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### Calculating and visualising correlation coefficients with `inspectdf` (and why correlations matrices make life hard)

In a previous post, we explored categorical data using the `inspectdf` package. In this post, we tackle a different exploratory problem of calculating and visualising correlation coefficients. To install `inspectdf` from CRAN, you’ll first need to run:

```installed.packages("inspectdf")
```

We’ll begin the tutorial by loading the `inspectdf` and `dplyr` packages, the latter we’ll need for some dataframe manipulation.

```library(inspectdf)
library(dplyr)
```

For this walk-through, we’ll explore the `storms` dataset which comes from the `dplyr` package and has many numeric columns. The data includes the positions and attributes of 198 tropical storms, measured every six hours during the lifetime of a storm.

```# check out the storms dataset
?storms
```

#### What’s wrong with `cor()`?

Most R users will be familiar with the built-in `stats` function, `cor()` which can be used to produce a matrix of correlation coefficients of pairs of numeric variables. So why not just use this? Here’s a short list of pain points that occur when using this function:

##### 1. `cor()` requires numeric inputs only

Correlations are only defined for numeric pairs of variables, so perhaps this shouldn’t be a surprise. But it means we can’t simply pass a dataframe with mixed types to `cor()` and expect that it will be smart enough to return correlations for just the numeric columns. Consequently this fails:

```cor(storms)

## Error in cor(storms): 'x' must be numeric
```
##### 2. Correlation matrices are hard to read

It isn’t hard get what we want from `cor()` by first selecting the numeric columns using a bit of `dplyr`:

```cor(storms %>% select_if(is.numeric))

##                     year        month           day          hour
## year         1.000000000 -0.011488006  0.0183703369  0.0015741629
## month       -0.011488006  1.000000000 -0.1830702018 -0.0051201358
## day          0.018370337 -0.183070202  1.0000000000  0.0007164624
## hour         0.001574163 -0.005120136  0.0007164624  1.0000000000
## lat         -0.121252667 -0.065922836 -0.0508598742  0.0026823666
## long         0.060387523  0.048382680  0.0406477301 -0.0091876627
## wind         0.048966015  0.126682358 -0.0064971154  0.0018333102
## pressure    -0.072615741 -0.134238300 -0.0010113895  0.0016030589
## ts_diameter           NA           NA            NA            NA
## hu_diameter           NA           NA            NA            NA
##                      lat         long         wind     pressure
## year        -0.121252667  0.060387523  0.048966015 -0.072615741
## month       -0.065922836  0.048382680  0.126682358 -0.134238300
## day         -0.050859874  0.040647730 -0.006497115 -0.001011389
## hour         0.002682367 -0.009187663  0.001833310  0.001603059
## lat          1.000000000 -0.104014683  0.076141764 -0.103772744
## long        -0.104014683  1.000000000  0.004737422  0.058467333
## wind         0.076141764  0.004737422  1.000000000 -0.942249266
## pressure    -0.103772744  0.058467333 -0.942249266  1.000000000
## ts_diameter           NA           NA           NA           NA
## hu_diameter           NA           NA           NA           NA
##             ts_diameter hu_diameter
## year                 NA          NA
## month                NA          NA
## day                  NA          NA
## hour                 NA          NA
## lat                  NA          NA
## long                 NA          NA
## wind                 NA          NA
## pressure             NA          NA
## ts_diameter           1          NA
## hu_diameter          NA           1
```

The result is a matrix of pairwise correlations. There are several problems with this:

• Matrices are great for linear algebra but terrible for visual inspection. This particular matrix is wide and has been truncated and spread over multiple lines.
• It isn’t easy to tell which variables are most or least correlated by eye-balling this matrix, it’s a jumble of numbers and the row and column indices aren’t easy to follow.
• Nearly half of the output is totally unnecessary: correlation matrices are always symmetric, which means that you only need about half of what is printed.
• It’s tricky to do any further analysis of the coefficients in this format – a dataframe would be handy!
##### 3. `cor()` doesn’t produce confidence intervals

If possible, we should try to interpret point estimates in the context of their sampling distribution, for example by considering a confidence interval.

