Advanced Statistical Modeling

 Advanced statistical modeling techniques, such as non-linear regression, generalized linear models, and multilevel models, aim to capture more complex relationships between variables than simple linear regression.

The selection of a model depends on several factors. Firstly, the type of data that is being analyzed is essential. For example, if the data has a non-linear relationship between the variables, polynomial regression may be a better option than linear regression.

Secondly, the analysis's objectives are essential. For instance, stepwise regression may be helpful if the aim is to identify the most significant predictors of an outcome variable. It is also essential to consider the strengths and limitations of each model. Ridge regression is functional when multicollinearity exists among the predictor variables. Still, it may need to improve in non-linear solid relationships between the variables.

Trying multiple models and comparing their performance is often beneficial in determining the best model for a given dataset. Techniques like cross-validation can assess the predictive power of each model and select the best one for the specific task.

This section will delve into the details of advanced modeling frequently used in various statistical analyses. We will explore the intricacies, assumptions, and applications of these models in different settings. By the end of this section, you will better understand how these models work and when to use them to draw meaningful insights from data.

This section will delve into the details of advanced modeling frequently used in various statistical analyses. We will explore these models' intricacies, assumptions, and applications in different settings. By the end of this section, you will better understand how these models work and when to use them to draw meaningful insights from data.

Generalized Linear Models

1. Generalized Linear Regression (Gaussian)

2. Logistic Regression (Binary)

3. Probit Regression

4. Ordinal Regression

5. Multinomial Logistic

6. Poisson Regression

      6.1. Standard Poisson Regression (Count Data)

6.2. Poisson Regression Model with Offset (Rate Data)

6.3. Poisson Regression Models for Overdispersed Data

6.4. Zero-Inflated Models

6.5. Hurdle Model

7. Gamma Regression

8. Beta Regression

9. Generalized Additive Model (GAM)

Regularized Generalized Linear Model

1. Regularized Generalized Linear Model (Gaussian)

2. Regularized Logistic Regression

3. Regularized Multinomial Logistic Model

4. Regularized Poisson Regression Model

5. Generalized Additive Model with Lasso

Non-linear Regression

1. Humped Curve

2. Polynomial Models

3. Exponential Models

4. Asymptotic Models

5. S-Shaped Functions or Sigmoid Models

6. Self-starting Function

Multilevel or Mixed-Effect Models

1. Random Intercept Model

2. Random Slope Model

3. Generalized Multilevel Model

• 3.1. Multilevel Logistic Model

• 3.2. Multilevel Multinomial Model

• 3.3. Multilevel Ordinal Model

• 3.4. Multilevel Poisson Model

• 3.5 Generalized Linear Mixed Models Using Adaptive Gaussian Quadrature

• 3.6. Generalized Additive Mixed Models

Panel Regression

1. Linear Models for Panel Data in R

2. Generalized Linear Models for Panel Data

3. Panel Regression Models fit via {panelr} Package

Multivariate Statistics

1. Principal Component Analysis (PCA)

2. Factor Analysis

3. Correspondence Analysis

4. Discriminant Analysis

5. Multivariate Analysis of Variance (MANOVA)

6. Partial Least Squares Regression

 Survival Analysis

1. Nonparametric Survival Analysis

2. Cox Proportional Hazards Model

3. Landmark Analysis

4. Aalen’s Additive Regression Model

5. Risk Regression

6. Joint Modeling of Longitudinal and Survival Data

7. Conditional Survival Analysis

Quantile Regression

Zia Ahmed, Ph.D

 University at Buffalo