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# 7 A general approach to doing statistical analyses

Running statistical analyses is a relatively methodical and well-defined process, even if there is often a lot of trial and error involved. Sometimes it may feel overwhelming and complicated, which it definitely can be, but it doesn’t have to be. By taking a structured approach to running statistical analyses, you can make it easier on yourself and feel more in control.

In R, statistical methods are often created and developed by researchers with little to no training in software development and who often use them differently. This has some advantages, like having the cutting edge statistical methods available to us, but has a major disadvantage of often having to learn a completely different way of running a statistical analysis, even if it is fairly similar to ones you’ve used before. So having a framework for running statistical analyses, regardless of who created them, can provide that needed structure and vastly simplify the analysis. This session will be covering a general framework for running statistical analyses, regardless of the exact statistical method.

## 7.1 Learning objectives

The overall objective for this session is to:

- Describe the basic framework underlying most statistical analyses and use R to generate statistical results using this framework.

More specific objectives are to:

- Describe the general “workflow” and steps involved in stating the research question, constructing a model to help answer the question, preparing the data to match the requirements of the model, fitting it to the data, and finally extracting the results from the fitted model.
- Categorize the model definition step as a distinct, theory-driven step, separate from the data, and use parsnip functions to help with defining your model.
- Identify various data transformation techniques and evaluate which are good options given the data. Use functions in the recipes package to apply these transformations to your data.
- Use the broom package to extract the model results to later present them in graphical format (with ggplot2).
- Continue applying the concepts and functions used from the previous sessions.

Specific “anti”-objectives:

- Will
**not**know how to choose and apply the appropriate statistical model or test, nor understand any statistical theory, nor interpret the statistical results correctly, nor determine the relevant data transformations for the statistical approach. What we show, we show*only as demonstration purposes only*, they could be entirely wrong in how to do them correctly if an expert were to review them.

## 7.2 Exercise: What does a “model” mean?

Time: ~8 minutes.

In science and especially statistics, we talk a lot about “models”. But what does model actually mean? What different types of definitions can you think of? Is there a different understanding of model in statistics compared to other areas?

- Take 1 minute to think about your understanding of a model.
- Then, over the next 4 minutes, discuss with your neighbour about the meaning of “model” and see if you can come to a shared understanding.
- Finally, over the next 3 minutes, we will share all together what a model is in the context of data analysis.

## 7.3 Theory and “workflow” on statistical modeling

Going back to our own `lipidomics`

dataset, we need to do the first step: Creating the question. While we don’t have much data, there are a surprising number of questions we could ask. But we will keep it very simple, very basic, and very exploratory.

- What is the estimated relationship of each metabolite with T1D compared to the controls, adjusting for the influence of age and gender?
- What is the variability for the estimate in each relationship?

Next, because we are working within a “reproducible analysis” framework specifically with the use of targets, let’s convert these questions in outputs to include as pipeline targets, along with a basic idea for the final functions that will make up these targets and their inputs and outputs. These targets will probably be quite different by the end, but it’s a good start to think about what it should look like in the end.

- All results for estimated relationships (in case we want to use it for other output)
- All results for variation in estimates of relationships (in case we want to use it for other output)
- Plot of statistical estimate for each relationship
- Plot of variation in estimates for each relationship

Potential function names might be:

`calculate_estimates()`

`calculate_variation()`

`plot_estimates()`

`plot_variation()`

## 7.4 Defining the model

Now that we’ve talked about the workflow around making models and have already written out some research questions, let’s make a basic, graphical theoretical model:

Or mathematically:

\[T1D = metabolite + age + gender\]

So, T1D status (or `class`

in the `lipidomics`

dataset) is our **outcome** and the individual metabolite, age, and gender are our **predictors**. Technically, age and gender would be “confounders” or “covariates”, since we include them only because we think they influence the relationship between the metabolite and T1D.

If we convert the formula into a form with the variables we have in the dataset as well as selecting only one metabolite for now (the cholesterol metabolite, which we add “metabolite” to differentiate it from other potential variables), it would be:

\[class = metabolite\_cholesterol + age + gender\]

Now that we have a theoretical model, we need to choose our model type. Since T1D is binary (either you have it or you don’t), the most likely choice is logistic regression, which requires a binary outcome variable. So we have the theoretical model and the type of model to use - how do we express this as code in R? There are many ways of doing the same thing in R, but some are a bit easier than others. One such approach, that is quite generic and fits with the ideals of the tidyverse, is a similar universe of packages called the tidymodels.

