# Accuracy indices

{lvmisc} contains a group of useful functions to compute basic indices of accuracy. These functions can be divided in those which compute element-wise values and those which compute average values:

- Element-wise:
  - `error()`
  - `error_abs()`
  - `error_pct()`
  - `error_abs_pct()`
  - `error_sqr()`
- Average:
  - `mean_error()`
  - `mean_error_abs()`
  - `mean_error_pct()`
  - `mean_error_abs_pct()`
  - `mean_error_sqr()`
  - `mean_error_sqr_root()`
  - `bias()`
  - `loa()`

You may notice that the majority of these functions have common prefixes (`error_` and `mean_error_`), intended to facilitate the use, as most text editors have an auto-complete feature. Also all of the accuracy indices functions take `actual` and `predicted` as arguments, and the functions that return average values have `na.rm = TRUE` in addition.

Let’s now see how each function computes its results

## Element-wise

#### Error: `error()`

It simply subtracts the `predicted` from the `actual` values.

Formula: \[a_i - p_i\]

#### Absolute error: `error_abs()`

It returns the absolute values of the `error()` function.

Formula: \[|a_i - p_i|\]

#### Percent error: `error_pct()`

Divides the error by the `actual` values.

Formula: \[\frac{a_i - p_i}{a_i}\cdot100\]

#### Absolute percent error: `error_abs_pct()`

Returns the absolute values of the `error_pct()` function.

Formula: \[\frac{|a_i - p_i|}{|a_i|}\cdot100\]

#### Squared error: `error_sqr()`

It squares the values of the `error()` function.

Formula: \[(a_i - p_i)^2\]

## Average

#### Mean error: `mean_error()`

It is the average of the error.

Formula: \[\frac{1}{N}\sum_{i = 1}^{N}(a_i - p_i)\]

#### Mean absolute error: `mean_error_abs()`

Computes the average of the absolute error.

Formula: \[\frac{1}{N}\sum_{i = 1}^{N}|a_i - p_i|\]

#### Mean percent error: `mean_error_pct()`

The average of the percent error.

Formula: \[\frac{1}{N}\sum_{i = 1}^{N}\frac{a_i - p_i}{a_i}\cdot100\]

#### Mean absolute percent error: `mean_error_abs_pct()`

It is the average of the absolute percent error.

Formula: \[\frac{1}{N}\sum_{i = 1}^{N}\frac{|a_i - p_i|}{|a_i|}\cdot100\]

#### Mean squared error: `mean_error_sqr()`

Averages the mean squared error.

Formula: \[\frac{1}{N}\sum_{i = 1}^{N}(a_i - p_i)^2\]

#### Root mean squared error: `mean_error_sqr_root()`

It takes the square root of the mean squared error.

Formula: \[\sqrt{\frac{1}{N}\sum_{i = 1}^{N}(a_i - p_i)^2}\]

#### Bias: `bias()`

Alias to `mean_error()`.

#### Limits of agreement: `loa()`

Formula: \[bias \pm 1.96\sigma\]

Where \(\sigma\) is the standard deviation.