# 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.