Análise de Dados Categóricos

Desde um diagnóstico de doença positivo ou negativo até a escolha de todos os itens que se aplicam a uma pesquisa, os resultados são frequentemente organizados em categorias para que as pessoas possam entendê-los com mais facilidade. No entanto, analisar dados de respostas categóricas requer técnicas especializadas.

O objetivo deste texto é ajudar estudantes e pesquisadores a aprender a analisar adequadamente dados categóricos utilizando amplamente a linguagem R. Usamos R não apenas como método de análise de dados, mas também como ferramenta de aprendizado. Por exemplo, usamos simulação de dados para ajudar os leitores a entender as suposições subjacentes de um procedimento e, em seguida, avaliar o desempenho desse procedimento.

O foco deste livro está na análise de dados, e não na análise matemática. Oferecemos vários exemplos de uma ampla gama de disciplinas - medicina, psicologia, esportes, ecologia e outras - e fornecemos código R extenso e saída à medida que trabalhamos com os exemplos. O uso do cálculo é principalmente de um foco conceitual e não matemático.

Conteúdo

• Capítulo 1- Dados Categóricos: Introdução
• 1.1 Analisando uma resposta binária
• 1.1.1 As distribuições Bernoulli e binomial de probabilidade
• 1.1.2 Inferência para a probabilidade de sucesso
• 1.1.3 Níveis de confiança verdadeiros para intervalos de confiança
• 1.2 Duas variáveis binárias
• 1.2.1 Notação e modelo
• 1.2.2 Intervalos de confiança para a diferença de duas probabilidades
• 1.2.3 Teste para a diferença de duas probabilidades
• 1.2.4 Riscos relativos
• 1.2.5 Odds ratios ou Razões de chaces
• 1.2.6 Dados de pares combinados
• 1.2.7 Tabelas de contingência maiores
• 1.3 Exercícios

• Capítulo 2- Regressão com resposta binária
• 2.1 Modelos de regressão linear
• 2.2 Modelos de regressão logística
• 2.2.1 Estimação de parâmetros
• 2.2.2 Testes de hipóteses para parâmetros de regressão
• 2.2.3 Razões de chances (odds ratios)
• 2.2.4 Probabilidade de sucesso
• 2.2.5 Interações e transformações para variáveis explicativas
• 2.2.6 Variáveis explicativas categóricas
• 2.2.7 Convergência dos estimadores dos parâmetros
• 2.2.8 Simulações Monte carlo
• 2.3 Modelos lineares generalizados
• 2.3.1 Modelos lineares generalizados com ligação paramétrica (em elaboração)
• 2.3.2 Modelos lineares generalizados com ligação não paramétrica (em elaboração)
• 2.3.3 \(R^2\) para modelos lineares generalizados (em elaboração)
• 2.4 Exercícios

• Capítulo 3- Analisando uma resposta multicategórica
• 3.1 Distribuição de probabilidade multinomial
• 3.2 Tabelas de contingência \(I\times J\) e procedimentos de inferência
• 3.2.1 Uma distribuição multinomial
• 3.2.2 \(I\) distribuições multinomiais
• 3.2.3 Teste de independência
• 3.3 Modelos de regressão de resposta nominal
• 3.3.1 Odds ratio
• 3.3.2 Tabelas de contingência
• 3.4 Modelos de regressão de resposta ordinal
• 3.4.1 Odds ratio
• 3.4.2 Tabelas de contingência
• 3.4.3 Modelo de probabilidades não proporcionais
• 3.5 Modelos de regressão adicionais
• 3.6 Exercícios

• Capítulo 4- Analisando uma resposta de contagem
• 4.1 Modelo de Poisson para dados de contagem
• 4.1.1 Distribuição de Poisson
• 4.1.2 Verossimilhança e inferência de Poisson
• 4.2 Modelos de regressão de Poisson para respostas de contagem
• 4.2.1 Modelo para média: Ligação logarítmica
• 4.2.2 Estimação e inferência de parâmetros
• 4.2.3 Variáveis explicativas categóricas
• 4.2.4 Regressão de Poisson para tabelas de contingência: modelos loglineares
• 4.2.5 Grandes modelos loglineares
• 4.2.6 Variáveis categóricas ordinais
• 4.3 Regressão da taxa de Poisson
• 4.4 Inflação de zeros
• 4.5 Exercícios

• Capítulo 5- Seleção e validação do modelo
• 5.1 Seleção de variáveis
• 5.1.1 Visão geral da seleção de variáveis
• 5.1.2 Critérios de comparação de modelos
• 5.1.3 Regressão de todos os subconjuntos
• 5.1.4 Seleção de variável passo a passo
• 5.1.5 Métodos modernos de seleção de variáveis
• 5.1.6 Média do modelo
• 5.2 Ferramentas para avaliar o ajuste do modelo
• 5.2.1 Resíduos
• 5.2.2 Adequação do ajuste
• 5.2.3 Influência
• 5.2.4 Diagnósticos para modelos de resposta multicategoria
• 5.3 Superdispersão
• 5.3.1 Causas e implicações
• 5.3.2 Detecção
• 5.3.3 Soluções
• 5.4 Exemplos
• 5.4.1 Conjunto de dados de regressão logística - placekicking
• 5.4.2 Regressão de Poisson - conjunto de dados de consumo de álcool
• 5.5 Exercícios

• Capítulo 6- Tópicos adicionais (em elaboração)
• 6.1 Respostas binárias e erro de teste
• 6.1.1 Estimando a probabilidade de sucesso
• 6.1.2 Modelos de regressão binária
• 6.1.3 Outros métodos
• 6.2 Inferência exata
• 6.2.1 Teste exato de Fisher para independência
• 6.2.2 Teste de permutação para independência
• 6.2.3 Regressão logística exata
• 6.2.4 Procedimentos adicionais de inferência exata
• 6.3 Análise de dados categóricos em projetos de pesquisa complexos
• 6.3.1 O paradigma de amostragem por inquérito
• 6.3.2 Visão geral das abordagens de análise
• 6.3.3 Contagens ponderadas de células
• 6.3.4 Inferência sobre proporções populacionais
• 6.3.5 Tabelas de contingência e modelos loglineares
• 6.3.6 Regressão logística
• 6.4 Dados “Escolha todos os que se aplicam”
• 6.4.1 Tabela de resposta do item
• 6.4.2 Teste de independência marginal
• 6.4.3 Modelagem de regressão
• 6.5 Modelos mistos e equações de estimação para dados correlacionados
• 6.5.1 Efeitos aleatórios
• 6.5.2 Modelos de efeitos mistos
• 6.5.3 Ajuste do modelo
• 6.5.4 Inferência
• 6.5.5 Modelo marginal usando equações de estimação generalizadas
• 6.6 Métodos bayesianos para dados categóricos
• 6.6.1 Estimando a probabilidade de sucesso
• 6.6.2 Modelos de regressão
• 6.6.3 Ferramentas computacionais alternativas
• 6.7 Exercícios

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