Introdução: A Teoria de Resposta ao Item constitui-se em um novo grupo de modelos psicométricos de construção, validação e avaliação de instrumentos de aferição em desfechos em saúde. Dentre tais modelos, o Modelo de Rasch se destaca como uma possibilidade de testar a Teoria de Mensuração Conjunta e, portanto, desenvolver escalas de medida com estrutura intervalar. De fato, as robustas estratégias estatísticas utilizadas recentemente demandam que as variáveis apresentem propriedades intervalares para que resultados fidedignos sejam obtidos. Na área da saúde mental, o Modelo de Rasch agrega a possibilidade de que os construtos sejam avaliados quanto à dimensionalidade. Os instrumentos podem ser explorados quanto à invariância dos itens, calibragem, adequação das escalas de resposta e adequação dos itens ao modelo teórico subjacente.Objetivos: Explorar a aplicação do Modelo de Rasch no desenvolvimento de instrumentos de qualidade de vida e atitudes frente ao envelhecimento. Utilizar o Modelo de Rasch na validação cultural de um instrumento de depressão geriátrica, assim como testar a adequação de uma escala de resposta Likert de acordo com o nível educacional, através da aplicação do Modelo de Rasch. Método: Dados internacionais de qualidade de vida, atitudes frente ao envelhecimento e depressão foram utilizados nestes estudos. Os dados são provenientes do Projeto WHOQOL-OLD e AAQ, coordenado pela Organização Mundial de Saúde em 20 países. Uma combinação de Teoria Clássica emPsicometria e Modelo de Rasch foi utilizada para a análise dos dados. O Modelo de Rasch foi implementado através do software RUMM2020. Resultados: A utilização do Modelo de Rasch possibilitou um refinamento dos instrumentos testados, gerando instrumentos com novos formatos mais adequados. No instrumento WHOQOL-OLD, em sua versão em Português, dois domínios dos seis apresentaram interação item-total insuficiente. O remodelamento da escala de resposta e a exclusão de itens de performance inadequada acarretaram melhora da escala. O instrumento Atitudes Frente ao Envelhecimento também necessitou de exclusão de itens e agrupamento de categorias de resposta, em sua versão em Português, para que seu desempenho psicométrico fosse adequado. Em relação ao nível de escolaridade, a análise dos dados gerados pelo instrumento WHOQOL-BREF em uma amostra internacional de idosos por Modelo de Rasch evidenciou que uma escala Likert de cinco pontos não é adequada para sujeitos analfabetos, em oposição aos achados com sujeitos universitários. A escala de depressão geriátrica GDS também foi analisada em uma amostra brasileira. O formato original de 15 itens se mostrou inadequado, e a exclusão de itens é fundamental para que o desempenho deste instrumento seja satisfatório. Por fim, o impacto de sintomas depressivos clínicos e subclínicos na qualidade de vida de idosos foi avaliado. Mesmo níveis subclínicos de depressão mostraram-se significativamente associados a decréscimo de qualidade de vida e atitudes frente ao envelhecimento em uma amostra de 5566 idosos. Conclusão: A aplicação do Modelo de Rasch no desenvolvimento e validação de instrumentos na área da saúde mental mostrou-se marcadamente relevante. Tal modelo proporcionou que as escalas possam ser examinadas em detalhes. A avaliação dos itens de modo individual permite que a sua adequação seja determinada e que o instrumento seja refinado de acordo com as modificações sugeridas pelas análises de Rasch. Por fim, o Modelo de Rasch permite o teste de invariância dos itens, que assume particular importância na utilização transcultural de instrumentos na área da saúde mental. / Background: Item Response Theory represents a novel group of psychometric models for constructing, validating and evaluating health outcome instruments. Among these models, the Rasch Model is able to test the Theory of Conjoint Measurement and, so, develop intervalar scales. In fact, the recently applied robust statistical strategies demand that the variables have an intervalar structure, so that reliable results are obtained. In the mental health field, the Rasch Model assures that the constructs may be tested for dimensionality. The instruments may be explored regarding item invariance, targetting, response scales adequacy and item fit to the underlying theoretical model. Objectives: To explore the role of the Rasch Model for the development of quality of life and attitudes to aging instruments. In addition, to apply the Rasch Model in the cultural validation of a geriatric depression scale, as well as test the suitability of a 5-point Likert response scale according to the educational level. Method: International data on quality of life, attitudes to aging and depression were analyzed in these studies. Data were drawn from the