Package 'A3'

Title: Accurate, Adaptable, and Accessible Error Metrics for Predictive Models
Description: Supplies tools for tabulating and analyzing the results of predictive models. The methods employed are applicable to virtually any predictive model and make comparisons between different methodologies straightforward.
Authors: Scott Fortmann-Roe
Maintainer: Scott Fortmann-Roe <scottfr@berkeley.edu>
License: GPL (>= 2)
Version: 1.0.0
Built: 2024-02-04 07:42:41 UTC
Source: CRAN

Help Index


A3 Error Metrics for Predictive Models

Description

A package for the generation of accurate, accessible, and adaptable error metrics for developing high quality predictions and inferences. The name A3 (pronounced "A-Cubed") comes from the combination of the first letters of these three primary adjectives.

Details

The overarching purpose of the outputs and tools in this package are to make the accurate assessment of model errors more accessible to a wider audience. Furthermore, a standardized set of reporting features are provided by this package which create consistent outputs for virtually any predictive model. This makes it straightforward to compare, for instance, a linear regression model to more exotic techniques such as Random forests or Support vector machines.

The standard outputs for each model fit provided by the A3 package include:

The primary functions that will be used are a3 for arbitrary modeling functions and a3.lm for linear models. This package also includes print.A3 and plot.A3 for outputting the A3 results.

Author(s)

Scott Fortmann-Roe scottfr@berkeley.edu http://Scott.Fortmann-Roe.com


A3 Results for Arbitrary Model

Description

This function calculates the A3 results for an arbitrary model construction algorithm (e.g. Linear Regressions, Support Vector Machines or Random Forests). For linear regression models, you may use the a3.lm convenience function.

Usage

a3(formula, data, model.fn, model.args = list(), ...)

Arguments

formula

the regression formula.

data

a data frame containing the data to be used in the model fit.

model.fn

the function to be used to build the model.

model.args

a list of arguments passed to model.fn.

...

additional arguments passed to a3.base.

Value

S3 A3 object; see a3.base for details

References

Scott Fortmann-Roe (2015). Consistent and Clear Reporting of Results from Diverse Modeling Techniques: The A3 Method. Journal of Statistical Software, 66(7), 1-23. <http://www.jstatsoft.org/v66/i07/>

Examples

## Standard linear regression results:

 summary(lm(rating ~ ., attitude))

 ## A3 Results for a Linear Regression model:

 # In practice, p.acc should be <= 0.01 in order
 # to obtain finer grained p values.

 a3(rating ~ ., attitude, lm, p.acc = 0.1)


 ## A3 Results for a Random Forest model:

 # It is important to include the "+0" in the formula
 # to eliminate the constant term.

 require(randomForest)
 a3(rating ~ .+0, attitude, randomForest, p.acc = 0.1)

 # Set the ntrees argument of the randomForest function to 100

 a3(rating ~ .+0, attitude, randomForest, p.acc = 0.1, model.args = list(ntree = 100))

 # Speed up the calculation by doing 5-fold cross-validation.
 # This is faster and more conservative (i.e. it should over-estimate error)

 a3(rating ~ .+0, attitude, randomForest, n.folds = 5, p.acc = 0.1)

 # Use Leave One Out Cross Validation. The least biased approach,
 # but, for large data sets, potentially very slow.

 a3(rating ~ .+0, attitude, randomForest, n.folds = 0, p.acc = 0.1)

 ## Use a Support Vector Machine algorithm.

 # Just calculate the slopes and R^2 values, do not calculate p values.

 require(e1071)
 a3(rating ~ .+0, attitude, svm, p.acc = NULL)

Base A3 Results Calculation

Description

This function calculates the A3 results. Generally this function is not called directly. It is simpler to use a3 (for arbitrary models) or a3.lm (specifically for linear regressions).

