aglm: Fit an AGLM model with no cross-validation
In aglm: Accurate Generalized Linear Model
Description
Usage
Arguments
Value
Author(s)
References
Examples
Description
A basic fitting function with given α and λ (s).
See aglm-package for more details on α and λ.
Usage
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aglm(
x,
y,
qualitative_vars_UD_only = NULL,
qualitative_vars_both = NULL,
qualitative_vars_OD_only = NULL,
quantitative_vars = NULL,
use_LVar = FALSE,
extrapolation = "default",
add_linear_columns = TRUE,
add_OD_columns_of_qualitatives = TRUE,
add_interaction_columns = FALSE,
OD_type_of_quantitatives = "C",
nbin.max = NULL,
bins_list = NULL,
bins_names = NULL,
family = c("gaussian", "binomial", "poisson"),
...
)
Arguments
x
A design matrix.
Usually a data.frame object is expected, but a matrix object is fine if all columns are of a same class.
Each column may have one of the following classes, and aglm will automatically determine how to handle it:
-
numeric: interpreted as a quantitative variable. aglm performs discretization by binning, and creates dummy variables suitable for ordered values (named O-dummies/L-variables).
-
factor (unordered) or logical : interpreted as a qualitative variable without order. aglm creates dummy variables suitable for unordered values (named U-dummies).
-
ordered: interpreted as a qualitative variable with order. aglm creates both O-dummies and U-dummies.
These dummy variables are added to x and form a larger matrix, which is used internally as an actual design matrix.
See our paper for more details on O-dummies, U-dummies, and L-variables.
If you need to change the default behavior, use the following options: qualitative_vars_UD_only, qualitative_vars_both, qualitative_vars_OD_only, and quantitative_vars.
y
A response variable.
qualitative_vars_UD_only
Used to change the default behavior of aglm for given variables.
Variables specified by this parameter are considered as qualitative variables and only U-dummies are created as auxiliary columns.
This parameter may have one of the following classes:
-
integer: specifying variables by index.
-
character: specifying variables by name.
qualitative_vars_both
Same as qualitative_vars_UD_only, except that both O-dummies and U-dummies are created for specified variables.
qualitative_vars_OD_only
Same as qualitative_vars_UD_only, except that both only O-dummies are created for specified variables.
quantitative_vars
Same as qualitative_vars_UD_only, except that specified variables are considered as quantitative variables.
use_LVar
Set to use L-variables.
By default, aglm uses O-dummies as the representation of a quantitative variable.
If use_LVar=TRUE, L-variables are used instead.
extrapolation
Used to control values of linear combination for quantitative variables, outside where the data exists.
By default, values of a linear combination outside the data is extended based on the slope of the edges of the region where the data exists.
You can set extrapolation="flat" to get constant values outside the data instead.
add_linear_columns
By default, for quantitative variables, aglm expands them by adding dummies and the original columns, i.e. the linear effects, are remained in the resulting model.
You can set add_linear_columns=FALSE to drop linear effects.
add_OD_columns_of_qualitatives
Set to FALSE if you do not want to use O-dummies for qualitative variables with order (usually, columns with ordered class).
add_interaction_columns
If this parameter is set to TRUE, aglm creates an additional auxiliary variable x_i * x_j for each pair (x_i, x_j) of variables.
OD_type_of_quantitatives
Used to control the shape of linear combinations obtained by O-dummies for quantitative variables (deprecated).
nbin.max
An integer representing the maximum number of bins when aglm perform binning for quantitative variables.
bins_list
Used to set custom bins for variables with O-dummies.
bins_names
Used to set custom bins for variables with O-dummies.
family
A family object or a string representing the type of the error distribution.
Currently aglm supports gaussian, binomial, and poisson.
...
Other arguments are passed directly when calling glmnet().
Value
A model object fitted to the data.
Functions such as predict and plot can be applied to the returned object.
See AccurateGLM-class for more details.
