missing – paulvanderlaken.com

Daniel Oehm wrote this interesting blog about how to simulate realistic data using a Bayesian network.

Bayesian networks are a type of probabilistic graphical model that uses Bayesian inference for probability computations. Bayesian networks aim to model conditional dependence, and therefore causation, by representing conditional dependence by edges in a directed graph. Through these relationships, one can efficiently conduct inference on the random variables in the graph through the use of factors.
Devin Soni via Medium

As Bayes nets represent data as a probabilistic graph, it is very easy to use that structure to simulate new data that demonstrate the realistic patterns of the underlying causal system. Daniel’s post shows how to do this with bnlearn.

New data is simulated from a Bayes net (see above) by first sampling from each of the root nodes, in this case sex. Then followed by the children conditional on their parent(s) (e.g. sport | sex and hg | sex) until data for all nodes has been drawn. The numbers on the nodes below indicate the sequence in which the data is simulated, noting that rcc is the terminal node.
Daniel Oehms in his blog

The original and simulated datasets are compared in a couple of ways 1) observing the distributions of the variables 2) comparing the output from various models and 3) comparing conditional probability queries. The third test is more of a sanity check. If the data is generated from the original Bayes net then a new one fit on the simulated data should be approximately the same. The more rows we generate the closer the parameters will be to the original values.

The original data alongside the generated data in Daniel’s example

As you can see, a Bayesian network allows you to generate data that looks, feels, and behaves a lot like the data on which you based your network on in the first place.

This can be super useful if you want to generate a synthetic / fake / artificial dataset without sharing personal or sensitive data.

Moreover, the underlying Bayesian net can be very useful to compute missing values. In Daniel’s example, he left out some values on purpose (pretending they were missing) and imputed them with the Bayes net. He found that the imputed values for the missing data points were quite close to the original ones:

For two variables, the original values plotted against the imputed replacements.

In the original blog, Daniel goes on to show how to further check the integrity of the simulated data using statistical models and shares all his code so you can try this out yourself. Please do give his website a visit as Daniel has many more interesting statistics blogs!

A recent open access paper by Nicholas Tierney and Dianne Cook — professors at Monash University — deals with simpler handling, exploring, and imputation of missing values in data.They present new methodology building upon tidy data principles, with a goal to integrating missing value handling as an integral part of data analysis workflows. New data structures are defined (like the nabular) along with new functions to perform common operations (like gg_miss_case).

These new methods have bundled among others in the R packages naniar and visdat, which I highly recommend you check out. To put in the author’s own words:

The naniar and visdat packages build on existing tidy tools and strike a compromise between automation and control that makes analysis efficient, readable, but not overly complex. Each tool has clear intent and effects – plotting or generating data or augmenting data in some way. This reduces repetition and typing for the user, making exploration of missing values easier as they follow consistent rules with a declarative interface.

The below showcases some of the highly informational visuals you can easily generate with naniar‘s nabulars and the associated functionalities.

For instance, these heatmap visualizations of missing data for the airquality dataset. (A) represents the default output and (B) is ordered by clustering on rows and columns. You can see there are only missings in ozone and solar radiation, and there appears to be some structure to their missingness.

Another example is this upset plot of the patterns of missingness in the airquality dataset. Only Ozone and Solar.R have missing values, and Ozone has the most missing values. There are 2 cases where both Solar.R and Ozone have missing values.

You can also generate a histogram using nabular data in order to show the values and missings in Ozone. Values are imputed below the range to show the number of missings in Ozone and colored according to missingness of ozone (‘Ozone_NA‘). This displays directly that there are approximately 35-40 missings in Ozone.

Alternatively, scatterplots can be easily generated. Displaying missings at 10 percent below the minimum of the airquality dataset. Scatterplots of ozone and solar radiation (A), and ozone and temperature (B). These plots demonstrate that there are missings in ozone and solar radiation, but not in temperature.

Finally, this parallel coordinate plot displays the missing values imputed 10% below range for the oceanbuoys dataset. Values are colored by missingness of humidity. Humidity is missing for low air and sea temperatures, and is missing for one year and one location.