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#### Causal Analysis using R Interrupted Time Series

### Brief Overview of ITS
#  - Interrupted time series (ITS) is a quasi-experimental method used to evaluate the impact 
#    of an intervention by analyzing an outcome measured over time before and after the 
#    intervention occurs.
#  - The technique works by modeling changes in both the level and slope of the time series 
#    that follow the intervention, estimating both immediate and long-term effects.
# -  ITS is valuable when randomization is not feasible and can provide strong evidence 
#    for causal inference, but requires multiple data points on both sides of the intervention.

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This scirpt shows how to perform dimensionality reduction using Shallow Autoencoder in R.   The R packages neuralnet and mlbench are used to show how ot fit an autoencoder (which is a simple neural network) for a synthetic data set.  Subsequent analyses such as visualizing the latent space,  computing the reconstruction errors, anamoly detection,  clustering in latent space and comparing autoencoder to PCA. 

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This R script is a step by step tutorial on how to implement the DO Calculus developed by Judea Pearl.  The R packages used include: causaleffect, mediation, igraph and dplyr.  We demonstrate how to create a simulated data set, how to define a DAG,  how to estimate the expression identified by the DO Calculus and how to use that expression to calculate average causal effect (ACE).
A link to a video demonstration on YouTube is:  https://youtu.be/yNzpoWRgZdE 

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#### Causal Analysis using R  The Weak Instrument Test

# Load necessary packages
library(AER)  # for ivreg
library(car)  # for linearHypothesis (optional)

set.seed(11152025)

# Generate synthetic data
n <- 500

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### Causal Analysis using R   Instrumental Variables

## Instrumental variables (IVs) are special variables used in statistics and econometrics 
## to estimate causal effects when ordinary regression methods would be biased due to 
## endogeneity—meaning the explanatory variable is correlated with unobserved factors or the error term.

## Two Key Criterias of IVs
## It is correlated with the problematic (endogenous) explanatory variable.
## It is not correlated with the error term and only affects the outcome through 
## the explanatory variable (called the exclusion restriction).

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### Causal Analysis using R:  A More Sophiscated Example of Bayesian Networks


##In this video, we present an example of using the R package bnlearn
##for Bayesian Network Analysis
## The Following topics are covered:
#Generates a mixed-type synthetic data set

#Applies multiple structure learning algorithms

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### Causal Analysis using R   A Simple Case Bayesian Network Analysis

##Bayesian Networks are directed acyclic graphs representing variables and their dependencies.

##Nodes represent variables; edges show conditional dependencies between them.
A
##Each node has a probability function based on its parent nodes.

## They use Bayes' theorem to update probabilities with new evidence.

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### Causal Analysis using R  The Difference in Difference Method

##DiD estimates causal effects by comparing changes over time between treatment and control groups.

##It uses before-and-after differences in outcomes to isolate the treatment effect.

##The critical assumption is parallel trends, meaning both groups would follow similar outcome paths 
#if untreated.

##Suitable for observational data where randomization is not possible.

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### Causal Analysis using R:  Sophisticated DAGs


###Generate Data
 
# Install if needed
#if (!requireNamespace("simDAG", quietly = TRUE)) {
#  install.packages("simDAG")
#}

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### How to Implement Directed Acyclic Graphs for Causal Inference in R:  The Simple Case

##A Directed Acyclic Graph (DAG) is a finite graph composed of nodes connected 
##     by directed edges with no cycles, meaning it's impossible to start at any node 
##     and follow a sequence of edge directions that returns to the same node.
##in DAGs, nodes to be arranged in a linear order that respects the direction of 
##     edges and represents dependencies or causal relationships.
##Directed Acyclic Graphs (DAGs) are used in causal inference to visually represent 
##     assumptions about causal relationships, identify confounders, guide variable 
##     selection for adjustment, and clarify the pathways affecting causal effect estimation