models.qmd

---
title: "Models"
editor: source
execute: 
  echo: false
  warning: false
  message: false
---

## Model Definition

A generalized Bayesian linear model using the [stan_glm()](https://mc-stan.org/rstanarm/reference/stan_glm.html) function was used, where the dependent variable is the margin of victory and the independent variable is the point spread (absolute). This model was the byproduct of 8,206 observations.

$$y_i = \beta_0  + \beta_1 x_{1,i} + \epsilon_i$$

with $y = victory\_margin$, $x_1 = spread$, and $\epsilon_i \sim N(0, \sigma^2)$.


```{r}
library(tidyverse)
library(rstanarm)
```

```{r}
# Data files
list_of_files <- list.files(path = "data",
                            recursive = TRUE,
                            pattern = "\\.csv$",
                            full.names = TRUE)  
```

```{r}
# Import data
x <- read_csv(list_of_files, id = "file_name", show_col_types = FALSE) |> 
  janitor::clean_names() |> 
  drop_na() |>
  mutate(date = as.Date(date, "%m/%d/%Y"),
         spread = abs(line)) |> 
  mutate(victory_margin = abs(home_score - visitor_score)) |> 
  select(date, home_team, visitor, home_score, visitor_score, line, spread, victory_margin) |> 
  rename(home = home_team)
```

```{r}
# Model
obj_fit <- stan_glm(data = x,
         formula = victory_margin ~ spread,
         family = gaussian,
         refresh = 0,
         seed = 9)
```


```{r}
gtsummary::tbl_regression(obj_fit)
```