---
title: "initial_parameters"
output: rmarkdown::html_vignette
vignette: >
  %\VignetteIndexEntry{initial_parameters}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

```{r, include = FALSE}
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

## Without providing initial parameters

If the function to fit (`fun` argument) is one of the predefined functions (`cum_normal_fun`, `logistic_fun` or `weibull_fun`), `quickpsy` calculates the initials parameters for you

```{r fig.height=2, fig.width=6}
library(quickpsy)

fit <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"),
                fun = logistic_fun, 
                bootstrap = "none") 

plot(fit)
```

## A vector initial parameters

The initial parameters could be a vector 

```{r fig.height=2, fig.width=6}
library(quickpsy)

fit <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"),
                parini = c(-100, 70), # the default function is cum_normal_fun
                bootstrap = "none") 

plot(fit)
```

## A list of initial parameters

The initial parameters could be a list in which each component constraints the lower and upper bounds of the parameter (for example, `list(c(par1min, par1max), c(par2min, par2max))`)

```{r fig.height=2, fig.width=6}
library(quickpsy)

fit <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"),
                parini = list(c(-300, 300), c(10, 200)),
                bootstrap = "none") 

plot(fit)
```
In addition of the upper and lower bound, you can also specify the initial guess of the parameters

```{r fig.height=2, fig.width=6}
library(quickpsy)

fit <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"),
                parini = list(c(-300, 300), c(10, 200)),
                parinivector = c(-100, 70), 
                bootstrap = "none") 

plot(fit)
```

## A dataframe of initial parameters

The initial parameters could be a dataframe specifiying the initial parameters for each condition. It should have the same structure that the component `par` of quickpsy. It is up to you how to build this dataframe. For example:

```{r, message=FALSE}
library(dplyr)
library(tidyr) 

participants <- qpdat %>% distinct(participant)
conditions <- qpdat %>% distinct(cond)

parini <- conditions %>% 
  crossing(participants) %>% 
  crossing(tibble(parn = c("p1", "p2"))) %>% 
  arrange(cond) %>% 
  bind_cols(tibble(par = c(rep(c(-100, 70), 3), 
                           rep(c(-150, 100), 3))))
parini
```

```{r fig.height=2, fig.width=6}
fit <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"),
                parini = parini, bootstrap = "none")

plot(fit) 
```

The dataframe could also contain the constraints of the parameters

```{r}
parini <- conditions %>% 
  crossing(participants) %>% 
  crossing(tibble(parn = c("p1", "p2"))) %>% 
  arrange(cond) %>% 
  bind_cols(tibble(parmin = c(rep(c(-300, 10), 3), 
                         rep(c(-500, 5), 3)),
                   parmax = c(rep(c(300, 200), 3), 
                         rep(c(500, 400), 3))))
parini
```
## Data frame of functions (dev version of quickpsy)

When the `fun` argument is a data frame of functions, you should specify all the parameters included in the functions 


```{r fig.height=2, fig.width=6, message=FALSE}
library(dplyr)

fun_df <- tibble(cond = c("cond1", "cond2"), 
                 fun = c(function(x, p) (1 + exp(-p[2] * (x - p[1])))^(-1), 
                         function(x, p) (1 + exp(-p[2] * (x - p[3])))^(-1)))

fit <- quickpsy(qpdat, phase, resp, grouping = c("participant", "cond"), 
                fun = fun_df, # shared slope parameter
                parini = c(-100, 0.02, -100), 
                bootstrap = "none") 

plot(fit, color = cond)
```