Author(s)
Kenji Kondo,
Kazuhisa Takahashi and Hikari Banno (worked on L-Variable related features)
References
Suguru Fujita, Toyoto Tanaka, Kenji Kondo and Hirokazu Iwasawa. (2020)
AGLM: A Hybrid Modeling Method of GLM and Data Science Techniques,
https://www.institutdesactuaires.com/global/gene/link.php?doc_id=16273&fg=1
Actuarial Colloquium Paris 2020
Examples
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#################### Gaussian case ####################
library(MASS) # For Boston
library(aglm)
## Read data
xy <- Boston # xy is a data.frame to be processed.
colnames(xy)[ncol(xy)] <- "y" # Let medv be the objective variable, y.
## Split data into train and test
n <- nrow(xy) # Sample size.
set.seed(2018) # For reproducibility.
test.id <- sample(n, round(n/4)) # ID numbders for test data.
test <- xy[test.id,] # test is the data.frame for testing.
train <- xy[-test.id,] # train is the data.frame for training.
x <- train[-ncol(xy)]
y <- train$y
newx <- test[-ncol(xy)]
y_true <- test$y
## Fit the model
model <- aglm(x, y) # alpha=1 (the default value)
## Predict for various alpha and lambda
lambda <- 0.1
y_pred <- predict(model, newx=newx, s=lambda)
rmse <- sqrt(mean((y_true - y_pred)^2))
cat(sprintf("RMSE for lambda=%.2f: %.5f \n\n", lambda, rmse))
lambda <- 1.0
y_pred <- predict(model, newx=newx, s=lambda)
rmse <- sqrt(mean((y_true - y_pred)^2))
cat(sprintf("RMSE for lambda=%.2f: %.5f \n\n", lambda, rmse))
alpha <- 0
model <- aglm(x, y, alpha=alpha)
lambda <- 0.1
y_pred <- predict(model, newx=newx, s=lambda)
rmse <- sqrt(mean((y_true - y_pred)^2))
cat(sprintf("RMSE for alpha=%.2f and lambda=%.2f: %.5f \n\n", alpha, lambda, rmse))
#################### Binomial case ####################
library(aglm)
library(faraway)
## Read data
xy <- nes96
## Split data into train and test
n <- nrow(xy) # Sample size.
set.seed(2018) # For reproducibility.
test.id <- sample(n, round(n/5)) # ID numbders for test data.
test <- xy[test.id,] # test is the data.frame for testing.
train <- xy[-test.id,] # train is the data.frame for training.
x <- train[, c("popul", "TVnews", "selfLR", "ClinLR", "DoleLR", "PID", "age", "educ", "income")]
y <- train$vote
newx <- test[, c("popul", "TVnews", "selfLR", "ClinLR", "DoleLR", "PID", "age", "educ", "income")]
## Fit the model
model <- aglm(x, y, family="binomial")
## Make the confusion matrix
lambda <- 0.1
y_true <- test$vote
y_pred <- levels(y_true)[as.integer(predict(model, newx, s=lambda, type="class"))]
print(table(y_true, y_pred))
#################### use_LVar and extrapolation ####################
library(MASS) # For Boston
library(aglm)
## Randomly created train and test data
set.seed(2021)
sd <- 0.2
x <- 2 * runif(1000) + 1
f <- function(x){x^3 - 6 * x^2 + 13 * x}
y <- f(x) + rnorm(1000, sd = sd)
xy <- data.frame(x=x, y=y)
x_test <- seq(0.75, 3.25, length.out=101)
y_test <- f(x_test) + rnorm(101, sd=sd)
xy_test <- data.frame(x=x_test, y=y_test)
## Plot
nbin.max <- 10
models <- c(cv.aglm(x, y, use_LVar=FALSE, extrapolation="default", nbin.max=nbin.max),
cv.aglm(x, y, use_LVar=FALSE, extrapolation="flat", nbin.max=nbin.max),
cv.aglm(x, y, use_LVar=TRUE, extrapolation="default", nbin.max=nbin.max),
cv.aglm(x, y, use_LVar=TRUE, extrapolation="flat", nbin.max=nbin.max))
titles <- c("O-Dummies with extrapolation=\"default\"",
"O-Dummies with extrapolation=\"flat\"",
"L-Variables with extrapolation=\"default\"",
"L-Variables with extrapolation=\"flat\"")
par.old <- par(mfrow=c(2, 2))
for (i in 1:4) {
model <- models[[i]]
title <- titles[[i]]
pred <- predict(model, newx=x_test, s=model@lambda.min, type="response")
plot(x_test, y_test, pch=20, col="grey", main=title)
lines(x_test, f(x_test), lty="dashed", lwd=2) # the theoretical line
lines(x_test, pred, col="blue", lwd=3) # the smoothed line by the model
}
par(par.old)
aglm documentation built on June 9, 2021, 5:08 p.m.