Why do we teach tidymodels? Because they are built by software developers, employed by RStudio (who also employs the people who build the tidyverse), and they have a strong reputation for writing good documentation. Plus, the tidymodels set of packages also make creating and using models quite generic, so by teaching you these sets of tools, you can relatively easily change the model type, or how you process the data, or other specifications without having to learn a whole new package or set of tools.

The reason tidymodels can do that is because they designed it in a way that makes a clear separation in the components of the model building workflow that was described above, through the use of specific packages for each component.

Package | Description |
---|---|

parsnip | Model definition, such as type (e.g. `linear_reg()` ) and “engine” (e.g. `glm()` ). |

recipes | Model-specific data transformations, such as removing missing values, or standardizing the data. |

workflows | Combining model definition, data, and transformations to calculate the estimates and uncertainty. |

We’ll start with the parsnip package. Functions in this package are used to set the details of the model you want to use. Specifically, functions to indicate the model *“type”* (e.g. linear regression) and the `set_engines()`

function to determine the “engine” to run the type (which R-based algorithm to use, like `glm()`

compared to `lm()`

). Check out the Examples page for code you might use depending on the model you want. The most commonly used model types would be `linear_reg()`

, `logistic_reg()`

, and `multinom_reg()`

.

We want to use logistic regression. So, open the `doc/lesson.Rmd`

file and in the `setup`

code chunk add `library(tidymodels)`

, so it looks like:

```
```{r setup}
::tar_config_set(store = here::here("_targets"))
targetslibrary(tidyverse)
library(tidymodels)
source(here::here("R/functions.R"))
<- tar_read(lipidomics)
lipidomics ```
```

Then, **delete** everything below this code chunk.

Since we will be using tidymodels, we need to install it, as well as explicitly add the parsnip, recipes, and workflows packages. Like tidyverse, we need to set tidymodels differently because it is a “meta-package”. We might need to force installing it with `install.packages("tidymodels")`

so renv recognizes it.

```
use_package("tidymodels", "depends")
# install.packages("tidymodels")
use_package("parsnip")
use_package("recipes")
use_package("workflows")
```

Before continuing, let’s **commit** the changes to the Git history. Next, in the `doc/lesson.Rmd`

file, on the bottom of the document create a new header and code chunk:

```
## Building the model
```{r}
```
```

In the new code chunk, we will set up the model specs:

```
log_reg_specs <- logistic_reg() %>%
set_engine("glm")
log_reg_specs
```

```
Logistic Regression Model Specification (classification)
Computational engine: glm
```

Running this on it’s own doesn’t show much, as you can see. But we’ve now set the model we want to use.

## 7.5 Exercise: How would you define a linear regression with parsnip?

Time: ~10 minutes.

Using parsnip’s “Examples” vignette as well as the code we wrote for the logistic regression above as a template, write parsnip code that would define a simple (an engine of`"lm"`

) linear regression model. Begin by making a new Markdown header and code chunk at the bottom of the `doc/lesson.Rmd`

file, like listed below:

```
## Exercises
### Linear regression model definition
```{r}
```
```

After writing the code, run styler (`Ctrl-Shift-P`

, then type “style file”). We will eventually delete these exercise text in the R Markdown file, but for now, commit the changes to the Git history.

**Click for the solution**. Only click if you are struggling or are out of time.

