Cohen, 1968) aangewezen is voor ordinale gegevens. Een interpretatie van de kwadratische (Schuster, 2004) en lineaire (Vanbelle and Albert, 2009c) weegschema's wordt gegeven. Overeenstemmingsindices die overeenkomen met Cohen's Kappa (Fleiss, 1971) en intraklasse-kappa (Landis and Koch, 1977c) coëfficiënten kunnen worden gebruikt om de overeenstemming tussen verschillende beoordelaars te beschrijven. Daarna wordt de familie van kappa-achtige overeenstemmingscoëfficiënten uitgebreid tot het geval van één geïsoleerde beoordelaar en een groep van beoordelaars (Vanbelle and Albert, 2009a) en tot het geval van twee groepen van beoordelaars (Vanbelle and Albert, 2009b). Deze overeenstemmingscoëfficiënten zijn afgeleid van een populatie-gebaseerd model en kunnen worden herleid tot de welbekende Cohen's coëfficiënt in het geval van twee individuele beoordelaars. De voorgestelde overeenstemmingsindices worden ook vergeleken met bestaande methodes, de consensusmethode en Schoutens overeenstemmingsindex (Schouten, 1982). De superioriteit van de nieuwe benadering over de laatstgenoemde wordt aangetoond. In het tweede deel van het werk worden hypothesetesten en gegevensmodellering besproken. Vooreerst wordt de methode voorgesteld door Fleiss (1981) om verschillende onafhankelijke overeenstemmingsindices te vergelijken, voorgesteld. Daarna wordt een bootstrapmethode, oorspronkelijk ontwikkeld door McKenzie et al. (1996) om twee onafhankelijke overeenstemmingsindices te vergelijken, uitgebreid tot verschillende afhankelijke overeenstemmingsindices (Vanbelle and Albert, 2008). Al deze methoden kunnen ook worden toegepast op de overeenstemmingsindices die in het eerste deel van het werk zijn beschreven. Ten slotte wordt een overzicht gegeven van regressiemethodes om het eect van continue en categorische covariabelen op de overeenstemming tussen twee of meer beoordelaars te testen. Dit omvat de gewogen kleinste kwadraten methode, die alleen werkt met categorische covariabelen (Barnhart and Williamson, 2002) en een regressiemethode gebaseerd op twee sets van gegeneraliseerde schattingsvergelijkingen. De laatste methode was ontwikkeld voor de intraklasse kappa coëfficiënt (Klar et al., 2000), Cohen's kappa coëfficiënt (Williamson et al., 2000) en de gewogen kappa coëfficiënt (Gonin et al., 2000). Ten slotte wordt een heuristische methode voorgesteld die alleen van toepassing is op het geval van onafhankelijk waarnemingen (Lipsitz et al., 2001, 2003). Ze blijkt equivalent te zijn met de benadering van de gegeneraliseerde schattingsvergelijkingen. Deze regressiemethoden worden vergeleken met de bootstrapmethode uitgebreid door Vanbelle and Albert (2008) maar werden niet veralgemeend tot de overeenstemming tussen een enkele beoordelaar en een groep van beoordelaars, en ook niet tussen twee groepen van beoordelaars.