Usage

a3.base(formula, data, model.fn, simulate.fn, n.folds = 10,
  data.generating.fn = replicate(ncol(x), a3.gen.default), p.acc = 0.01,
  features = TRUE, slope.sample = NULL, slope.displacement = 1)

Arguments

formula

the regression formula.

data

a data frame containing the data to be used in the model fit.

model.fn

function used to generate a model.

simulate.fn

function used to create the model and generate predictions.

n.folds

the number of folds used for cross-validation. Set to 0 to use Leave One Out Cross Validation.

data.generating.fn

the function used to generate stochastic noise for calculation of exact p values.

p.acc

the desired accuracy for the calculation of exact p values. The entire calculation process will be repeated 1/p.acc1/p.acc times so this can have a dramatic affect on time required. Set to NULL to disable the calculation of p values.

features

whether to calculate the average slopes, added R2R^2 and p values for each of the features in addition to the overall model.

slope.sample

if not NULL the sample size for use to calculate the average slopes (useful for very large data sets).

slope.displacement

the amount of displacement to take in calculating the slopes. May be a single number in which case the same slope is applied to all features. May also be a named vector where there is a name for each feature.

Value

S3 A3 object containing:

model.R2

The cross validated R2R^2 for the entire model.

feature.R2

The cross validated R2R^2's for the features (if calculated).

model.p

The p value for the entire model (if calculated).

feature.p

The p value for the features (if calculated).

all.R2

The R2R^2's for the model features, and any stochastic simulations for calculating exact p values.

observed

The observed response for each observation.

predicted

The predicted response for each observation.

slopes

Average slopes for each of the features (if calculated).

all.slopes

Slopes for each of the observations for each of the features (if calculated).

table

The A3 results table.


Stochastic Data Generators

Description

The stochastic data generators generate stochastic noise with (if specified correctly) the same properties as the observed data. By replicating the stochastic properties of the original data, we are able to obtain the exact calculation of p values.

Usage

a3.gen.default(x, n.reps)

Arguments

x

the original (observed) data series.

n.reps

the number of stochastic repetitions to generate.

Details

Generally these will not be called directly but will instead be passed to the data.generating.fn argument of a3.base.

Value

A list of of length n.reps of vectors of stochastic noise. There are a number of different methods of generating noise:

a3.gen.default

The default data generator. Uses a3.gen.bootstrap.

a3.gen.resample

Reorders the original data series.

a3.gen.bootstrap

Resamples the original data series with replacement.

a3.gen.normal

Calculates the mean and standard deviation of the original series and generates a new series with that distribution.

a3.gen.autocor

Assumesa first order autocorrelation of the original series and generates a new series with the same properties.

Examples

# Calculate the A3 results assuming an auto-correlated set of observations.
 # In usage p.acc should be <=0.01 in order to obtain more accurate p values.

 a3.lm(rating ~ ., attitude, p.acc = 0.1,
   data.generating.fn = replicate(ncol(attitude), a3.gen.autocor))
 

 ## A general illustration:

 # Take x as a sample set of observations for a feature
 x <- c(0.349, 1.845, 2.287, 1.921, 0.803, 0.855, 2.368, 3.023, 2.102, 4.648)

 # Generate three stochastic data series with the same autocorrelation properties as x
 rand.x <- a3.gen.autocor(x, 3)

 plot(x, type="l")
 for(i in 1:3) lines(rand.x[[i]], lwd = 0.2)

A3 for Linear Regressions

Description

This convenience function calculates the A3 results specifically for linear regressions. It uses R's glm function and so supports logistic regressions and other link functions using the family argument. For other forms of models you may use the more general a3 function.

Usage

a3.lm(formula, data, family = gaussian, ...)

Arguments

formula

the regression formula.

data

a data frame containing the data to be used in the model fit.

family

the regression family. Typically 'gaussian' for linear regressions.

...

additional arguments passed to a3.base.

Value

S3 A3 object; see a3.base for details

Examples

## Standard linear regression results:

 summary(lm(rating ~ ., attitude))

 ## A3 linear regression results:

 # In practice, p.acc should be <= 0.01 in order
 # to obtain fine grained p values.

 a3.lm(rating ~ ., attitude, p.acc = 0.1)

 # This is equivalent both to:

 a3(rating ~ ., attitude, glm, model.args = list(family = gaussian), p.acc = 0.1)

 # and also to:

 a3(rating ~ ., attitude, lm, p.acc = 0.1)

Cross-Validated R2R^2

Description

Applies cross validation to obtain the cross-validated R2R^2 for a model: the fraction of the squared error explained by the model compared to the null model (which is defined as the average response). A pseudo R2R^2 is implemented for classification.