```
linear_reg_specs <- linear_reg() %>%
set_engine("lm")
```

## 7.6 Data transformations specific to modeling

Setting the model type was pretty easy right? The more difficult part comes next with the data transformations. recipes functions are almost entirely used to apply transformations that a model might specifically need, like mean-centering, removing missing values, and other aspects of data processing.

Let’s consider our `lipidomics`

dataset. In order for us to start our statistical analysis, we need the data to be structured in a certain way to be able to smoothly use it as input in our model. We have at least three easy observations on necessary transformations of the data, two of which ca be fixed with a single tidyr function, while the third one can be fixed with recipes. Can you spot them?

`lipidomics`

```
# A tibble: 504 × 6
code gender age class metabolite value
<chr> <chr> <dbl> <chr> <chr> <dbl>
1 ERI109 M 25 CT TMS (interntal standard) 208.
2 ERI109 M 25 CT Cholesterol 19.8
3 ERI109 M 25 CT Lipid CH3- 1 44.1
4 ERI109 M 25 CT Lipid CH3- 2 147.
5 ERI109 M 25 CT Cholesterol 27.2
6 ERI109 M 25 CT Lipid -CH2- 587.
7 ERI109 M 25 CT FA -CH2CH2COO- 31.6
8 ERI109 M 25 CT PUFA 29.0
9 ERI109 M 25 CT Phosphatidylethanolamine 6.78
10 ERI109 M 25 CT Phosphatidycholine 41.7
# … with 494 more rows
```

The first observation isn’t always an issue and depends heavily on the model type you use. Since we are using logistic regression, the model assumes that each row is an individual person. But our data is in the long format, so each person has multiple rows. The second observation is that there seems to be a data input error, since there are three `Cholesterol`

values, while all other metabolites only have one:

```
# A tibble: 36 × 3
code metabolite n
<chr> <chr> <int>
1 ERI109 Cholesterol 3
2 ERI111 Cholesterol 3
3 ERI140 Cholesterol 3
4 ERI142 Cholesterol 3
5 ERI143 Cholesterol 3
6 ERI144 Cholesterol 3
7 ERI145 Cholesterol 3
8 ERI146 Cholesterol 3
9 ERI147 Cholesterol 3
10 ERI149 Cholesterol 3
# … with 26 more rows
```

We can fix both the long format and multiple cholesterol issues by using `tidyr::pivot_wider()`

. Before we do, the last issue is that each metabolite has quite large differences in the values and ranges of data. Again, whether this is an issue depends on what we want to do, but in our research question we want to know how each metabolite influences T1D. In order to best interpret the results and compare across metabolites, we should ideally have all the metabolites with a similar range and distribution of values.

Let’s fix the first two issues first. While we probably only need to use `pivot_wider()`

, we should probably first tidy up the metabolite names first so they make better column names. We do that by combining `mutate()`

with `snakecase::to_snake_case()`

. In the `doc/lesson.Rmd`

file, we rename the metabolite names before using `pivot_wider()`

. Since we want an easy way of identifying columns that are metabolites, we will add a `"metabolite_"`

prefix using the argument `names_prefix`

. To actually fix the multiple cholesterol issue, we should look more into the data documentation or contact the authors. But for this course, we will merge the values by calculating a mean before pivoting. We do this by setting the `values_fn`

with `mean`

.

```
lipidomics_wide <- lipidomics %>%
mutate(metabolite = snakecase::to_snake_case(metabolite)) %>%
pivot_wider(
names_from = metabolite,
values_from = value,
values_fn = mean,
names_prefix = "metabolite_"
)
lipidomics_wide
```

```
# A tibble: 36 × 16
code gender age class metab…¹ metab…² metab…³ metab…⁴ metab…⁵
<chr> <chr> <dbl> <chr> <dbl> <dbl> <dbl> <dbl> <dbl>
1 ERI109 M 25 CT 208. 18.6 44.1 147. 587.
2 ERI111 M 39 CT 219. 20.8 28.1 153. 585.
3 ERI163 W 58 CT 57.1 15.5 75.1 144. 558.
4 ERI375 M 24 CT 19.2 10.2 22.0 220. 606.
5 ERI376 M 26 CT 35.4 13.5 29.5 282. 554.
6 ERI391 M 31 CT 30.4 9.53 38.0 220. 597.
7 ERI392 M 24 CT 21.7 9.87 34.8 215. 607.
8 ERI79 W 26 CT 185. 17.6 109. 153. 546.
9 ERI81 M 52 CT 207. 17.0 49.6 150. 593.
10 ERI83 M 25 CT 322. 19.7 29.9 153. 606.
# … with 26 more rows, 7 more variables:
# metabolite_fa_ch_2_ch_2_coo <dbl>, metabolite_pufa <dbl>,
# metabolite_phosphatidylethanolamine <dbl>,
# metabolite_phosphatidycholine <dbl>,
# metabolite_phospholipids <dbl>, metabolite_mufa_pufa <dbl>,
# metabolite_cd_cl_3_solvent <dbl>, and abbreviated variable
# names ¹metabolite_tms_interntal_standard, …
```

Since we’re using a function-oriented workflow and since we will be using this code again later on, let’s convert both the “metabolite to snakecase” and “pivot to wider” code into their own functions, before moving them over into the `R/functions.R`

file.