WHOQOL-OLD and AAQ Project, coordinated by the World Health Organization in 20 countries. A combination of Classical Test Theory and Rasch Model was used to data analysis. The Rasch Model was implemented by RUMM2020 software. Results: The application of the Rasch Model determined a refinement of the original instruments, deriving more adequate versions. The Portuguese version of the WHOQOL-OLD instrument presented insufficient item-total interaction in two domains out of six. Rescoring the response scale and deleting items led to 14 improvement of the instrument. The Attitudes to Aging Questionnaire (Portuguese version) has also demanded rescoring and item deletion in order to present adequate psychometric performance. Regarding the educational level, the Rasch analysis of data obtained using the WHOQOL-BREF in an international sample of older adults indicated that a 5-point Likert scale is not suitable for illiterate subjects. In opositte, this Likert scale is suitable for graduate older adults. The Geriatric Depression Scale was explored in a Brazilian sample. Its original 15-item format has proven to be inadequate, and item exclusion is crucial to obtain a satisfactory performance. Finally, the impact of clinical and subclinical depressive symptoms in quality of life was assessed. Even subthreshold symptomatology is significantly associated to impairments in quality of life and attitudes to aging in a sample of 5566 older adults. Conclusion: The application of the Rasch Model to the development and validation of mental health instruments has proven to be highly relevant. This model brings the possibilty of examining scales in depth. The individual assessment of each item makes it possible to determine item fit and, thus, to refine the instruments according to the alterations claimed by the Rasch analysis. Finally, the Rasch Model implements the item invariance test, which is particularly important for utilizing instruments in transcultural investigations

Objetivo: Este estudo avalia a estrutura do IDATE (Inventário de Ansiedade Traço-Estado) utilizando a análise psicométrica de Rasch, propondo-se ao refinamento e redução do instrumento. Métodos: Consiste em estudo transversal em amostra de 900 pacientes em perioperatório de cirurgias eletivas, com idade variando de 18 a 60 anos e ASA I-III. Informações demográficas foram coletadas empregando-se um questionário estruturado. O instrumento de mensuração IDATE foi aplicado na tarde que antecedia a cirurgia, antes da sedação pré-operatória. Resultados: As escalas de estado e traço de ansiedade foram analisadas separadamente pelo modelo de Rasch. A análise demonstrou invariância no nível de ansiedade traço e estado no formato original de ambas as escalas, resultando em instabilidade no desempenho dos itens. Subsequentemente, a escala refinada foi retestada em duas amostras randomizadas de 300 sujeitos cada, sendo confirmados os resultados. O desempenho foi adequado, independentemente do gênero. Na análise, alguns itens da escala estado foram eliminados (itens 3,4,9,10,12,15 e 20) devido à inadequação ao modelo estatístico. Os itens restantes mostraram unidimensionalidade, independência local e adequado índice de consistência interna. Na escala original de traço, identificaram-se muitas falhas. Primeiro, a escala de resposta tipo Likert 4 pontos provou ser inadequada, e desordens threshold foram encontradas nos 20-itens. A escala original de traço mostrou insuficiente interação e muitos itens individuais mal ajustados. Seguindo a análise e retestando a segunda amostra randomizada, alguns itens foram excluídos (itens 4, 6, 11, 14, 15 e 19). A versão refinada obteve independência local, unidimensionalidade e adequados modelos estatísticos para a fase de sedação pré-operatória. Discussão: Os resultados indicam que a aplicação do modelo de Rasch conduz ao refinamento das escalas clássicas de IDATE estado e traço, sugerindo também que as versões sucintas apresentam desempenho psicométrico mais adequado e estão livres de desordens no limiar de resposta (threshold) e DIF (funcionamento diferencial de itens). / Objetive: This study evaluates the STAI structure using a Rasch psychometric approach and it proposes a refined and shorter STAI version. Methods: A cross-sectional study was performed with 900 inpatients scheduled for elective surgery. Age varied from 18 to 60 years (ASA physical status I-III). Demographic information was collected using a structured questionnaire. The measuring instrument (the State-Trait Anxiety Inventory) was applied to all patients in the afternoon before the surgery, before of the patients Results: Rasch analysis of the state and trait anxiety scales was performed separately. This analysis demonstrated that the original format of state and