CausalImpact

https://google.github.io/CausalImpact/
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CausalImpact is an R package that uses Bayesian structural time-series models to estimate the causal...
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### Create Example Dataset

Source: https://google.github.io/CausalImpact/CausalImpact.html

Generate a synthetic dataset with a response variable and a predictor, including an artificial intervention effect.

```R
set.seed(1)
x1 <- 100 + arima.sim(model = list(ar = 0.999), n = 100)
y <- 1.2 * x1 + rnorm(100)
y[71:100] <- y[71:100] + 10
data <- cbind(y, x1)
```

--------------------------------

### Install and Load CausalImpact

Source: https://google.github.io/CausalImpact

Install the package from CRAN and load it into the R environment.

```R
install.packages("CausalImpact")
library(CausalImpact)
```

--------------------------------

### Get CausalImpact Package Version

Source: https://google.github.io/CausalImpact/CausalImpact.html

Retrieve the currently installed version of the CausalImpact R package.

```R
packageVersion("CausalImpact")
```

--------------------------------

### Inspect Dataset

Source: https://google.github.io/CausalImpact/CausalImpact.html

Verify the dimensions and structure of the generated dataset.

```R
dim(data)
```

```R
head(data)
```

--------------------------------

### Run Causal Analysis

Source: https://google.github.io/CausalImpact/CausalImpact.html

Define the pre- and post-intervention periods and execute the CausalImpact analysis.

```R
pre.period <- c(1, 70)
post.period <- c(71, 100)
```

```R
impact <- CausalImpact(data, pre.period, post.period)
```

--------------------------------

### CausalImpact FAQ

Source: https://google.github.io/CausalImpact/CausalImpact.html

Frequently asked questions about the CausalImpact package, including citation information and model assumption verification.

```APIDOC
## FAQ

### How do I cite the package in my work?
We recommend referencing the use of the CausalImpact R package as shown in the example below:

“CausalImpact 1.2.1, Brodersen et al., Annals of Applied Statistics (2015). http://google.github.io/CausalImpact/”

To find out which package version you are using, type `packageVersion("CausalImpact")`.

### How can I check whether the model assumptions are fulfilled?

It’s the elephant in the room with any causal analysis on observational data: how can we verify the assumptions that go into the model? Here are a few ways of getting started.

1.  **Covariate Stability**: It is critical to reason why the covariates that are included in the model (this was _x1_ in the example) _were not themselves affected_ by the intervention. Sometimes it helps to plot all covariates and do a visual sanity check.
2.  **Pre-Intervention Prediction Accuracy**: Examine how well the outcome data _y_ can be predicted _before the beginning of the intervention_. This can be done by running `CausalImpact()` on an imaginary intervention. Then check how well the model predicted the data following this imaginary intervention. We would expect not to find a significant effect, i.e., counterfactual estimates and actual data should agree reasonably closely.
3.  **Transparency**: When presenting or writing up results, be sure to list the above assumptions explicitly, including the priors in `model.args`, and discuss them with your audience.
```

--------------------------------

### Define Pre and Post Periods with Dates

Source: https://google.github.io/CausalImpact/CausalImpact.html

Specify the pre-intervention and post-intervention periods using date objects for CausalImpact analysis.

```R
pre.period <- as.Date(c("2014-01-01", "2014-03-11"))
post.period <- as.Date(c("2014-03-12", "2014-04-10"))
```

--------------------------------

### Estimate Custom BSTS Model for CausalImpact

Source: https://google.github.io/CausalImpact/CausalImpact.html

Set up and estimate a time-series model using the bsts package, including a local level component, to be used with CausalImpact.

```R
ss <- AddLocalLevel(list(), y)
bsts.model <- bsts(y ~ x1, ss, niter = 1000)
```

--------------------------------

### Create Time Series Data with Dates

Source: https://google.github.io/CausalImpact/CausalImpact.html

Prepare time-series data using dates for CausalImpact. This involves creating a sequence of dates and a zoo object with the time points.

```R
time.points <- seq.Date(as.Date("2014-01-01"), by = 1, length.out = 100)
data <- zoo(cbind(y, x1), time.points)
head(data)
```

```text
##                   y       x1
## 2014-01-01 105.2950 88.21513
## 2014-01-02 105.8943 88.48415
## 2014-01-03 106.6209 87.87684
## 2014-01-04 106.1572 86.77954
## 2014-01-05 101.2812 84.62243
## 2014-01-06 101.4484 84.60650
```

--------------------------------

### Prepare Data for Custom Model in CausalImpact

Source: https://google.github.io/CausalImpact/CausalImpact.html

Set observed data in the post-treatment period to NA and store the actual observed response for use with a custom bsts model.

```R
post.period <- c(71, 100)
post.period.response <- y[post.period[1] : post.period[2]]
y[post.period[1] : post.period[2]] <- NA
```

--------------------------------

### Custom Model Specification with BSTS

Source: https://google.github.io/CausalImpact/CausalImpact.html

This section explains how to use the bsts package to define a custom time-series model for CausalImpact analysis. It covers setting up the model, fitting it with bsts, and then passing the fitted model to CausalImpact.

```APIDOC
## Custom Model Specification with BSTS

### Description
This section explains how to use the bsts package to define a custom time-series model for CausalImpact analysis. It covers setting up the model, fitting it with bsts, and then passing the fitted model to CausalImpact.

### Method
This is a conceptual guide, not a direct API call. The process involves R code.

### Endpoint
N/A (R package usage)

### Parameters
#### Available Options for `model.args` in BSTS:
- `niter` (Number) - Number of MCMC samples to draw. Defaults to **1000**.
- `standardize.data` (Boolean) - Whether to standardize all columns of the data before fitting the model. Defaults to **TRUE**.
- `prior.level.sd` (Number) - Prior standard deviation of the Gaussian random walk of the local level. Defaults to **0.01**.
- `nseasons` (Number) - Period of the seasonal components. Set to a whole number greater than 1 to include a seasonal component. Defaults to **1** (no seasonal component).
- `season.duration` (Number) - Duration of each season (number of data points per season). Defaults to **1**.
- `dynamic.regression` (Boolean) - Whether to include time-varying regression coefficients. Defaults to **FALSE**.

### R Code Example
```R
# Set observed data in the post-treatment period to NA
post.period <- c(71, 100)
post.period.response <- y[post.period[1] : post.period[2]]
y[post.period[1] : post.period[2]] <- NA

