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- Health.vic
- Как делать боковое равновесие в художественной гимнастике
- Можно ли купаться в гранитных карьерах
- 1. Installing the package
- Войти на сайт
- Причины и лечение слезоточивости: почему слезятся глаза на улице
- A very warm welcome to the Rosengart Collection!
- 2. Creating an example dataset

This R package implements an approach to estimating the causal effect of a designed intervention on a time series. For example, how many additional daily clicks were generated by an advertising campaign?

Answering a question like this can be difficult when a randomized experiment is not available. Given a response time series e.

This model is then used to try and predict the counterfactual, i. For a quick overview, watch the tutorial video. For details, see: Brodersen et al. As with all non-experimental approaches to causal inference, valid conclusions require strong assumptions.

In the case of CausalImpact, we assume that there is a set control time series that were themselves not affected by the intervention.

If they were, we might falsely under- or overestimate the true effect. The model also assumes that the relationship between covariates and treated time series, as established during the pre-period, remains stable throughout the post-period see model.

The package is designed to make counterfactual inference as easy as fitting a regression model, but much more powerful, provided the assumptions above are met. The package has a single entry point, the function CausalImpact.

Given a response time series and a set of control time series, the function constructs a time-series model, performs posterior inference on the counterfactual, and returns a CausalImpact object.

The results can be summarized in terms of a table, a verbal description, or a plot.

## Health.vic

To illustrate how the package works, we create a simple toy dataset. It consists of a response variable y and a predictor x1. The example data has observations. We create an intervention effect by lifting the response variable by 10 units after timepoint To estimate a causal effect, we begin by specifying which period in the data should be used for training the model pre-intervention period and which period for computing a counterfactual prediction post-intervention period.

This says that time points 1 … 70 will be used for training, and time points 71 … will be used for computing predictions. Alternatively, we could specify the periods in terms of dates or time points; see Section 5 for an example. This instructs the package to assemble a structural time-series model, perform posterior inference, and compute estimates of the causal effect. The return value is a CausalImpact object. The easiest way of visualizing the results is to use the plot function that is part of the package:.

## Как делать боковое равновесие в художественной гимнастике

By default, the plot contains three panels. The first panel shows the data and a counterfactual prediction for the post-treatment period. The second panel shows the difference between observed data and counterfactual predictions. This is the pointwise causal effect, as estimated by the model.

The third panel adds up the pointwise contributions from the second panel, resulting in a plot of the cumulative effect of the intervention. Remember, once again, that all of the above inferences depend critically on the assumption that the covariates were not themselves affected by the intervention.

The model also assumes that the relationship between covariates and treated time series, as established during the pre-period, remains stable throughout the post-period. It is often more natural to feed a time-series object into CausalImpact rather than a data frame. For example, we might create a data variable as follows:.

We can now specify the pre-period and the post-period in terms of time points rather than indices:. The Average column talks about the average across time during the post-intervention period in the example: time points 71 through The Cumulative column sums up individual time points, which is a useful perspective if the response variable represents a flow quantity such as queries, clicks, visits, installs, sales, or revenue rather than a stock quantity such as number of users or stock price.

This is because we observed an average value of 99 but would have expected an average value of only Since this excludes 0, we correctly conclude that the intervention had a causal effect on the response variable. Since we generated the data ourselves, we know that we injected a true effect of 10, and so the model accurately recovered ground truth.

One reason for this is that we ensured, by design, that the covariate x1 was not itself affected by the intervention.

In practice, we must always reason whether this assumption is justified. For additional guidance about the correct interpretation of the summary table, the package provides a verbal interpretation, which we can print using:. However, there are several options that allow us to gain a little more control over this process.

These options are passed into model.

## Можно ли купаться в гранитных карьерах

More samples lead to more accurate inferences. Defaults to This is equivalent to an empirical Bayes approach to setting the priors. It ensures that results are invariant to linear transformations of the data. Defaults to TRUE. Expressed in terms of data standard deviations. Defaults to 0.

## 1. Installing the package

When in doubt, a safer option is to use 0. In order to include a seasonal component, set this to a whole number greater than 1. For example, if the data represent daily observations, use 7 for a day-of-week component. This interface currently only supports up to one seasonal component. To specify multiple seasonal components, use bsts to specify the model directly, then pass the fitted model in as bsts. Defaults to 1 , which means no seasonal component is used. Defaults to 1. For example, to add a day-of-week component to data with daily granularity, use model.

To add a day-of-week component to data with hourly granularity, set model. In combination with a time-varying local trend or even a time-varying local level, this often leads to overspecification, in which case a static regression is safer.

Instead of using the default model constructed by the CausalImpact package, we can use the bsts package to specify our own model.

## Войти на сайт

This provides the greatest degree of flexibility. Before constructing a custom model, we set the observed data in the post-treatment period to NA, reflecting the fact that the counterfactual response is unobserved after the intervention. We keep a copy of the actual observed response in the variable post.

We next set up and estimate a time-series model using the bsts package. Here is a simple example:. Finally, we call CausalImpact. Instead of providing input data, we simply pass in the fitted model object bsts. We also need to provide the actual observed response.

## Причины и лечение слезоточивости: почему слезятся глаза на улице

This is needed so that the package can compute the difference between predicted response stored in bsts. To find out which package version you are using, type packageVersion "CausalImpact". See the bottom of this page for full bibliographic details. Here are a few ways of getting started. First of all, 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.

Next, it is a good idea to 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.

## A very warm welcome to the Rosengart Collection!

We would expect not to find a significant effect, i. Finally, when presenting or writing up results, be sure to list the above assumptions explicitly, including the priors in model. The response variable i. If one of your covariates contains missing values, consider imputing i. By default, plot creates three panels, showing the counterfactual, pointwise, and cumulative impact estimates. One way of customizing the plot is to specify which panels should be included:.

This creates a plot without cumulative impact estimates. This is sensible whenever the response variable represents a stock quantity that cannot be meaningfully summed up across time e. The plot function for CausalImpact objects returns a ggplot2 object. This means we can customize the plot using standard ggplot2 functions. For example, to increase the font size, we can do:.

## 2. Creating an example dataset

The size of the intervals is specified by the argument alpha , which defaults to 0. Analyses may easily contain tens or hundreds of potential predictors i. Which of these were informative? We can plot the posterior probability of each predictor being included in the model using:. Inferring causal impact using Bayesian structural time-series models.

Annals of Applied Statistics , , Vol. Version 1. Authors: Kay H.