Confidence intervals aren’t available using `cor()`, although can be generated using `cor.test()`. A big draw back here is that intervals and perform hypothesis tests can only be performed one at a time – we may want this for many (or all) correlation coefficients.

##### 4. `cor()` and `cor.test()` don’t provide visualisation methods out of the box

Tables are all very well, but it’s much easier to use graphics to visually interrogate correlations. There are many other packages that do help with this, but in general they use a matrix or grid plot with coloured cells to display correlations which are typically messy and difficult to read.

#### Using `inspect_cor()` to calculate correlations

`inspect_cor()` attempts to address some of the issues above. To calculate correlations for the `storms` data, simply run

```storms %>% inspect_cor()

## # A tibble: 45 x 6
##    col_1       col_2         corr  p_value  lower  upper
##    <chr>       <chr>        <dbl>    <dbl>  <dbl>  <dbl>
##  1 pressure    wind        -0.942 0.       -0.945 -0.940
##  2 hu_diameter pressure    -0.842 0.       -0.853 -0.831
##  3 hu_diameter wind         0.774 0.        0.758  0.788
##  4 hu_diameter ts_diameter  0.684 0.        0.663  0.704
##  5 ts_diameter pressure    -0.683 0.       -0.703 -0.663
##  6 ts_diameter wind         0.640 0.        0.617  0.662
##  7 ts_diameter lat          0.301 1.25e-73  0.266  0.335
##  8 day         month       -0.183 3.59e-76 -0.205 -0.161
##  9 hu_diameter lat          0.164 1.59e-22  0.127  0.201
## 10 ts_diameter month        0.139 1.67e-16  0.102  0.176
## # … with 35 more rows
```

The result is tabular rather than a matrix. Together, the first two columns contain the names of every unique pair of numeric columns, while the `corr` column contains the correlation coefficients. For example, the first row says that the correlation between `pressure` and `wind` is about -0.942. The rows are arranged in descending order of the absolute correlation – making it easy to see which pairs are most strongly correlated.

The `p_value` column contains p-values associated with the null hypothesis that the true correlation coefficient is 0. The `lower` and `upper` columns contain the lower and upper reaches of a 95% confidence interval. In this case, the confidence interval for the correlation between `pressure` and `wind` is `(-0.945, -0.940)`. The interval type can be changing the `alpha` argument in `inspect_cor()`, for example 90% confidence intervals can be generated using ```inspect_cor(storms, alpha = 0.1)```.

##### Using `show_plot()` to visualise correlation coefficients

The dataframe of coefficients above is already a bit easier to handle than `cor()`’s matrix output. We can go further and visualise these graphically using `show_plot()`:

```storms %>%
inspect_cor() %>%
show_plot()
``` Some key points

• Each row in the plot corresponds to a unique pair of numeric columns, the correlation coefficient is show as a black vertical line.
• The gray and pink bars around the coefficients are the confidence intervals.
• The gray bars are confidence intervals that straddle 0 (also shown by the long vertical dashed line) indicating that the true coefficient is not significantly different to 0.

A side note that is not specific to `inspect_cor()` is that we should be careful when interpreting the significance of individual coefficients when there are many correlation coefficients overall. For example, if `alpha = 0.05` and all of the true coefficients are 0, we’d still expect to see 1 in 20 significant coefficients just by chance.

##### Using `inspect_cor()` and `show_plot()` to visualise the correlation with a single feature

Another common exploratory step is to assess the linear association between possible predictor variables and a target variable, often as a precursor to regression analysis or building a predictive model.

As an example, suppose we’d like to see which features of a storm are most strongly correlated with `wind`, the maximum sustained wind speed of the storm. We don’t need to calculate all correlation coefficients for this (for big data sets this is time consuming), only the ones that involve the `wind` variable.

With `inspect_cor()` this is also straightforward, by simply adding the argument `with_col = "wind"`:

```storms %>%
inspect_cor(with_col = "wind") %>%
show_plot()
``` The strongest association here is with `pressure`, the air pressure at the storm’s center. I have very little meteorological experience but it seems sensible that those should be strongly associated.