Define Explanatory modelling.

Explanatory modeling, also known as causal modeling or explanatory analysis, is a statistical or analytical approach used to understand the relationships between variables and to explain the underlying mechanisms or causes of observed phenomena. Unlike descriptive modeling, which focuses on summarizing and describing data patterns, explanatory modeling aims to identify and quantify the factors that influence or contribute to the outcomes of interest. Here's a detailed explanation of explanatory modeling:

1. Identification of Relationships:

   • Explanatory modeling begins by identifying the relationships between the dependent variable (the outcome or response variable) and one or more independent variables (predictor or explanatory variables). These relationships may be linear or nonlinear and can involve direct or indirect causal pathways.

2. Hypothesis Testing:

   • Explanatory modeling often involves formulating hypotheses about the relationships between variables based on prior knowledge, theoretical frameworks, or empirical evidence. Hypotheses are then tested using statistical methods to determine the strength, significance, and direction of associations between variables.

3. Model Specification:

   • Once the relationships between variables are identified, explanatory models are specified to represent these relationships mathematically. This typically involves selecting an appropriate regression model or causal modeling technique, such as linear regression, logistic regression, structural equation modeling (SEM), or causal Bayesian networks.
   • Model specification includes defining the functional form of the model, selecting the appropriate independent variables to include in the model, and determining potential interactions or nonlinear effects.

4. Parameter Estimation:

   • After specifying the model, parameter estimation techniques are used to estimate the coefficients or parameters of the model. This involves fitting the model to the observed data using statistical algorithms or optimization methods to determine the best-fitting values of the model parameters.
   • Parameter estimation techniques vary depending on the type of model and the estimation method used. For example, least squares estimation is commonly used in linear regression models, while maximum likelihood estimation is often used in logistic regression and SEM.

5. Model Evaluation:

   • Explanatory models are evaluated to assess their goodness of fit, predictive accuracy, and generalizability to new data. Model evaluation involves examining various statistical measures, such as R-squared (for regression models), likelihood ratio tests, goodness-of-fit indices (for SEM), and validation metrics (for predictive models).
   • Model evaluation helps determine whether the model adequately explains the observed data, whether it is statistically significant, and whether it can be generalized to other populations or contexts.

6. Interpretation of Results:

   • Once the model is evaluated, the results are interpreted to understand the relationships between variables and draw conclusions about the underlying mechanisms or causal pathways. Interpretation involves examining the sign, magnitude, and significance of coefficients, as well as assessing the practical implications of the findings.
   • The interpretation of results may also involve conducting sensitivity analyses, exploring alternative model specifications, or testing additional hypotheses to further elucidate the relationships between variables.

In summary, explanatory modeling is a statistical or analytical approach used to understand the causal relationships between variables and explain the underlying mechanisms of observed phenomena. It involves hypothesis testing, model specification, parameter estimation, model evaluation, and interpretation of results to identify and quantify the factors that influence the outcomes of interest. Explanatory modeling is widely used in various fields, including social sciences, economics, public health, and environmental studies, to inform decision-making, policy development, and scientific inquiry.