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Note that we can't provide technical support on individual packages. You should contact the package authors for that.
Description Usage Arguments Value Author(s) References Examples
Description
A basic fitting function with given α and λ (s). See aglm-package for more details on α and λ.
Usage
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | aglm(
x,
y,
qualitative_vars_UD_only = NULL,
qualitative_vars_both = NULL,
qualitative_vars_OD_only = NULL,
quantitative_vars = NULL,
use_LVar = FALSE,
extrapolation = "default",
add_linear_columns = TRUE,
add_OD_columns_of_qualitatives = TRUE,
add_interaction_columns = FALSE,
OD_type_of_quantitatives = "C",
nbin.max = NULL,
bins_list = NULL,
bins_names = NULL,
family = c("gaussian", "binomial", "poisson"),
...
)
|
Arguments
x |
A design matrix.
Usually a
These dummy variables are added to If you need to change the default behavior, use the following options: |
y |
A response variable. |
qualitative_vars_UD_only |
Used to change the default behavior of
|
qualitative_vars_both |
Same as |
qualitative_vars_OD_only |
Same as |
quantitative_vars |
Same as |
use_LVar |
Set to use L-variables.
By default, |
extrapolation |
Used to control values of linear combination for quantitative variables, outside where the data exists.
By default, values of a linear combination outside the data is extended based on the slope of the edges of the region where the data exists.
You can set |
add_linear_columns |
By default, for quantitative variables, |
add_OD_columns_of_qualitatives |
Set to |
add_interaction_columns |
If this parameter is set to |
OD_type_of_quantitatives |
Used to control the shape of linear combinations obtained by O-dummies for quantitative variables (deprecated). |
nbin.max |
An integer representing the maximum number of bins when |
bins_list |
Used to set custom bins for variables with O-dummies. |
bins_names |
Used to set custom bins for variables with O-dummies. |
family |
A |
... |
Other arguments are passed directly when calling |
Value
A model object fitted to the data.
Functions such as predict and plot can be applied to the returned object.
See AccurateGLM-class for more details.
Author(s)
Kenji Kondo,
Kazuhisa Takahashi and Hikari Banno (worked on L-Variable related features)
References
Suguru Fujita, Toyoto Tanaka, Kenji Kondo and Hirokazu Iwasawa. (2020)
AGLM: A Hybrid Modeling Method of GLM and Data Science Techniques,
https://www.institutdesactuaires.com/global/gene/link.php?doc_id=16273&fg=1
Actuarial Colloquium Paris 2020
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 | #################### Gaussian case ####################
library(MASS) # For Boston
library(aglm)
## Read data
xy <- Boston # xy is a data.frame to be processed.
colnames(xy)[ncol(xy)] <- "y" # Let medv be the objective variable, y.