Usage

a3.r2(y, x, simulate.fn, cv.folds)

Arguments

y

a vector or responses.

x

a matrix of features.

simulate.fn

a function object that creates a model and predicts y.

cv.folds

the cross-validation folds.

Value

A list comprising of the following elements:

R2

the cross-validated R2R^2

predicted

the predicted responses

observed

the observed responses


Boston Housing Prices

Description

A dataset containing the prices of houses in the Boston region and a number of features. The dataset and the following description is based on that provided by UCI Machine Learning Repository (http://archive.ics.uci.edu/ml/datasets/Housing).

Usage

data(housing)

Details

References

Frank, A. & Asuncion, A. (2010). UCI Machine Learning Repository [http://archive.ics.uci.edu/ml]. Irvine, CA: University of California, School of Information and Computer Science.

Harrison, D. and Rubinfeld, D.L. Hedonic prices and the demand for clean air, J. Environ. Economics & Management, vol.5, 81-102, 1978.


Ecosystem Multifunctionality

Description

This dataset relates multifunctionality to a number of different biotic and abiotic features in a global survey of drylands. The dataset was obtained from (http://www.sciencemag.org/content/335/6065/214/suppl/DC1). The dataset contains the features listed below.

Usage

data(multifunctionality)

Details

References

Maestre, F. T., Quero, J. L., Gotelli, N. J., Escudero, A., Ochoa, V., Delgado-Baquerizo, M., et al. (2012). Plant Species Richness and Ecosystem Multifunctionality in Global Drylands. Science, 335(6065), 214-218. doi:10.1126/science.1215442


Plot A3 Results

Description

Plots an 'A3' object results. Displays predicted versus observed values for each observation along with the distribution of slopes measured for each feature.

Usage

## S3 method for class 'A3'
plot(x, ...)

Arguments

x

an A3 object.

...

additional options provided to plotPredictions, plotSlopes and plot functions.

Examples

data(housing)
 res <- a3.lm(MED.VALUE ~ NOX + ROOMS + AGE + HIGHWAY + PUPIL.TEACHER, housing, p.acc = NULL)
 plot(res)

Plot Predicted versus Observed

Description

Plots an 'A3' object's values showing the predicted versus observed values for each observation.

Usage

plotPredictions(x, show.equality = TRUE, xlab = "Observed Value",
  ylab = "Predicted Value", main = "Predicted vs Observed", ...)

Arguments

x

an A3 object,

show.equality

if true plot a line at 45-degrees.

xlab

the x-axis label.

ylab

the y-axis label.

main

the plot title.

...

additional options provided to the plot function.

Examples

data(multifunctionality)
 x <- a3.lm(MUL ~ ., multifunctionality, p.acc = NULL, features = FALSE)
 plotPredictions(x)

Plot Distribution of Slopes

Description

Plots an 'A3' object's distribution of slopes for each feature and observation. Uses Kernel Density Estimation to create an estimate of the distribution of slopes for a feature.

Usage

plotSlopes(x, ...)

Arguments

x

an A3 object.

...

additional options provided to the plot and density functions.

Examples

require(randomForest)
 data(housing)

 x <- a3(MED.VALUE ~ NOX + PUPIL.TEACHER + ROOMS + AGE + HIGHWAY + 0,
   housing, randomForest, p.acc = NULL, n.folds = 2)

 plotSlopes(x)

Print Fit Results

Description

Prints an 'A3' object results table.

Usage

## S3 method for class 'A3'
print(x, ...)

Arguments

x

an A3 object.

...

additional arguments passed to the print function.

Examples

x <- a3.lm(rating ~ ., attitude, p.acc = NULL)
 print(x)

Nicely Formatted Fit Results

Description

Creates a LaTeX table of results. Depends on the xtable package.

Usage

## S3 method for class 'A3'
xtable(x, ...)

Arguments

x

an A3 object.

...

additional arguments passed to the print.xtable function.

Examples

x <- a3.lm(rating ~ ., attitude, p.acc = NULL)
 xtable(x)