trait scales fails to show invariance across the trait-state anxiety level, which results in the unstable performance of items. The refined scale was retested in two subsequent random samples of 300 subjects each, and the results were confirmed. The performance was adequate regardless of gender. In the analysis, some items of the state scale (items 3,4,9,10,12,15 and 20) were deleted due to poor fit statistics. The remaining 13 items showed unidimensionality, local independence, and adequate index of internal consistency. Also, the original trait scale displayed several weaknesses. First, the 4 point Likert response scale proved to be inadequate, and threshold disorders were found in all twenty items. Also, the original trait scale showed insufficient item-trait interaction and several individual item misfits. Following the rescoring process, and retesting in a second random sample, items were excluded (namely items 4, 6, 11, 14, 15 and 19). The refined version showed local independence, unidimensionality and adequate fit statistics.receive preoperative sedatives. Discussion: The results indicate that the application of the Rasch Model led to the refinement of the classic state and trait STAI scales. In addition, suggest that these shorter versions present more adequate psychometric performance and are free of threshold disorders and differential item functioning problems.

Introdução: A Teoria de Resposta ao Item constitui-se em um novo grupo de modelos psicométricos de construção, validação e avaliação de instrumentos de aferição em desfechos em saúde. Dentre tais modelos, o Modelo de Rasch se destaca como uma possibilidade de testar a Teoria de Mensuração Conjunta e, portanto, desenvolver escalas de medida com estrutura intervalar. De fato, as robustas estratégias estatísticas utilizadas recentemente demandam que as variáveis apresentem propriedades intervalares para que resultados fidedignos sejam obtidos. Na área da saúde mental, o Modelo de Rasch agrega a possibilidade de que os construtos sejam avaliados quanto à dimensionalidade. Os instrumentos podem ser explorados quanto à invariância dos itens, calibragem, adequação das escalas de resposta e adequação dos itens ao modelo teórico subjacente.Objetivos: Explorar a aplicação do Modelo de Rasch no desenvolvimento de instrumentos de qualidade de vida e atitudes frente ao envelhecimento. Utilizar o Modelo de Rasch na validação cultural de um instrumento de depressão geriátrica, assim como testar a adequação de uma escala de resposta Likert de acordo com o nível educacional, através da aplicação do Modelo de Rasch. Método: Dados internacionais de qualidade de vida, atitudes frente ao envelhecimento e depressão foram utilizados nestes estudos. Os dados são provenientes do Projeto WHOQOL-OLD e AAQ, coordenado pela Organização Mundial de Saúde em 20 países. Uma combinação de Teoria Clássica emPsicometria e Modelo de Rasch foi utilizada para a análise dos dados. O Modelo de Rasch foi implementado através do software RUMM2020. Resultados: A utilização do Modelo de Rasch possibilitou um refinamento dos instrumentos testados, gerando instrumentos com novos formatos mais adequados. No instrumento WHOQOL-OLD, em sua versão em Português, dois domínios dos seis apresentaram interação item-total insuficiente. O remodelamento da escala de resposta e a exclusão de itens de performance inadequada acarretaram melhora da escala. O instrumento Atitudes Frente ao Envelhecimento também necessitou de exclusão de itens e agrupamento de categorias de resposta, em sua versão em Português, para que seu desempenho psicométrico fosse adequado. Em relação ao nível de escolaridade, a análise dos dados gerados pelo instrumento WHOQOL-BREF em uma amostra internacional de idosos por Modelo de Rasch evidenciou que uma escala Likert de cinco pontos não é adequada para sujeitos analfabetos, em oposição aos achados com sujeitos universitários. A escala de depressão geriátrica GDS também foi analisada em uma amostra brasileira. O formato original de 15 itens se mostrou inadequado, e a exclusão de itens é fundamental para que o desempenho deste instrumento seja satisfatório. Por fim, o impacto de sintomas depressivos clínicos e subclínicos na qualidade de vida de idosos foi avaliado. Mesmo níveis subclínicos de depressão mostraram-se significativamente associados a decréscimo de qualidade de vida e atitudes frente ao envelhecimento em uma amostra de 5566 idosos. Conclusão: A aplicação do Modelo de Rasch no desenvolvimento e validação de instrumentos na área da saúde mental mostrou-se marcadamente relevante. Tal modelo proporcionou que as escalas possam ser examinadas em detalhes. A avaliação dos itens de modo individual permite que a sua adequação seja determinada e que o instrumento seja