---
title: "Introduction to hypr"
author: "Maximilian M. Rabe"
date: "Oct 9th, 2019"
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---

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

## Background

`hypr` is a package for easy translation between experimental (null) hypotheses, hypothesis matrices and contrast matrices, as used for coding factor contrasts in linear regression models. The package can be used to derive contrasts from hypotheses and vice versa.

## Creating a hypr object

The `hypr()` function accepts any set of null hypothesis equations as comma-separated arguments. An empty `hypr` object can be created by calling the function without arguments, i.e. empty parantheses.

```{r}
trtC <- hypr(mu1~0, mu2~mu1, mu3~mu1, mu4~mu1)
```

If you want to provide names for contrasts, you can name the function arguments as follows but this is optional:

```{r}
trtC <- hypr(base = mu0~0, trt1 = mu1~mu0, trt2 = mu2~mu0, trt3 = mu3~mu0)
```


When calling this function, a `hypr` object named `trtC` is generated which contains all four hypotheses from above as well as the hypothesis and contrast matrices derived from those. We can display a summary like any other object in R:

```{r}
trtC
```

As you can see, the level names in `hypr` objects are automatically derived from the hypotheses and sorted alphabetically. You may also provide a different sorting by explicitly providing level names for the `levels` argument:

```{r}
hypr(one~0, two~one, three~one, four~one, levels = c("one", "two", "three", "four"))
```

In the example above, a `hypr` object is created in which the hypothesis and contrast matrices are ordered `one`, `two`, `three`, `four`. If `levels` was not provided, the matrices in the resulting object would be ordered alphabetically, i.e. `four`, `one`, `three`, `two`.

The character vector passed as the `levels` argument must contain all levels named in the hypotheses. If it does not, an error will be thrown. However, it *may* contain level names that are not named in any of the null hypotheses. This will expand the hypothesis and contrast matrices by that level but not affect the coding of the other levels:

```{r}
hypr(one~0, two~one, three~one, four~one, levels = c("one", "two", "three", "four", "five"))
```

## Using and manipulating hypr objects

These properties can also be directly accessed with the appropriate methods:

```{r}
formula(trtC) # a list of equations
levels(trtC) # a vector of corresponding factor levels (variables in equations)
names(trtC) # a vector of corresponding contrast names
hmat(trtC) # the hypothesis matrix
thmat(trtC) # the transposed hypothesis matrix (as displayed in the summary)
cmat(trtC) # the contrast matrix
```

All of these methods can also be used to manipulate `hypr` objects. For example, if you would like to create a `hypr` object from a given contrast matrix, you could create an empty `hypr` object and then update its contrast matrix:

```{r}
otherC <- hypr()
cmat(otherC) <- cbind(int = 1, contr.treatment(4)) # add intercept to treatment contrast
otherC
```

## Deriving contrasts

You can always use `cmat` to derive the complete contrast matrix from a `hypr` object. Note, however, that depending on the contrast scheme used, it might be necessary to remove the intercept contrast from the matrix before assigning it to a factor for regression analysis.

For example, the `trtC` object from above contains such an intercept:

```{r}
cmat(trtC)
```

You can set `remove_intercept=TRUE` to drop the intercept:

```{r}
cmat(trtC, remove_intercept = TRUE)
```

Other contrast coding schemes such as Helmert contrasts do not yield an intercept term:

```{r}
helC <- hypr(m2~m1, m3~(m1+m2)/2, m4~(m1+m2+m3)/3)
cmat(helC)
```

Setting `remove_intercept=TRUE` would throw an error because the function cannot find the intercept column.

```{r, eval=FALSE}
cmat(helC, remove_intercept = TRUE) # throws an error
```

Therefore, when you are unsure whether to set `remove_intercept` to `TRUE` or `FALSE` (default) but would like to use the sensible default of removing an intercept when there is one, you can set `remove_intercept=NULL`. A useful wrapper function which uses this as a default is `contr.hypothesis`:

```{r}
contr.hypothesis(trtC) # removes `base` column
contr.hypothesis(helC) # removes nothing
```

`contr.hypothesis` can also come in handy if you don't really need the `hypr` object but would only like to specify the hypotheses and return the contrast matrix. In that case, you can just use `contr.hypothesis` like the `hypr` function:

```{r}
contr.hypothesis(m1~0, m2~m1, m3~m1)
contr.hypothesis(m2~m1, m3~(m1+m2)/2, m4~(m1+m2+m3)/3)
```