## Code

```
library(tidyverse)
library(marginaleffects)
library(brms)
library(tidybayes)
library(modelr)
options(
mc.cores = 4,
brms.threads = 4,
brms.backend = "cmdstanr",
brms.file_refit = "on_change"
)
```

statistics

prediction

A post on how to predict values of intercept-only models.

Published

March 18, 2024

I frequently need to calculate a single proportion or single mean with confidence intervals. My preferred way for getting these is to run intercept-only models, such as a logistic regression for proportions and standard regression for means. In this post I show to run these models and obtain the estimates with confidence intervals, using the same workflow from my tutorial blog posts.

Run the following setup code if you want to follow along.

I found some survey data including a question about whether the respondent follows a vegan diet. The relevant column is called `vegan`

and contains a 1 for ‘Yes’ and a 0 for “No”. With this data we can determine the proportion of vegans and the associated confidence interval.

My frequentist approach consists of running a logistic regression using the `glm()`

function. The outcome variable is the `vegan`

column and there are no predictors; only an intercept.

We can use the `predictions()`

function from the marginaleffects package to obtain the proportion. By default, this function calculates the regression-adjusted predicted values for every observation in the original dataset. That’s not what we want; we want only one prediction. We can specify what we want to calculate predictors for using the `newdata`

argument. My preferred way for specifying predictor values is using helper functions like `datagrid()`

. With this function you can specify which predictors you want to include and for which values of each predictor you want to calculate predictions. The problem is that we don’t have any predictors, so what to specify? If we use the `datagrid()`

function from marginaleffects, the answer is nothing.

rowid | estimate | p.value | s.value | conf.low | conf.high | vegan |
---|---|---|---|---|---|---|

1 | 0.0120167 | 0 | 961.5991 | 0.0095016 | 0.0151874 | 0.0120167 |

This gives us the estimate of interest, as well as a 95% confidence interval.

Now let’s do the same thing but using a Bayesian approach, without using the marginaleffects package. Below we run a model using the `brm()`

function from brms.

`Warning: Rows containing NAs were excluded from the model.`

To get predicted values, I’ll use the `data_grid()`

fuction from the modelr package and the `add_epred_draws()`

and `median_qi()`

functions from the tidybayes package. The logic is to specify a data frame using `data_grid()`

with predictor values and then add predicted values using `add_epred_draws()`

to this data frame, which are then summarized using `median_qi()`

. However, if we run the following code, we get an error.

```
Error in `data_grid()`:
! Must supply at least one of `...` and `.model`
```

That’s because the function `data_grid()`

can’t be empty. Using `datagrid()`

from the marginaleffects package also wouldn’t work.

To fix the error, we need to specify the model using the `.model`

argument of the function.

.row | .epred | .lower | .upper | .width | .point | .interval |
---|---|---|---|---|---|---|

1 | 0.0121273 | 0.0095111 | 0.0151626 | 0.95 | median | qi |

That works.

We could also create the data frame ourselves without using `data_grid()`

.

.row | .epred | .lower | .upper | .width | .point | .interval |
---|---|---|---|---|---|---|

1 | 0.0121273 | 0.0095111 | 0.0151626 | 0.95 | median | qi |

But it looks weird to me to create a data frame with 1 row and no values in it (although technically that’s what the data grid functions also do).

You can run intercept-only regression models to obtain estimates of single proportions or means. These estimates, together with their confidence intervals, can be obtained using prediction functions and telling them to predict values from empty data frames, which can be created using helper functions like `datagrid()`

from the marginaleffects package and `data_grid()`

from the modelr package.