refinado de acordo com as modificações sugeridas pelas análises de Rasch. Por fim, o Modelo de Rasch permite o teste de invariância dos itens, que assume particular importância na utilização transcultural de instrumentos na área da saúde mental. / Background: Item Response Theory represents a novel group of psychometric models for constructing, validating and evaluating health outcome instruments. Among these models, the Rasch Model is able to test the Theory of Conjoint Measurement and, so, develop intervalar scales. In fact, the recently applied robust statistical strategies demand that the variables have an intervalar structure, so that reliable results are obtained. In the mental health field, the Rasch Model assures that the constructs may be tested for dimensionality. The instruments may be explored regarding item invariance, targetting, response scales adequacy and item fit to the underlying theoretical model. Objectives: To explore the role of the Rasch Model for the development of quality of life and attitudes to aging instruments. In addition, to apply the Rasch Model in the cultural validation of a geriatric depression scale, as well as test the suitability of a 5-point Likert response scale according to the educational level. Method: International data on quality of life, attitudes to aging and depression were analyzed in these studies. Data were drawn from the WHOQOL-OLD and AAQ Project, coordinated by the World Health Organization in 20 countries. A combination of Classical Test Theory and Rasch Model was used to data analysis. The Rasch Model was implemented by RUMM2020 software. Results: The application of the Rasch Model determined a refinement of the original instruments, deriving more adequate versions. The Portuguese version of the WHOQOL-OLD instrument presented insufficient item-total interaction in two domains out of six. Rescoring the response scale and deleting items led to 14 improvement of the instrument. The Attitudes to Aging Questionnaire (Portuguese version) has also demanded rescoring and item deletion in order to present adequate psychometric performance. Regarding the educational level, the Rasch analysis of data obtained using the WHOQOL-BREF in an international sample of older adults indicated that a 5-point Likert scale is not suitable for illiterate subjects. In opositte, this Likert scale is suitable for graduate older adults. The Geriatric Depression Scale was explored in a Brazilian sample. Its original 15-item format has proven to be inadequate, and item exclusion is crucial to obtain a satisfactory performance. Finally, the impact of clinical and subclinical depressive symptoms in quality of life was assessed. Even subthreshold symptomatology is significantly associated to impairments in quality of life and attitudes to aging in a sample of 5566 older adults. Conclusion: The application of the Rasch Model to the development and validation of mental health instruments has proven to be highly relevant. This model brings the possibilty of examining scales in depth. The individual assessment of each item makes it possible to determine item fit and, thus, to refine the instruments according to the alterations claimed by the Rasch analysis. Finally, the Rasch Model implements the item invariance test, which is particularly important for utilizing instruments in transcultural investigations

Objetivo: Este estudo avalia a estrutura do IDATE (Inventário de Ansiedade Traço-Estado) utilizando a análise psicométrica de Rasch, propondo-se ao refinamento e redução do instrumento. Métodos: Consiste em estudo transversal em amostra de 900 pacientes em perioperatório de cirurgias eletivas, com idade variando de 18 a 60 anos e ASA I-III. Informações demográficas foram coletadas empregando-se um questionário estruturado. O instrumento de mensuração IDATE foi aplicado na tarde que antecedia a cirurgia, antes da sedação pré-operatória. Resultados: As escalas de estado e traço de ansiedade foram analisadas separadamente pelo modelo de Rasch. A análise demonstrou invariância no nível de ansiedade traço e estado no formato original de ambas as escalas, resultando em instabilidade no desempenho dos itens. Subsequentemente, a escala refinada foi retestada em duas amostras randomizadas de 300 sujeitos cada, sendo confirmados os resultados. O desempenho foi adequado, independentemente do gênero. Na análise, alguns itens da escala estado foram eliminados (itens 3,4,9,10,12,15 e 20) devido à inadequação ao modelo estatístico. Os itens restantes mostraram unidimensionalidade, independência local e adequado índice de consistência interna. Na escala original de traço, identificaram-se muitas falhas. Primeiro, a escala de resposta tipo Likert 4 pontos provou ser inadequada, e desordens threshold foram