```
metabolite_values_to_snakecase <- function(data) {
data %>%
dplyr::mutate(metabolite = snakecase::to_snake_case(metabolite))
}
lipidomics %>%
metabolite_values_to_snakecase()
```

```
# A tibble: 504 × 6
code gender age class metabolite value
<chr> <chr> <dbl> <chr> <chr> <dbl>
1 ERI109 M 25 CT tms_interntal_standard 208.
2 ERI109 M 25 CT cholesterol 19.8
3 ERI109 M 25 CT lipid_ch_3_1 44.1
4 ERI109 M 25 CT lipid_ch_3_2 147.
5 ERI109 M 25 CT cholesterol 27.2
6 ERI109 M 25 CT lipid_ch_2 587.
7 ERI109 M 25 CT fa_ch_2_ch_2_coo 31.6
8 ERI109 M 25 CT pufa 29.0
9 ERI109 M 25 CT phosphatidylethanolamine 6.78
10 ERI109 M 25 CT phosphatidycholine 41.7
# … with 494 more rows
```

This on its own should work. *However*, the column we want to change might not always be called `metabolite`

, or we might want to change it later. So, to make this function a bit more generic, we can use something called “curly-curly” (it looks like `{{}}`

when used) and “non-standard evaluation” (NSE).

We can use curly-curly (combined with `across()`

) to apply `snakecase::to_snake_case()`

to columns of our choice.

```
column_values_to_snakecase <- function(data, cols) {
data %>%
dplyr::mutate(dplyr::across({{ cols }}, snakecase::to_snake_case))
}
lipidomics %>%
column_values_to_snakecase(metabolite)
```

```
# A tibble: 504 × 6
code gender age class metabolite value
<chr> <chr> <dbl> <chr> <chr> <dbl>
1 ERI109 M 25 CT tms_interntal_standard 208.
2 ERI109 M 25 CT cholesterol 19.8
3 ERI109 M 25 CT lipid_ch_3_1 44.1
4 ERI109 M 25 CT lipid_ch_3_2 147.
5 ERI109 M 25 CT cholesterol 27.2
6 ERI109 M 25 CT lipid_ch_2 587.
7 ERI109 M 25 CT fa_ch_2_ch_2_coo 31.6
8 ERI109 M 25 CT pufa 29.0
9 ERI109 M 25 CT phosphatidylethanolamine 6.78
10 ERI109 M 25 CT phosphatidycholine 41.7
# … with 494 more rows
```

Move this new function over into the `R/functions.R`

file, add Roxygen comments (have the cursor inside the function, type `Ctrl-Shift-P`

, then type “roxygen”), run styler (`Ctrl-Shift-P`

, then type “style file”), `source()`

the modified `R/functions.R`

file, and add the new function above the `pivot_wider()`

code in the `doc/lessons.Rmd`

file.

```
#' Convert column value strings into snakecase.
#'
#' @param data Data with string columns.
#' @param cols The column to convert into snakecase.
#'
#' @return A data frame.
#'
column_values_to_snakecase <- function(data, cols) {
data %>%
dplyr::mutate(dplyr::across({{ cols }}, snakecase::to_snake_case))
}
```

## 7.7 Exercise: Convert the pivot code into a function

Time: ~10 minutes.

Just like with the `mutate()`

, take the `pivot_wider()`

code and convert it into a new function.

- Name the new function
`metabolites_to_wider`

. - Include two arguments in the new
`function()`

:`data`

and`values_fn`

. Set the default for`values_fn`

to be`mean`

. We add this argument in case we want to merge the duplicate cholesterol variables with something other than the mean. - Use
`data %>%`

at the beginning, like we did with the`column_values_to_snakecase()`

. Inside the`pivot_wider()`

code, replace`values_fn = mean`

with`values_fn = values_fn`

. - Use
`tidyr::`

before the`pivot_wider()`

function. - Add Roxygen comments (have the cursor inside the function, type
`Ctrl-Shift-P`

, then type “roxygen”). - Move the function into the
`R/functions.R`

file. - Replace the code in the
`doc/lesson.Rmd`

file to make use of the new functions.

**Click for the solution**. Only click if you are struggling or are out of time.

