Package 'polyreg'

FSR

Description

FSR

Usage

FSR(Xy, max_poly_degree = 3, max_interaction_degree = 2,
  outcome = NULL, linear_estimation = FALSE,
  threshold_include = 0.01, threshold_estimate = 0.001,
  min_models = NULL, max_fails = 2, standardize = FALSE,
  pTraining = 0.8, file_name = NULL, store_fit = "none",
  max_block = 250, noisy = TRUE, seed = NULL)
## S3 method for class 'FSR'
summary(object, estimation_overview = TRUE,
  results_overview = TRUE, model_number = NULL, ...)
## S3 method for class 'FSR'
print(x, ...)

Arguments

Xy	matrix or data.frame; outcome must be in final column. Categorical variables (> 2 levels) should be passed as factors, not dummy variables or integers, to ensure the polynomial matrix is constructed properly.
max_poly_degree	highest power to raise continuous features; default 3 (cubic).
max_interaction_degree	highest interaction order; default 2 (allow x_i*x_j). Also interacts each level of factors with continuous features.
outcome	Treat y as either 'continuous', 'binary', 'multinomial', or NULL (auto-detect based on response).
linear_estimation	Logical: model outcome as linear and estimate with ordinary least squares? Recommended for speed on large datasets even if outcome is categorical. (For multinomial outcome, this means treated response as vector.) If FALSE, estimator chosen based on 'outcome' (i.e., OLS for continuous outcomes, glm() to estimate logistic regression models for 'binary' outcomes, and nnet::multinom() for 'multinomial').
threshold_include	minimum improvement to include a recently added term in the model (change in fit originally on 0 to 1 scale). -1.001 means 'include all'. Default: 0.01. (Adjust R^2 for linear models, Pseudo R^2 for logistic regression, out-of-sample accuracy for multinomial models. In latter two cases, the same adjustment for number of predictors is applied as pseudo-R^2.)
threshold_estimate	minimum improvement to keep estimating (pseudo R^2 so scale 0 to 1). -1.001 means 'estimate all'. Default: 0.001.
min_models	minimum number of models to estimate. Defaults to the number of features (unless P > N).
max_fails	maximum number of models to FSR() can fail on computationally before exiting. Default == 2.
standardize	if TRUE (not default), standardizes continuous variables.
pTraining	portion of data for training
file_name	If a file name (and path) is provided, saves output after each model is estimated as an .RData file. ex: file_name = "results.RData". See also store_fit for options as to how much to store in the outputted object.
store_fit	If file_name is provided, FSR() will return coefficients, measures of fit, and call details. Save entire fit objects? Options include "none" (default, just save those other items), "accepted_only" (only models that meet the threshold), and "all".
max_block	Most of the linear algebra is done recursively in blocks to ease memory managment. Default 250. Changing up or down may slow things...
noisy	display measures of fit, progress, etc. Recommended.
seed	Automatically set but can also be passed as paramater.
estimation_overview	logical: describe how many models were planned, sample size, etc.?
results_overview	logical: give overview of best fit model, etc?
model_number	If non-null, an integer indicating which model to display a summary of.
object	an FSR object, can be used with predict().
x	an FSR object, can be used with print().
...	ignore.

Value

list with slope coefficients, model and estimation details, and measures of fit (object of class 'FSR').

Examples

out <- FSR(mtcars)

---

Get polynomial terms

Description

Generate polynomial terms of predictor variables for a data frame or data matrix.

Usage

getPoly(xdata = NULL, deg = 1, maxInteractDeg = deg,
        Xy = NULL, standardize = FALSE,
        noisy = TRUE, intercept = FALSE, returnDF = TRUE, 
        modelFormula = NULL, retainedNames = NULL, ...)

