What statistical methods are essential for multivariate analysis?

Para realiza uma analise multivariada, ou seja quando vc basicamente possui uma matriz de informa??es sem um variável dependente (caso mais normal), técnicas como Análise de correspondência, Análise de componentes principais, Análise fatorial e Análise de cluster.

PCA reduces data dimensionality by identifying a smaller set of uncorrelated variables (principal components) that explain most of the data's variance. For example when analyzing gene expression data from cancer patients, PCA can identify a smaller set of genes that best differentiate between healthy and cancerous tissues. This can lead to the development of more targeted cancer therapies.

Similar to PCA, factor analysis identifies latent variables (factors) that explain the correlations between observed variables. It is useful when the underlying structure of the data is unknown. For example, when analyzing patient survey data on mental health, factor analysis can identify underlying factors such as anxiety and depression from responses to various questions. This information can be used to develop more effective mental health screening tools.

Unlike the previous methods, cluster analysis doesn't rely on predefined groups. It groups observations (patients, genes, etc.) based on similarities in their characteristics. For example, clustering patients with chronic diseases based on their medical history and lifestyle factors can help identify subgroups of patients with similar disease progression and treatment needs, allowing for personalized treatment plans.

Discriminant analysis aims to classify observations into predefined groups based on a set of independent variables. It's useful for tasks like patient diagnosis or predicting disease risk. For example, while analyzing patient data to differentiate between patients with different types of cancer, discriminant analysis can help identify a combination of variables that best distinguishes between different cancer types, aiding in early and accurate diagnosis.

Multiple linear regression (MLR) extends linear regression to analyze the relationship between one dependent variable and multiple independent variables. It helps assess the individual and combined effects of these independent variables on the outcome. For example, when studying the factors influencing hospital readmission rates, MLR can analyze how factors like age, diagnosis, and socioeconomic status contribute to the likelihood of a patient being readmitted to the hospital.

There are many statistical tests which can be used to find the associations between the different variables. It is recommended to test the data in terms of the normality and homogeneity tests of variance initially. Further various parametric and non parametric tests can be performed depending on the data.