As mentioned in the other vignettes, the *openEBGM* package is capable of calculating \(EBGM\) and quantile scores from the posterior distribution. *openEBGM* makes it easy to calculate such quantities using a class and object system. While creation of objects of class openEBGM is not necessary (see previous vignette), it provides access to methods for some common generic functions and reduces the number of function calls needed.

To create the object, we first need to calculate the hyperparameter estimates.

```
library(openEBGM)
data(caers)
proc <- processRaw(caers, stratify = FALSE, zeroes = FALSE)
squashed <- squashData(proc)
theta_init <- data.frame(alpha1 = c(0.2, 0.1, 0.3, 0.5, 0.2),
beta1 = c(0.1, 0.1, 0.5, 0.3, 0.2),
alpha2 = c(2, 10, 6, 12, 5),
beta2 = c(4, 10, 6, 12, 5),
p = c(1/3, 0.2, 0.5, 0.8, 0.4))
hyper_estimate <- autoHyper(squashed, theta_init = theta_init,
zeroes = FALSE, squashed = TRUE, N_star = 1)
```

Once we have the hyperparameter estimates and the processed data, we can calculate the \(EBGM\) scores and any desired quantile(s) from the posterior distribution.

```
ebout <- ebScores(proc, hyper_estimate = hyper_estimate,
quantiles = c(5, 95)) #For the 5th and 95th percentiles
ebout_noquant <- ebScores(proc, hyper_estimate = hyper_estimate,
quantiles = NULL) #For no quantiles
```

As seen above, we can calculate the \(EBGM\) scores with or without adding quantiles. If using quantiles, we can specifying any number of quantiles.

Once the object has been created, we can use class-specific methods for some of R’s generic functions (namely, `print()`

, `summary()`

, and `plot()`

).

```
#We can print an openEBGM object to get a quick look at the contents
print(ebout)
#>
#> There were 131 var1-var2 pairs with a QUANT_05 greater than 2
#>
#> Top 5 Highest QUANT_05 Scores
#> var1 var2
#> 13924 REUMOFAN PLUS WEIGHT INCREASED
#> 8187 HYDROXYCUT REGULAR RAPID RELEASE CAPLETS EMOTIONAL DISTRESS
#> 13886 REUMOFAN PLUS IMMOBILE
#> 7793 HYDROXYCUT HARDCORE CAPSULES CARDIO-RESPIRATORY DISTRESS
#> 8220 HYDROXYCUT REGULAR RAPID RELEASE CAPLETS INJURY
#> N E QUANT_05
#> 13924 16 0.40643623 15.68
#> 8187 19 0.89690107 11.65
#> 13886 6 0.07866508 10.16
#> 7793 8 0.30482718 8.99
#> 8220 11 0.56317044 8.98
print(ebout_noquant, threshold = 3)
#>
#> There were 556 var1-var2 pairs with an EBGM score greater than 3
#>
#> Top 5 Highest EBGM Scores
#> var1
#> 13924 REUMOFAN PLUS
#> 13886 REUMOFAN PLUS
#> 8187 HYDROXYCUT REGULAR RAPID RELEASE CAPLETS
#> 4093 EMERGEN-C (ASCORBIC ACID, B-COMPLEX, ELECTROLYTE,
#> 7832 HYDROXYCUT HARDCORE CAPSULES
#> var2 N E EBGM
#> 13924 WEIGHT INCREASED 16 0.40643623 23.26
#> 13886 IMMOBILE 6 0.07866508 18.28
#> 8187 EMOTIONAL DISTRESS 19 0.89690107 16.78
#> 4093 COUGH 6 0.14481526 16.03
#> 7832 MULTIPLE INJURIES 5 0.09237187 15.63
```

When quantiles are present, simply printing the object shows, by default, how many *var1-var2* pairs exist that have QUANT\(>x\), where \(x\) is the minimum quantile threshold used for the data (default 2). In the absence of quantiles, it simply outputs the number of *var1-var2* pairs that have an \(EBGM\) score greater than the specified threshold. In both cases, it also shows a quick look at the *var1-var2* pairs with the highest \(x\) or \(EBGM\), depending on whether quantiles were calculated or not.