Arguments

xdata	Data matrix or data frame without response variable. Categorical variables (> 2 levels) should be passed as factors, not dummy variables or integers, to ensure the polynomial matrix is constructed properly.
deg	The max degree of power terms. Default 1 so just returns model matrix by default.
maxInteractDeg	The max degree of nondummy interaction terms. x1 * x2 is degree 2. x1^3 * x2^2 is degree 5. Implicitly constrained by deg. For example, if deg = 3 and maxInteractDegree = 2, x1^1 * x2^2 (i.e., degree 3) will be included but x1^2 * x2^2 (i.e., degree 4) will not.
Xy	The dataframe with the response in the final column (provide xdata or Xy but not both).Categorical variables (> 2 levels) should be passed as factors, not dummy variables or integers, to ensure the polynomial matrix is constructed properly.
standardize	Standardize all continuous variables? (Default: FALSE.)
noisy	Output progress updates? (Default: TRUE.)
intercept	Include intercept? (Default: FALSE.)
returnDF	Return a data.frame (as opposed to model.matrix)? (Default: TRUE.)
modelFormula	Internal use. Formula used to generate the training model matrix. Note: anticipates that polynomial terms are generated using internal functions of library(polyreg). Also, providing modelFormula bypasses deg and maxInteractDeg.
retainedNames	Internal use. colnames of polyMatrix object$xdata. Requires modelFormula be inputted as well.
...	Additional arguments to be passed to model.matrix() via polyreg:::model_matrix(). Note na.action = "na.omit".

Details

The getPoly function takes in a data frame or data matrix and generates polynomial terms of predictor variables.

Note the subtleties involving dummy variables. The square, cubic and so on terms are the same as the original variable, and the various duplicates must be eliminated.

Similarly, after dummy variable are created from a categorical variable having more than two levels, the resulting columns will be orthogonal to each other. In almost all cases, this argument should be set to TRUE at the training stage, and then in predictions one should use the vector of names in the component in the return value; predict.polyFit does the latter automatically.

Note: If a column that is an R factor has levels with spaces in the names, this will interfere with the parsing, and must be avoided.

Value

The return value of getPoly is a polyMatrix object. This is an S3 class containing a model.matrix xdata of the generated polynomial terms. The predictor variables have column names V1, V2, etc. The object also contains modelFormula, the formula used to construct the model matrix, and XtestFormula, the formula which should be used out-of-sample (when y_test is not available).

Examples

N <- 125
rawdata <- data.frame(x1 = rnorm(N), 
                      x2 = rnorm(N),
                      group = sample(letters[1:5], N, replace=TRUE),
                      z = sample(c("treatment", "control"), N, replace=TRUE),
                      result = sample(c("win", "lose", "tie"), N, replace=TRUE))
head(rawdata)

P <- length(levels(rawdata$group)) - 1 + 
     length(levels(rawdata$z)) - 1 + 
     length(levels(rawdata$result)) - 1 + 
     sum(unlist(lapply(rawdata, is.numeric)))

# quadratic polynomial, includes interactions 
# since maxInteractDeg defaults to deg
X <- getPoly(rawdata, 2)$xdata 
ncol(X) # 40

# cubic polynomial, no interactions
X <- getPoly(rawdata, 3, 1)$xdata
ncol(X) # 13

# cubic polynomial, interactions
X <- getPoly(rawdata, 3, 2)$xdata
ncol(X) # 58

# cubic polynomial, interactions
X <- getPoly(rawdata, 3)$xdata
ncol(X) # 101

# making final column the response variable, y
# results in TRUE (fewer columns)
ncol(getPoly(Xy=rawdata, deg=2)$xdata) < ncol(getPoly(rawdata, 2)$xdata)

# preparing polynomial matrices for crossvalidation
# getPoly() returns a polyMatrix() object containing XtestFormula
# which should be used to ensure factors are handled correctly out-of-sample
Xtrain <- getPoly(rawdata[1:100,],2)
Xtest <- getPoly(rawdata[101:125,], 2, modelFormula = Xtrain$XtestFormula)

---

Miscellaneous

Description

Utilities

Usage

toFactors(df,cols)

Arguments

df	A data frame.
cols	A vector of column numbers.

Details

The toFactors function converts each df column in cols to a factor, returns new version of df. Should be used on categorical variables stored as integer codes before calling the library's main functions, including getPoly, FSR, or polyFit.

---

Silicon Valley programmers and engineers data

Description

This data set is adapted from the 2000 Census (5% sample, person records). It is mainly restricted to programmers and engineers in the Silicon Valley area. (Apparently due to errors, there are some from other ZIP codes.)

Has columns for age, education, occupation, gender, wage income and weeks worked. The education column has been collapsed to Master's degree, PhD and other.