encontradas nos 20-itens. A escala original de traço mostrou insuficiente interação e muitos itens individuais mal ajustados. Seguindo a análise e retestando a segunda amostra randomizada, alguns itens foram excluídos (itens 4, 6, 11, 14, 15 e 19). A versão refinada obteve independência local, unidimensionalidade e adequados modelos estatísticos para a fase de sedação pré-operatória. Discussão: Os resultados indicam que a aplicação do modelo de Rasch conduz ao refinamento das escalas clássicas de IDATE estado e traço, sugerindo também que as versões sucintas apresentam desempenho psicométrico mais adequado e estão livres de desordens no limiar de resposta (threshold) e DIF (funcionamento diferencial de itens). / Objetive: This study evaluates the STAI structure using a Rasch psychometric approach and it proposes a refined and shorter STAI version. Methods: A cross-sectional study was performed with 900 inpatients scheduled for elective surgery. Age varied from 18 to 60 years (ASA physical status I-III). Demographic information was collected using a structured questionnaire. The measuring instrument (the State-Trait Anxiety Inventory) was applied to all patients in the afternoon before the surgery, before of the patients Results: Rasch analysis of the state and trait anxiety scales was performed separately. This analysis demonstrated that the original format of state and trait scales fails to show invariance across the trait-state anxiety level, which results in the unstable performance of items. The refined scale was retested in two subsequent random samples of 300 subjects each, and the results were confirmed. The performance was adequate regardless of gender. In the analysis, some items of the state scale (items 3,4,9,10,12,15 and 20) were deleted due to poor fit statistics. The remaining 13 items showed unidimensionality, local independence, and adequate index of internal consistency. Also, the original trait scale displayed several weaknesses. First, the 4 point Likert response scale proved to be inadequate, and threshold disorders were found in all twenty items. Also, the original trait scale showed insufficient item-trait interaction and several individual item misfits. Following the rescoring process, and retesting in a second random sample, items were excluded (namely items 4, 6, 11, 14, 15 and 19). The refined version showed local independence, unidimensionality and adequate fit statistics.receive preoperative sedatives. Discussion: The results indicate that the application of the Rasch Model led to the refinement of the classic state and trait STAI scales. In addition, suggest that these shorter versions present more adequate psychometric performance and are free of threshold disorders and differential item functioning problems.

Doctor Educationis / One of the educational ideas used in mathematics education to improve mathematics achievement in schools is examination-driven teaching. Its effects have sparked intense debates in different didactic circles regarding its usefulness as a teaching technique. More specifically, researchers have consistently debated whether examination-driven teaching is a good or a bad approach that can be used beneficially for learners’ achievement. In South Africa, the urgent need to uplift the low performances of high school learners in Mathematics has led to a development of a project which is a partnership with the Western Cape Education Department (WCED) and the University of the Western Cape (UWC). This project used examination-driven teaching in the context of a continuous professional development to improve learners’ mathematics scores. Five secondary schools that were opportunistically sampled in the province of the Western Cape were exposed to examination-driven teaching. For evaluation, the project yearly developed and implemented high-stakes Grade 10 end-ofyear mathematics examinations, and the data subjected to analysis were learners’ mathematics scores for 2012, 2013 and 2014. A quantitative approach employing Rasch procedures and some statistical procedures were used to analyse the data. The study intended to answer the following questions: 1) Do learners’ achievement scores in a high-stakes Grade 10 mathematics examinations improve over time when an examination-driven teaching approach is being used as intervention? 2) Does socio-economic status of schools influence mathematics performances in the case of using examination-driven teaching ? 3) Are there differences over time in the achievement of learners in the two different papers comprising the examination? / Okitowamba, O. (2015) Tracking learners’ performances in high-stakes Grade 10 mathematics examinations. PhD thesis. University of the Western Cape. Bellville. http://hdl.handle.net/11394/5655.