```
#' Convert the metabolite long format into a wider one.
#'
#' @param data The lipidomics dataset.
#' @param values_fn A function to summarize the multiple cholesterol values.
#'
#' @return A wide data frame.
#'
metabolites_to_wider <- function(data, values_fn = mean) {
data %>%
tidyr::pivot_wider(
names_from = metabolite,
values_from = value,
values_fn = values_fn,
names_prefix = "metabolite_"
)
}
```

## 7.8 Using recipes to manage transformations

We’ve used dplyr and tidyr to start fixing some of the issues with the data. But we still have the third issue: How to make the results between metabolites comparable. That’s where we use recipes.

The first function is `recipe()`

and it takes two forms: with or without a formula. Remember the model formula we mentioned previously? Well, here is where we can use it to tell recipes about the model formula we intend to use so it knows on what variables to apply the chosen transformations.

For a few reasons that will be clearer later, we won’t ultimately use the formula form of `recipe()`

, but will show how it works. The

`recipe(class ~ metabolite_cholesterol + age + gender, data = lipidomics_wide)`

```
Recipe
Inputs:
role #variables
outcome 1
predictor 3
```

The alternative approach is to set “roles” using `update_roles()`

. Instead of using a formula and letting `recipe()`

infer the outcome and predictors, we can explicitly select which variables are which. This has some nice features that we will use later on.

```
recipe(lipidomics_wide) %>%
update_role(metabolite_lipid_ch_3_1, age, gender, new_role = "predictor") %>%
update_role(class, new_role = "outcome")
```

```
Recipe
Inputs:
role #variables
outcome 1
predictor 3
12 variables with undeclared roles
```

The next “step” is to select a transformation function.

## 7.9 Exercise: Which transformations make the most sense?

Time: ~15 minutes.

Look at the list of `step_*`

functions below and use the `?`

or F1 (while having the cursor on the function name) to access the help documentation. Consider the metabolite data in the `lipidomics`

dataset. Which of these transformations might you use?

```
recipes::step_log()
recipes::step_scale()
recipes::step_normalize()
recipes::step_center()
recipes::step_sqrt()
```

- With your neighbour (or group), justify which
`step_`

transformation you might use for the numeric metabolite data. - In the last 2 minutes of the exercise, we will all share our thoughts.

## 7.10 Creating a transformation “recipe”

You will use whichever transformation function your group decided on in the exercise above, but for the text of this website, we will use `step_normalize()`

. This function is useful because it makes each variable centered to zero and a value of 1 unit is translated to 1 standard deviation of the original distribution. This means we can more easily compare values between variables. If we add this to the end of the recipe:

```
recipe(lipidomics_wide) %>%
update_role(metabolite_lipid_ch_3_1, age, gender, new_role = "predictor") %>%
update_role(class, new_role = "outcome") %>%
step_normalize(starts_with("metabolite_"))
```

```
Recipe
Inputs:
role #variables
outcome 1
predictor 3
12 variables with undeclared roles
Operations:
Centering and scaling for starts_with("metabolite_")
```

Next thing to do is convert this into a function, using the same workflow we’ve been using (which means this needs to be in the `R/functions.R`

script). We’ll also use the curly-curly again, since we might use a different metabolite later. Note, when adding all the `packagename::`

to each function, the `starts_with()`

function comes from the tidyselect package.