The variable codes, e.g. occupational codes, are available from https://usa.ipums.org/usa/volii/occ2000.shtml. (Short code lists are given in the record layout, but longer ones are in the appendix Code Lists.)

Usage

data(pef)

---

Polynomial Fit

Description

Fit polynomial regression using a linear or logistic model; predict new data.

Usage

polyFit(xy, deg, maxInteractDeg=deg, use = "lm", glmMethod="one", 
     return_xy=FALSE, returnPoly=FALSE, noisy=TRUE)
## S3 method for class 'polyFit'
predict(object, newdata, ...)

Arguments

xy	Data frame with response variable in the last column. Latter is numeric, except in the classification case: Categorical variables (> 2 levels) must be passed as factors or character variables if use is 'glm'; an integer vector must be used for the for the 'mvrlm' case, or for the 2-class case (0s and 1s).
deg	The max degree for polynomial terms. A term such as uv, for instance, is considered degree 2.
maxInteractDeg	The max degree of interaction terms.
use	Set to 'lm' for linear regression, 'glm' for logistic regression, or 'mvrlm' for multivariate-response lm.
glmMethod	Defaults to 'one,' meaning the One Versus All Method. Use 'all' for All Versus All.
newdata	Data frame, one row for each "X" to be predicted. Must have the same column names as in xy (without "Y").
object	An item of class 'polyFit' containing output. Can be used with predict().
return_xy	Return data? Default: FALSE
returnPoly	return polyMatrix object? Defaults to FALSE since may be quite large.
noisy	Logical: display messages?
...	Additional arguments for getPoly().

Details

The polyFit function calls getPoly to generate polynomial terms from predictor variables, then fits the generated data to a linear or logistic regression model. (Powers of dummy variables will not be generated, other than degree 1, but interaction terms will calculated.)

When logistic regression for classification is indicated, with more than two classes, All-vs-All or One-vs-All methods, coded 'all' and 'one', can be applied to deal with multiclass problem.

Under the 'mvrlm' option in a classification problem, lm is called with multivariate response, using cbind and dummy variables for class membership as the response. Since predictors are used to form polynomials, this should be a reasonable model, and is much faster than 'glm'.

Value

The return value of polyFit() is an polyFit object. The orginal arguments are retained, along with the fitted models and so on.

The prediction function predict.polyFit returns the predicted value(s) for newdata. It also contains probability for each class as an attribute named prob. In the classification case, these will be the predicted class labels, 1,2,3,...

Examples

N <- 125
xyTrain <- data.frame(x1 = rnorm(N), 
                      x2 = rnorm(N),
                      group = sample(letters[1:5], N, replace=TRUE),
                      score = sample(100, N, replace = TRUE) # final column is y
                      )

pfOut <- polyFit(xyTrain, 2)

# 4 new test points
xTest <- data.frame(x1 = rnorm(4), 
                    x2 = rnorm(4),
                    group = sample(letters[1:5], 4, replace=TRUE))
  
predict(pfOut, xTest) # returns vector of 4 predictions

data(pef)
# predict wageinc
z <- polyFit(pef[,c(setdiff(1:6,5),5)],2)
predict(z,pef[2000,c(setdiff(1:6,5),5)])  # 56934.39
# predict occ
z <- polyFit(pef[,c(setdiff(1:6,3),3)],2,use='glm')
predict(z,pef[2000,c(setdiff(1:6,3),3)])  # '100', probs 0.43, 0.26,...

---

predict.FSR

Description

predict.FSR

Usage

## S3 method for class 'FSR'
predict(object, newdata, model_to_use = NULL,
  standardize = NULL, noisy = TRUE, ...)

Arguments

object	FSR output. Predictions will be made based on object$best_formula unless model_to_use is provided (as an integer).
newdata	New Xdata.
model_to_use	Integer optionally indicating a model to use if object$best_formula is not selected. Example: model_to_use = 3 will use object$models$formula[3].
standardize	Logical–standardize numeric variables? (If NULL, the default, bypasses and decides based on object$standardize.)
noisy	Display output?
...	ignore

Value

y_hat (predictions using chosen model estimates).

Examples

out <- FSR(mtcars[1:30,])
forecast <- predict(out, mtcars[31:nrow(mtcars),])

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Weather Time Series

Description

Various measurements on weather variables collected by NASA. Downloaded via nasapower; see that package for documentation.

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