Les maladies neurodégénératives, telles que la maladie d'Alzheimer (AD) et Charcot Marie Tooth (CMT), sont des maladies complexes. Leurs mécanismes pathologiques ne sont toujours pas bien compris et les progrès dans la recherche et le développement de nouvelles thérapies potentielles modifiant la maladie sont lents. Les données catégorielles, comme les échelles de notation et les données sur les études d'association génomique (GWAS), sont largement utilisées dans les maladies neurodégénératives dans le diagnostic, la prédiction et le suivi de la progression. Il est important de comprendre et d'interpréter ces données correctement si nous voulons améliorer la recherche sur les maladies neurodégénératives. Le but de cette thèse est d'utiliser la théorie psychométrique moderne: théorie de la réponse d’item pour analyser ces données catégoriques afin de mieux comprendre les maladies neurodégénératives et de faciliter la recherche de médicaments correspondante. Tout d'abord, nous avons appliqué l'analyse de Rasch afin d'évaluer la validité du score de neuropathie Charcot-Marie-Tooth (CMTNS), un critère important d'évaluation principal pour les essais cliniques de la maladie de CMT. Nous avons ensuite adapté le modèle Rasch à l'analyse des associations génétiques pour identifier les gènes associés à la maladie d'Alzheimer. Cette méthode résume les génotypes catégoriques de plusieurs marqueurs génétiques tels que les polymorphisme nucléotidique (SNPs) en un seul score génétique. Enfin, nous avons calculé l'information mutuelle basée sur la théorie de réponse d’item pour sélectionner les items sensibles dans ADAS-cog, une mesure de fonctionnement cognitif la plus utilisées dans les études de la maladie d'Alzheimer, afin de mieux évaluer le progrès de la maladie. / Neurodegenerative diseases, such as Alzheimer’s disease (AD) and Charcot Marie Tooth (CMT), are complex diseases. Their pathological mechanisms are still not well understood, and the progress in the research and development of new potential disease-modifying therapies is slow. Categorical data like rating scales and Genome-Wide Association Studies (GWAS) data are widely utilized in the neurodegenerative diseases in the diagnosis, prediction and progression monitor. It is important to understand and interpret these data correctly if we want to improve the disease research. The purpose of this thesis is to use the modern psychometric Item Response Theory to analyze these categorical data for better understanding the neurodegenerative diseases and facilitating the corresponding drug research. First, we applied the Rasch analysis in order to assess the validity of the Charcot-Marie-Tooth Neuropathy Score (CMTNS), a main endpoint for the CMT disease clinical trials. We then adapted the Rasch model to the analysis of genetic associations and used to identify genes associated with Alzheimer’s disease by summarizing the categorical genotypes of several genetic markers such as Single Nucleotide Polymorphisms (SNPs) into one genetic score. Finally, to select sensitive items in the most used psychometrical tests for Alzheimer’s disease, we calculated the mutual information based on the item response model to evaluate the sensitivity of each item on the ADAS-cog scale.

The purpose of this study was to determine if using a multistage approach for the empirical selection of anchor items would lead to more accurate DIF detection rates than the anchor selection methods proposed by Kopf, Zeileis, & Strobl (2015b). A simulation study was conducted in which the sample size, percentage of DIF, and balance of DIF were manipulated. The outcomes of interest were true positive rates, false positive rates, familywise false positive rates, anchor contamination rates, and familywise anchor contamination rates. Results showed the proposed multistage methods produced lower anchor contamination rates than the non-multistage methods under some conditions, but there were generally no meaningful differences in true positive and false positive rates.