```
#' A transformation recipe to pre-process the data.
#'
#' @param data The lipidomics dataset.
#' @param metabolite_variable The column of the metabolite variable.
#'
#' @return
#'
create_recipe_spec <- function(data, metabolite_variable) {
recipes::recipe(data) %>%
recipes::update_role({{ metabolite_variable }}, age, gender, new_role = "predictor") %>%
recipes::update_role(class, new_role = "outcome") %>%
recipes::step_normalize(tidyselect::starts_with("metabolite_"))
}
```

And test it out:

```
recipe_specs <- lipidomics_wide %>%
create_recipe_spec(metabolite_cholesterol)
recipe_specs
```

```
Recipe
Inputs:
role #variables
outcome 1
predictor 3
12 variables with undeclared roles
Operations:
Centering and scaling for tidyselect::starts_with("metabolite_")
```

Run styler (`Ctrl-Shift-P`

, then type “style file”), then commit the changes made to the Git history.

## 7.11 Fitting the model by combining the recipe, model definition, and data

We’ve now defined the model we want to use and created a transformation recipes specification. Now we can start putting them together and finally fit them to the data. This is done with the workflows package.

Why use this package, rather than simply run the statistical analysis and process the data as normal? When running multiple models (like we will do in the next section) that may require different data structures, the data transformation steps have to happen *right before* the data is fit to the model and need to be done on exactly the data used by the model. So if we have one data frame that we run multiple models on, but the transformation happens to the whole data frame, we could end up with issues due to how the transformations were applied. The workflows package keeps track of those things for us, so we can focus on the higher level thinking rather than on the small details of running the models.

The workflows package has a few main functions for combining the recipe with the model specs, as well as several for updating an existing workflow (which might be useful if you need to run many models of slightly different types). All model workflows need to start with `workflow()`

, followed by two main functions: `add_model()`

and `add_recipe()`

. Can you guess what they do?

```
workflow() %>%
add_model(log_reg_specs) %>%
add_recipe(recipe_specs)
```

```
══ Workflow ════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: logistic_reg()
── Preprocessor ────────────────────────────────────────────────────
1 Recipe Step
• step_normalize()
── Model ───────────────────────────────────────────────────────────
Logistic Regression Model Specification (classification)
Computational engine: glm
```

While this code is already pretty concise, let’s convert it into a function to make it simplified. We’ll use the same function-oriented workflow that we’ve used before, where the function should ultimately be inside the `R/functions.R`

file.

```
#' Create a workflow object of the model and transformations.
#'
#' @param model_specs The model specs
#' @param recipe_specs The recipe specs
#'
#' @return A workflow object
#'
create_model_workflow <- function(model_specs, recipe_specs) {
workflows::workflow() %>%
workflows::add_model(model_specs) %>%
workflows::add_recipe(recipe_specs)
}
```

Instead of using the previously created objects, let’s start the model creation from scratch:

```
model_workflow <- create_model_workflow(
logistic_reg() %>%
set_engine("glm"),
lipidomics_wide %>%
create_recipe_spec(metabolite_cholesterol)
)
model_workflow
```

```
══ Workflow ════════════════════════════════════════════════════════
Preprocessor: Recipe
Model: logistic_reg()
── Preprocessor ────────────────────────────────────────────────────
1 Recipe Step
• step_normalize()
── Model ───────────────────────────────────────────────────────────
Logistic Regression Model Specification (classification)
Computational engine: glm
```

Now, we can do the final thing: Fitting the data to the model with `fit()`

! 🙌

```
══ Workflow [trained] ══════════════════════════════════════════════
Preprocessor: Recipe
Model: logistic_reg()
── Preprocessor ────────────────────────────────────────────────────
1 Recipe Step
• step_normalize()
── Model ───────────────────────────────────────────────────────────
Call: stats::glm(formula = ..y ~ ., family = stats::binomial, data = data)
Coefficients:
(Intercept) genderW
0.1053 -0.7066
age metabolite_cholesterol
0.0069 1.0880
Degrees of Freedom: 35 Total (i.e. Null); 32 Residual
Null Deviance: 49.9
Residual Deviance: 42.8 AIC: 50.8
```

This gives us a lot of information, but what we are mostly interested in is the model estimates themselves. While this `fitted_model`

object contains a lot additional information inside, workflows thankfully has a function to extract the information we want. In this case, it is the `extract_fit_parsnip()`

function.

