index.Rmd

---
title: "Estimating and plotting generalized Euclidean preference parameters from conjoint data"
output: 
  html_document:
    toc: true
    number_sections: true
date: '2022-12-13'
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
library(knitr)
library(fixest)
library(tidyverse)
library(broom)
```


```{r, message = FALSE}
library(cjEuclid)
```


# Functions

The package has three functions and a wrapper.

## `lm_euclid` 

`lm_euclid`  fits a model with interactions and quadratic terms given a formula. It seeks to return the parameters of a generalized Euclidean model of the form:



For instance:

```{r}

r <- matrix(c(1, .15, .15, 2), 2, 2)
p <- c(.1, .5)

u <- function(butter = 0, guns = 0)
  -(c(butter, guns) - p) %*% r %*% (c(butter, guns) -p)


data <-
 fabricatr::fabricate(N = 100,
                      butter = rnorm(N), 
                      guns = rnorm(N))
data$rating <- sapply(1:nrow(data), function(i) u(data$butter[i], data$guns[i]))



euclid <-  lm_euclid(rating ~ guns + butter, data)

euclid


```
The function simply creates the Euclidian formula and passes it to `fixest`. 

You can provide any additional `fixest` functions you want as additional arguments.


## `euclid_fits`

`euclid_fits` is a simple helper to generate fitted values for a model given specified ranges and length

```{r}

predictions_df <- 
  euclid_fits(formula = rating ~ guns + butter, euclid$model, data, lengths = c(2,3))

predictions_df |> kable(digits = 3)
```


## `euclid_plot`

`euclid_plot` call ggplot to plot the predicted fits and adds ideal points

```{r}

predictions_df <- 
  euclid_fits(formula = rating ~ guns + butter, euclid$model, data, lengths = c(20,20))

euclid_plot(predictions_df, X = "guns", Y = "butter")

```

## `cj_euclid`


 `cj_euclid` wraps these functions and returns a list with the model, the fitted values, and the graph.
 
 

```{r}

euclid <- cj_euclid(rating ~ guns + butter, data)
euclid$graph


```

# Examples

The functions include multiple arguments to allow graphing multiple dimensions.  Here we illustrate plotting 2 dimensions with faceting by a third.

```{r, fig.height = 4, fig.width = 14}

# Data has three dimensions and two observations per subject

library(fabricatr)

data <-
 fabricate(
   ID = add_level(20),
   choice = add_level(2,
                      A = rnorm(N), B = rnorm(N), C = rnorm(N),
                      W = -(A^2 + (B-.3)^2 + (C --.67)^2) + .2*rnorm(N) + .5*A*B))


results <- 
  cj_euclid(W ~ A + B + C,
           fixed_effects = "ID",
           data = data,
           X = "B",
           Y = "C",
           Col = "A",
           mins = c(-2, -2, -2),
           maxs = c(2, 2, 2),
           lengths = c(5, 25, 35),
           y_vals = c("little", "some", "much"),
           x_vals = c("This", "that", "there"))

results
results$graph
```

more `ggplot`ting can be done later:

```{r, fig.height = 3, fig.width = 12}
results$graph + 
  ylab("another label and a flip") + coord_flip() 

```


## 4 d

```{r, eval = TRUE}

# Data has three dimensions and two observations per subject

data <-
 fabricate(
   ID = add_level(20),
   choice = add_level(2,
                      X1 = rnorm(N), X2 = rnorm(N), X3 = rnorm(N), X4 = rnorm(N), 
                      W = -(X1^2 + (X2-.3)^2 + (X3 --.67)^2 + X4^2)  + .2*rnorm(N)))


results <- 
  cj_euclid(W ~ X1 + X2 + X3 + X4,
           fixed_effects = "ID",
           data = data,
           X = "X1",
           Y = "X2",
           Row = "X3",
           Col = "X4",
           mins = c(-2, -1, -2, -2),
           maxs = c(2, 1, 2, 2),
           lengths = c(35, 25, 5, 3),
           y_vals = c("little", "some", "much"),
           x_vals = c("This", "that", "there"))

results$graph
```


## Subgroup plots

Can be done by treating a subgroup as a variable, by stitching multiple plots together, or by running lm_euclid adn cj_Euclid on multiple groups and then applying the plot function with the group as a dimension.


## Example when $A$ is not positive semi definite

```{r}
data <-
 fabricatr::fabricate(N = 40,
                      butter = rnorm(N), 
                      guns = rnorm(N),
                      rating  = -(butter^2 - (guns-.3)^2 + .2*rnorm(N)))

euclid <- cj_euclid(rating ~ guns + butter, data)

euclid

euclid$graph


```