*This post was last updated on 2024-03-18.*

```
---
title: "Predicting values of intercept only models"
description: "A post on how to predict values of intercept-only models."
date: 2024-03-18
categories:
- statistics
- prediction
code-fold: show
code-tools: true
toc: true
df-print: kable
---
I frequently need to calculate a single proportion or single mean with confidence intervals. My preferred way for getting these is to run intercept-only models, such as a logistic regression for proportions and standard regression for means. In this post I show to run these models and obtain the estimates with confidence intervals, using the same workflow from my tutorial blog posts.
Run the following setup code if you want to follow along.
```{r}
#| label: setup
#| message: false
library(tidyverse)
library(marginaleffects)
library(brms)
library(tidybayes)
library(modelr)
options(
mc.cores = 4,
brms.threads = 4,
brms.backend = "cmdstanr",
brms.file_refit = "on_change"
)
```
## Data
I found some survey [data](https://doi.org/10.17026/dans-x2z-n2bh) including a question about whether the respondent follows a vegan diet. The relevant column is called `vegan` and contains a 1 for 'Yes' and a 0 for "No". With this data we can determine the proportion of vegans and the associated confidence interval.
```{r}
#| label: data
#| message: false
data <- read_csv("data.csv")
head(data)
```
## Frequentist
My frequentist approach consists of running a logistic regression using the `glm()` function. The outcome variable is the `vegan` column and there are no predictors; only an intercept.
```{r}
#| label: frequentist-model
model <- glm(vegan ~ 1, family = binomial(), data = data)
```
We can use the `predictions()` function from the [marginaleffects](https://marginaleffects.com) package to obtain the proportion. By default, this function calculates the regression-adjusted predicted values for every observation in the original dataset. That's not what we want; we want only one prediction. We can specify what we want to calculate predictors for using the `newdata` argument. My preferred way for specifying predictor values is using helper functions like `datagrid()`. With this function you can specify which predictors you want to include and for which values of each predictor you want to calculate predictions. The problem is that we don't have any predictors, so what to specify? If we use the `datagrid()` function from marginaleffects, the answer is nothing.
```{r}
#| label: frequentist-data-grid
predictions(model, newdata = datagrid())
```
This gives us the estimate of interest, as well as a 95% confidence interval.
## Bayesian
Now let's do the same thing but using a Bayesian approach, without using the marginaleffects package. Below we run a model using the `brm()` function from [brms](https://paul-buerkner.github.io/brms/).
```{r}
#| label: bayesian-model
model <- brm(
vegan ~ 1,
family = bernoulli(link = "logit"),
data = data,
prior = prior(student_t(5, 0, 1.5), class = "Intercept"),
file = "models/model.rds",
silent = 2
)
```
To get predicted values, I'll use the `data_grid()` fuction from the [modelr](https://modelr.tidyverse.org) package and the `add_epred_draws()` and `median_qi()` functions from the [tidybayes](http://mjskay.github.io/tidybayes/) package. The logic is to specify a data frame using `data_grid()` with predictor values and then add predicted values using `add_epred_draws()` to this data frame, which are then summarized using `median_qi()`. However, if we run the following code, we get an error.
```{r}
#| label: bayesian-data-grid-wrong
#| error: true
data_grid() |>
add_epred_draws(model) |>
median_qi()
```
That's because the function `data_grid()` can't be empty. Using `datagrid()` from the marginaleffects package also wouldn't work.
To fix the error, we need to specify the model using the `.model` argument of the function.
```{r}
#| label: bayesian-data-grid
data_grid(.model = model) |>
add_epred_draws(model) |>
median_qi()
```
That works.
We could also create the data frame ourselves without using `data_grid()`.
```{r}
#| label: bayesian-tibble
tibble(.rows = 1) |>
add_epred_draws(model) |>
median_qi()
```
But it looks weird to me to create a data frame with 1 row and no values in it (although technically that's what the data grid functions also do).
## Summary
You can run intercept-only regression models to obtain estimates of single proportions or means. These estimates, together with their confidence intervals, can be obtained using prediction functions and telling them to predict values from empty data frames, which can be created using helper functions like `datagrid()` from the marginaleffects package and `data_grid()` from the modelr package.
*This post was last updated on `r format(Sys.Date(), "%Y-%m-%d")`.*
```