# Set up and estimate a time-series model using bsts
ss <- AddLocalLevel(list(), y)
bsts.model <- bsts(y ~ x1, ss, niter = 1000)

# Call CausalImpact with the fitted bsts model
impact <- CausalImpact(bsts.model = bsts.model,
                       post.period.response = post.period.response)

# Inspect results
plot(impact)
summary(impact)
summary(impact, "report")
```

### Response
N/A (R package usage)

### Response Example
N/A (R package usage)
```

--------------------------------

### Visualize Dataset

Source: https://google.github.io/CausalImpact/CausalImpact.html

Plot the response and predictor variables to visualize the data.

```R
matplot(data, type = "l")
```

--------------------------------

### Run CausalImpact with a Custom BSTS Model

Source: https://google.github.io/CausalImpact/CausalImpact.html

Call CausalImpact using a pre-fitted bsts model object and the actual observed post-period response.

```R
impact <- CausalImpact(bsts.model = bsts.model,
                       post.period.response = post.period.response)
```

--------------------------------

### Access Full Summary Data

Source: https://google.github.io/CausalImpact/CausalImpact.html

Retrieve the complete summary data for the CausalImpact analysis, including all numerical values at full precision.

```R
impact$summary
```

--------------------------------

### Plot predictor coefficients

Source: https://google.github.io/CausalImpact/CausalImpact.html

Visualize the posterior probability of each predictor's inclusion in the model.

```R
plot(impact$model$bsts.model, "coefficients")
```

--------------------------------

### Generate Verbal Summary Report

Source: https://google.github.io/CausalImpact/CausalImpact.html

Obtain a detailed verbal interpretation of the CausalImpact analysis results, providing a narrative explanation of the findings.

```R
summary(impact, "report")
```

--------------------------------

### Set confidence interval size

Source: https://google.github.io/CausalImpact/CausalImpact.html

Change the alpha argument to adjust the interval width, where alpha defaults to 0.05 for 95% intervals.

```R
impact <- CausalImpact(data, pre.period, post.period, alpha = 0.1)
```

--------------------------------

### Print Summary Table of Causal Impact

Source: https://google.github.io/CausalImpact/CausalImpact.html

Generate a numerical summary of the CausalImpact analysis, including average and cumulative effects, confidence intervals, and posterior probabilities.

```R
summary(impact)
```

```text
## Posterior inference {CausalImpact}
## 
##                          Average        Cumulative  
## Actual                   117            3511        
## Prediction (s.d.)        107 (0.37)     3196 (11.03) 
## 95% CI                   [106, 107]     [3174, 3217] 
##                                                     
## Absolute effect (s.d.)   11 (0.37)      316 (11.03) 
## 95% CI                   [9.8, 11]      [294.9, 337]
##                                                     
## Relative effect (s.d.)   9.9% (0.35%)   9.9% (0.35%)
## 95% CI                   [9.2%, 11%]    [9.2%, 11%] 
## 
## Posterior tail-area probability p:   0.001
## Posterior prob. of a causal effect:  99.9%
## 
## For more details, type: summary(impact, "report")
```

--------------------------------

### Run Causal Impact with Date Periods

Source: https://google.github.io/CausalImpact/CausalImpact.html

Perform a CausalImpact analysis using a time-series object with dates and specified pre/post periods. The plot will display time points on the x-axis.

```R
impact <- CausalImpact(data, pre.period, post.period)
plot(impact)
```

--------------------------------

### Customize plot panels

Source: https://google.github.io/CausalImpact/CausalImpact.html

Specify which panels to include in the output plot to avoid irrelevant cumulative impact estimates.

```R
plot(impact, c("original", "pointwise"))
```

--------------------------------

### Inspect CausalImpact Results

Source: https://google.github.io/CausalImpact/CausalImpact.html

Plot and summarize the results of a CausalImpact analysis, with an option for a detailed report.

```R
plot(impact)
summary(impact)
summary(impact, "report")
```

--------------------------------

### Adjust Causal Impact Model Arguments

Source: https://google.github.io/CausalImpact/CausalImpact.html

Customize the CausalImpact model by passing specific arguments, such as the number of iterations (niter) and seasonal components (nseasons).

```R
impact <- CausalImpact(..., model.args = list(niter = 5000, nseasons = 7))
```

--------------------------------

### Adjust plot font size

Source: https://google.github.io/CausalImpact/CausalImpact.html

Modify the returned ggplot2 object using standard ggplot2 functions like theme_bw.

```R
library(ggplot2)
impact.plot <- plot(impact) + theme_bw(base_size = 20)
plot(impact.plot)
```

--------------------------------

### Plot Causal Impact Results

Source: https://google.github.io/CausalImpact/CausalImpact.html

Visualize the results of a CausalImpact analysis. The default plot shows observed data, counterfactual predictions, pointwise effects, and cumulative effects.

```R
plot(impact)
```
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