```
fitted_model %>%
extract_fit_parsnip()
```

```
parsnip model object
Call: stats::glm(formula = ..y ~ ., family = stats::binomial, data = data)
Coefficients:
(Intercept) genderW
0.1053 -0.7066
age metabolite_cholesterol
0.0069 1.0880
Degrees of Freedom: 35 Total (i.e. Null); 32 Residual
Null Deviance: 49.9
Residual Deviance: 42.8 AIC: 50.8
```

To get this information in a tidier format, we use another function: `tidy()`

. This function comes from the broom package, which is part of the tidymodels. But we should explicitly add it to the dependencies:

`use_package("broom")`

Then, we add the `tidy()`

function to our model using the `%>%`

pipe. Since we are using a logistic regression model, we need to consider how we want the estimates to be presented, probably depending on how we want to visualize our results. If we set `exponentiate = TRUE`

in `tidy()`

, the output estimates will be odds ratios, if we set `exponentiate = FALSE`

, we will get the log odds ratios or the beta coefficient. Here we choose `exponentiate = TRUE`

:

```
fitted_model %>%
extract_fit_parsnip() %>%
tidy(exponentiate = TRUE)
```

```
# A tibble: 4 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 1.11 1.29 0.0817 0.935
2 genderW 0.493 0.779 -0.907 0.365
3 age 1.01 0.0377 0.183 0.855
4 metabolite_cholesterol 2.97 0.458 2.38 0.0175
```

We now have a data frame of our model results! Like we did with the `workflows()`

code that we converted into a function, we do the same thing here: Make another function (and move it to `R/functions.R`

)! 😛

```
#' Create a tidy output of the model results.
#'
#' @param workflow_fitted_model The model workflow object that has been fitted.
#'
#' @return A data frame.
#'
tidy_model_output <- function(workflow_fitted_model) {
workflow_fitted_model %>%
workflows::extract_fit_parsnip() %>%
broom::tidy(exponentiate = TRUE)
}
```

Replacing the code in the `doc/lesson.Rmd`

file to use the function.

```
fitted_model %>%
tidy_model_output()
```

```
# A tibble: 4 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 1.11 1.29 0.0817 0.935
2 genderW 0.493 0.779 -0.907 0.365
3 age 1.01 0.0377 0.183 0.855
4 metabolite_cholesterol 2.97 0.458 2.38 0.0175
```

If we revise the code so it is one pipe, it would look like:

```
create_model_workflow(
logistic_reg() %>%
set_engine("glm"),
lipidomics_wide %>%
create_recipe_spec(metabolite_cholesterol)
) %>%
fit(lipidomics_wide) %>%
tidy_model_output()
```

```
# A tibble: 4 × 5
term estimate std.error statistic p.value
<chr> <dbl> <dbl> <dbl> <dbl>
1 (Intercept) 1.11 1.29 0.0817 0.935
2 genderW 0.493 0.779 -0.907 0.365
3 age 1.01 0.0377 0.183 0.855
4 metabolite_cholesterol 2.97 0.458 2.38 0.0175
```

Let’s briefly cover what these columns and values mean.

Before ending, open the Git interface and commit the changes you made. Then push your changes up to GitHub.

## 7.12 Summary

- Create research questions that (ideally) are structured in a way to mimic how the statistical analysis will be done, preferably in a “formula” style like \(y = x1 + x2 + ... + error\) and in a diagram style with links connecting variables.
- Statistical analyses, while requiring some trial and error, are surprisingly structured in the workflow and steps taken. Use this structure to help guide you in completing tasks related to running analyses.
- Use parsnip functions to define the model you want to use, like
`logistic_reg()`

for logistic regression, and set the computational “engine” with`set_engine()`

. - Use recipes functions to set up the data transformation steps necessary to effectively run the statistical analysis, like adding variable “roles” (outcome vs predictor) using
`update_roles()`

and adding transformation steps using any of the dozen different`step_`

functions. - Use workflows functions to develop an analysis
`workflow()`

that combines the defined model with`add_model()`

, the transformation steps with`add_recipe()`

, and the data with`fit()`

. - Use broom to
`tidy()`

the model output, extracted using`extract_fit_parsnip()`

to get a data frame of the estimates and standard error for the variables in the model.