Last updated: 2020-04-07
Checks: 7 0
Knit directory: research/
This reproducible R Markdown analysis was created with workflowr (version 1.6.1). The Checks tab describes the reproducibility checks that were applied when the results were created. The Past versions tab lists the development history.
Great! Since the R Markdown file has been committed to the Git repository, you know the exact version of the code that produced these results.
Great job! The global environment was empty. Objects defined in the global environment can affect the analysis in your R Markdown file in unknown ways. For reproduciblity it’s best to always run the code in an empty environment.
The command set.seed(20200406) was run prior to running the code in the R Markdown file. Setting a seed ensures that any results that rely on randomness, e.g. subsampling or permutations, are reproducible.
Great job! Recording the operating system, R version, and package versions is critical for reproducibility.
Nice! There were no cached chunks for this analysis, so you can be confident that you successfully produced the results during this run.
Great job! Using relative paths to the files within your workflowr project makes it easier to run your code on other machines.
Great! You are using Git for version control. Tracking code development and connecting the code version to the results is critical for reproducibility.
The results in this page were generated with repository version 457280d. See the Past versions tab to see a history of the changes made to the R Markdown and HTML files.
Note that you need to be careful to ensure that all relevant files for the analysis have been committed to Git prior to generating the results (you can use wflow_publish or wflow_git_commit). workflowr only checks the R Markdown file, but you know if there are other scripts or data files that it depends on. Below is the status of the Git repository when the results were generated:
Ignored files:
Ignored: .DS_Store
Ignored: .RData
Ignored: .Rhistory
Ignored: .Rproj.user/
Ignored: analysis/.Rhistory
Note that any generated files, e.g. HTML, png, CSS, etc., are not included in this status report because it is ok for generated content to have uncommitted changes.
These are the previous versions of the repository in which changes were made to the R Markdown (analysis/hierarchical.Rmd) and HTML (docs/hierarchical.html) files. If you’ve configured a remote Git repository (see ?wflow_git_remote), click on the hyperlinks in the table below to view the files as they were in that past version.
| File | Version | Author | Date | Message |
|---|---|---|---|---|
| Rmd | 457280d | DBomber60 | 2020-04-07 | hierarchy |
| html | edf060d | DBomber60 | 2020-04-06 | Build site. |
| Rmd | a3a9fc4 | DBomber60 | 2020-04-06 | para |
| html | daeaf75 | DBomber60 | 2020-04-06 | Build site. |
| Rmd | f139f32 | DBomber60 | 2020-04-06 | init |
| html | befc64c | DBomber60 | 2020-04-06 | Build site. |
| Rmd | e28a21b | DBomber60 | 2020-04-06 | test |
Suppose we have results from several experiments on the effect of a certain drug. How should we use this data to estimate the drug’s effect? What is the error of the estimate?
To make this concrete,
experiment = LETTERS[1:8]
effect = rnorm(8)
df = data.frame(experiment = experiment, effect = effect)
kable(df)| experiment | effect |
|---|---|
| A | -0.2790875 |
| B | -0.3475191 |
| C | 0.4515379 |
| D | -0.5212846 |
| E | 0.7675587 |
| F | 0.0071625 |
| G | -0.9345939 |
| H | -0.1729252 |
Choose the best study. Clearly this is not optimal since you are not making use of the informatin you have; however, very smart people choose this option all the time.
Use some results from statistics class.
Our data then consists of \((\bar{y}_j, \sigma_j)\) for \(j \in 1,...,J\), where \(\bar{y}_j\) is the mean effect from experiment \(j\), and \(\sigma_j\) its standard error.
Our simplest route is to assume that \(\bar{y_j} \underset {iid}{\sim} N(\mu, \sigma_j)\), and to estimate \(\mu\). Conceptually, this assumes that each experiment provides an independent estimate of the drug’s true effect, \(\mu\).
Under this assumption, we can obtain an estimator \(\hat{\mu}\) by maximizing the likelihood of our data.
\[\begin{align} \hat{\mu} &= \underset{\mu}{\arg\max} \prod_j (2 \pi \sigma_j^2)^{-1/2} \exp \bigg(- \frac{( \bar{y}_j -\mu )^2 }{2 \sigma_j^2} \bigg) \\ &= \frac{\sum_j \bar{y}_j/ \sigma_j^2 }{\sum_j 1/ \sigma_j^2} \end{align}\]This seems okay. However, because the experimental conditions, for example the age or other attributes of the test subjects, length of the experiment and so on, are likely to affect the results, it does not feel right to assume the are no differences at all between the groups - an assumption we make by assuming a common \(\mu\). In statistician jargon, we would like to acknowledge the unobserved heterogeneity across groups (experiments).
sessionInfo()R version 3.6.2 (2019-12-12)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Catalina 10.15
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] knitr_1.27 workflowr_1.6.1
loaded via a namespace (and not attached):
[1] Rcpp_1.0.3 rprojroot_1.3-2 digest_0.6.23 later_1.0.0
[5] R6_2.4.1 backports_1.1.5 git2r_0.26.1 magrittr_1.5
[9] evaluate_0.14 highr_0.8 stringi_1.4.5 rlang_0.4.4
[13] fs_1.3.1 promises_1.1.0 whisker_0.4 rmarkdown_2.1
[17] tools_3.6.2 stringr_1.4.0 glue_1.3.1 httpuv_1.5.2
[21] xfun_0.12 yaml_2.2.0 compiler_3.6.2 htmltools_0.4.0