## Split data into train and test
n <- nrow(xy) # Sample size.
set.seed(2018) # For reproducibility.
test.id <- sample(n, round(n/4)) # ID numbders for test data.
test <- xy[test.id,] # test is the data.frame for testing.
train <- xy[-test.id,] # train is the data.frame for training.
x <- train[-ncol(xy)]
y <- train$y
newx <- test[-ncol(xy)]
y_true <- test$y
## Fit the model
model <- aglm(x, y) # alpha=1 (the default value)
## Predict for various alpha and lambda
lambda <- 0.1
y_pred <- predict(model, newx=newx, s=lambda)
rmse <- sqrt(mean((y_true - y_pred)^2))
cat(sprintf("RMSE for lambda=%.2f: %.5f \n\n", lambda, rmse))
lambda <- 1.0
y_pred <- predict(model, newx=newx, s=lambda)
rmse <- sqrt(mean((y_true - y_pred)^2))
cat(sprintf("RMSE for lambda=%.2f: %.5f \n\n", lambda, rmse))
alpha <- 0
model <- aglm(x, y, alpha=alpha)
lambda <- 0.1
y_pred <- predict(model, newx=newx, s=lambda)
rmse <- sqrt(mean((y_true - y_pred)^2))
cat(sprintf("RMSE for alpha=%.2f and lambda=%.2f: %.5f \n\n", alpha, lambda, rmse))
#################### Binomial case ####################
library(aglm)
library(faraway)
## Read data
xy <- nes96
## Split data into train and test
n <- nrow(xy) # Sample size.
set.seed(2018) # For reproducibility.
test.id <- sample(n, round(n/5)) # ID numbders for test data.
test <- xy[test.id,] # test is the data.frame for testing.
train <- xy[-test.id,] # train is the data.frame for training.
x <- train[, c("popul", "TVnews", "selfLR", "ClinLR", "DoleLR", "PID", "age", "educ", "income")]
y <- train$vote
newx <- test[, c("popul", "TVnews", "selfLR", "ClinLR", "DoleLR", "PID", "age", "educ", "income")]
## Fit the model
model <- aglm(x, y, family="binomial")
## Make the confusion matrix
lambda <- 0.1
y_true <- test$vote
y_pred <- levels(y_true)[as.integer(predict(model, newx, s=lambda, type="class"))]
print(table(y_true, y_pred))
#################### use_LVar and extrapolation ####################
library(MASS) # For Boston
library(aglm)
## Randomly created train and test data
set.seed(2021)
sd <- 0.2
x <- 2 * runif(1000) + 1
f <- function(x){x^3 - 6 * x^2 + 13 * x}
y <- f(x) + rnorm(1000, sd = sd)
xy <- data.frame(x=x, y=y)
x_test <- seq(0.75, 3.25, length.out=101)
y_test <- f(x_test) + rnorm(101, sd=sd)
xy_test <- data.frame(x=x_test, y=y_test)
## Plot
nbin.max <- 10
models <- c(cv.aglm(x, y, use_LVar=FALSE, extrapolation="default", nbin.max=nbin.max),
cv.aglm(x, y, use_LVar=FALSE, extrapolation="flat", nbin.max=nbin.max),
cv.aglm(x, y, use_LVar=TRUE, extrapolation="default", nbin.max=nbin.max),
cv.aglm(x, y, use_LVar=TRUE, extrapolation="flat", nbin.max=nbin.max))
titles <- c("O-Dummies with extrapolation=\"default\"",
"O-Dummies with extrapolation=\"flat\"",
"L-Variables with extrapolation=\"default\"",
"L-Variables with extrapolation=\"flat\"")
par.old <- par(mfrow=c(2, 2))
for (i in 1:4) {
model <- models[[i]]
title <- titles[[i]]
pred <- predict(model, newx=x_test, s=model@lambda.min, type="response")
plot(x_test, y_test, pch=20, col="grey", main=title)
lines(x_test, f(x_test), lty="dashed", lwd=2) # the theoretical line
lines(x_test, pred, col="blue", lwd=3) # the smoothed line by the model
}
par(par.old)
|
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