In variety testing as well as in psychological assessment, the situation occurs that in a two-way ANOVA-type model with only one replication per cell, analysis is done under the assumption of no interaction between the two factors. Tests for this situation are known only for fixed factors and normally distributed outcomes. In the following we will present five additivity tests and apply them to fixed and mixed models and to quantitative as well as to Bernoulli distributed data. We consider their performance via simulation studies with respect to the type-I-risk and power. Furthermore, two new approaches will be presented, one being a modification of Tukey's test and the other being a new experimental design to test for interactions.

Differential item functioning (DIF) is a psychometric issue routinely considered in educational and psychological assessment. However, it has not been studied in the context of a recently developed componential statistical model, the model with internal restrictions on item difficulty (MIRID; Butter, De Boeck, & Verhelst, 1998). Because the MIRID requires test questions measuring either single or multiple cognitive processes, it creates a complex environment for which traditional DIF methods may be inappropriate. This dissertation sought to extend the MIRID framework to detect DIF at the item-group level and the individual-item level. Such a model-based approach can increase the interpretability of DIF statistics by focusing on item characteristics as potential sources of DIF. In particular, group-level DIF may reveal comparative group strengths in certain secondary constructs. A simulation study was conducted to examine under different conditions parameter recovery, Type I error rates, and power of the proposed approach. Factors manipulated included sample size, magnitude of DIF, distributional characteristics of the groups, and the MIRID DIF models corresponding to discrete sources of differential functioning. The impact of studying DIF using wrong models was investigated. The results from the recovery study of the MIRID DIF model indicate that the four delta (i.e., non-zero value DIF) parameters were underestimated whereas item locations of the four associated items were overestimated. Bias and RMSE were significantly greater when delta was larger; larger sample size reduced RMSE substantially while the effects from the impact factor were neither strong nor consistent. Hypothesiswise and adjusted experimentwise Type I error rates were controlled in smaller delta conditions but not in larger delta conditions as estimates of zero-value DIF parameters were significantly different from zero. Detection power of the DIF model was weak. Estimates of the delta parameters of the three group-level DIF models, the MIRID differential functioning in components (DFFc), the MIRID differential functioning in item families (DFFm), and the MIRID differential functioning in component weights (DFW), were acceptable in general. They had good hypothesiswise and adjusted experimentwise Type I error control across all conditions and overall achieved excellent detection power. When fitting the proposed models to mismatched data, the false detection rates were mostly beyond the Bradley criterion because the zero-value DIF parameters in the mismatched model were not estimated adequately, especially in larger delta conditions. Recovery of item locations and component weights was also not adequate in larger delta conditions. Estimation of these parameters was more or less affected adversely by the DIF effect simulated in the mismatched data. To study DIF in MIRID data using the model-based approach, therefore, more research is necessary to determine the appropriate procedure or model to implement, especially for item-level differential functioning.

This thesis is submitted to the University of Manchester for the degree of Doctor of Philosophy (PhD). This study developed an experimental small group teaching method in the Realistic Mathematics Education tradition for teaching fractions using models and contexts to year 7 children in Brunei (N=89) whose effectiveness was evaluated using a treatment-control design: the E1 group was given the experimental lessons, the E2 group who was given “normal” lessons taught by the experimenter, and a whole class (E3) group which acted as the control group. The experimental teaching was video recorded and subject to semiotic analysis, aiming to describe the objectifications that realized ‘learning of fractions’ by the groups.The research addresses two research questions:1. How effective was the experimental teaching in helping learners make sense of fractions, with respect to equivalence of fractions and flexibility of unitizing?2. What were the semiotic learning and teaching processes in the experimental group of the RME-like lessons? This study used a mixed method approach with a quasi-experimental design (QED) for the quantitative side, and a semiotic analysis for the qualitative side. Quantitatively, the experimental teachings proved to be relatively effective with an effect size of 0.6 from the pre- to the delayed post-teaching test, compared to the E2 and the control groups.The basic findings pertaining to the semiotic analyses were:a. The mediation of the production of fractions in terms of length, from the production of fractions in terms of the number of parts which led to equivalence of fractions;b. The use of language and gesture help to objectify the equivalence of fractions and the flexibility of unitizing–in some case it involved gesturing to the self;c. The role of the Hour-Foot clock (HFC) as a model in a realistic context; andd. The complexity of the required chains of objectifications reflects the difficulties of the topic.