One can also use the `summary()`

function on an openEBM object to get further information about the calculations.

`summary(ebout)`

```
#>
#> Summary of the EB-Metrics
#> EBGM QUANT_05 QUANT_95
#> Min. : 0.200 Min. : 0.0700 Min. : 0.51
#> 1st Qu.: 2.010 1st Qu.: 0.4800 1st Qu.:12.19
#> Median : 2.390 Median : 0.5100 Median :14.73
#> Mean : 2.356 Mean : 0.5377 Mean :13.31
#> 3rd Qu.: 2.580 3rd Qu.: 0.5200 3rd Qu.:15.73
#> Max. :23.260 Max. :15.6800 Max. :33.48
```

As seen above, by default the `summary()`

function, when called on an openEBGM object, outputs some descriptive statistics on the \(EBGM\) and quantile scores, and a histogram of the \(EBGM\) scores. There are options to disable plot output, or to calculate the log_{2} transform of the scores, which provides a Bayesian information statistic (when applied to the \(EBGM\) score).

```
summary(ebout, plot.out = FALSE, log.trans = TRUE)
#>
#> Summary of the EB-Metrics
#> EBGM QUANT_05 QUANT_95
#> Min. :-2.322 Min. :-3.8365 Min. :-0.9714
#> 1st Qu.: 1.007 1st Qu.:-1.0589 1st Qu.: 3.6076
#> Median : 1.257 Median :-0.9714 Median : 3.8807
#> Mean : 1.161 Mean :-0.9833 Mean : 3.6316
#> 3rd Qu.: 1.367 3rd Qu.:-0.9434 3rd Qu.: 3.9754
#> Max. : 4.540 Max. : 3.9709 Max. : 5.0652
```

Finally, *openEBGM* provides a method for the `plot()`

function that can produce a variety of different plots. These are shown below.

`plot(ebout)`

As seen, by default, the `plot()`

function shows the top \(EBGM\) scores by *var1-var2* combinations (only *var1* is shown for space preservation) and “error bars” using the lowest and highest quantiles calculated. The sample size for each *var1-var2* combination is also plotted.

A specific event from *var2* may also be selected, and only the *var1-var2* combinations that include this particular event will be shown. An example is shown below.

```
plot(ebout, event = "CHOKING")
#> Warning in plot.openEBGM(ebout, event = "CHOKING"): 2 or more matches found
#> for event specified
```

In addition to the bar chart, the `plot()`

function can also create a histogram of the \(EBGM\) scores.

```
plot(ebout, plot.type = "histogram")
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
```

Again, one may choose an event from *var2* by which to subset the data when plotting.

```
plot(ebout, plot.type = "histogram", event = "CHOKING")
#> `stat_bin()` using `bins = 30`. Pick better value with `binwidth`.
```

Finally, the last type of plot included with the `plot()`

function shows the shrinkage performed by the algorithm. It is called the “Chirtel Squid Plot”, titled after its creator, Stuart Chirtel.

`plot(ebout, plot.type = "shrinkage")`

While a specific event may be selected by which to subset the data, it can lead to a less informative plot due to smaller sample size.

`plot(ebout, plot.type = "shrinkage", event = "CHOKING")`

*openEBGM* was designed to give the user a high level of control over data analysis choices (stratification, data squashing, etc.) using DuMouchel’s Gamma-Poisson Shrinkage (GPS) method (1999, 2001). The GPS method applies to any large contingency table, so *openEBGM* can be used to mine a variety of databases in which the rate of co-occurrence of two variables or items is of interest (sometimes known as the “market basket problem”). U.S. FDA products and adverse events is just one of many possible applications.