, Silvia Nagib Elian
[ctb, ths]| Title: | Routines for Fit, Inference and Diagnostics in Linear L1 and LAD Models |
|---|---|
| Description: | Diagnostics for linear L1 regression (also known as LAD - Least Absolute Deviations), including: estimation, confidence intervals, tests of hypotheses, measures of leverage, methods of diagnostics for L1 regression, special diagnostics graphs and measures of leverage. The algorithms are based in Dielman (2005) <doi:10.1080/0094965042000223680>, Elian et al. (2000) <doi:10.1080/03610920008832518> and Dodge (1997) <doi:10.1006/jmva.1997.1666>. This package builds on the 'quantreg' package, which is a well-established package for tuning quantile regression models. There are also tests to verify if the errors have a Laplace distribution based on the work of Puig and Stephens (2000) <doi:10.2307/1270952>. |
| Authors: | Kevin Allan Sales Rodrigues [aut, cre]
, Silvia Nagib Elian
[ctb, ths] |
| Maintainer: | Kevin Allan Sales Rodrigues <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 1.0.0 |
| Built: | 2025-01-24 02:55:44 UTC |
| Source: | https://github.com/cran/diagL1 |
A dataset containing lithogenic bile concentrations in 29 Pima Indians. For 29 females, the data give age and percent saturation of bile cholesterol.
data(bile)data(bile)
A data frame with 29 rows and 2 variables.
Age: age in years of each female indian
Concentration: percent saturation of bile cholesterol
Goodall, C. (1983). Examining Residuals. In Hoaglin, D. C., Mosteller, F. and Tukey, J. W. (1983). Understanding Robust and Exploratory Data Analysis. Wiley series in probability and mathematical statistics.
This function can be used to construct standard errors, confidence intervals and tests of hypotheses regarding linear L1 regression models. The bootstrap method used compute xypairs bootstrap for linear L1 regression.
boot_het.regL1(x, y, groups, R = 1000)boot_het.regL1(x, y, groups, R = 1000)
x |
the regression design matrix. |
y |
the regression response vector. |
groups |
vector with the group index associated with the observation, observations with the same index belong to the same group. |
R |
the number of bootstrap replications. |
A list consisting of four elements: a vector of lambda mle estimate for each bootstrap sample and another vector with empirical quantiles. A matrix B of dimension R by p is returned with the R resampled estimates of the vector of L1 linear regression parameters. A matrix U of sampled indices.
boot.rq Bootstrapping Quantile Regression from package quantreg.
set.seed(123) x1 = matrix(rnorm(20), ncol = 2) y1 = x1[, 1] + x1[, 2] + rlaplace(10, 0, 5) x2 = matrix(rnorm(20), ncol = 2) y2 = x2[, 1] + x2[, 2] + rlaplace(10, 0, 10) x3 = matrix(rnorm(20), ncol = 2) y3 = x3[, 1] + x3[, 2] + rlaplace(10, 0, 15) x4 = matrix(rnorm(20), ncol = 2) y4 = x4[, 1] + x4[, 2] + rlaplace(10, 0, 20) x5 = matrix(rnorm(20), ncol = 2) y5 = x5[, 1] + x5[, 2] + rlaplace(10, 0, 30) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,10),rep(2,10),rep(3,10),rep(4,10),rep(5,10)) bt1 = boot_het.regL1(x, y, group_index, 1000) bt1$lambda_mle_hetset.seed(123) x1 = matrix(rnorm(20), ncol = 2) y1 = x1[, 1] + x1[, 2] + rlaplace(10, 0, 5) x2 = matrix(rnorm(20), ncol = 2) y2 = x2[, 1] + x2[, 2] + rlaplace(10, 0, 10) x3 = matrix(rnorm(20), ncol = 2) y3 = x3[, 1] + x3[, 2] + rlaplace(10, 0, 15) x4 = matrix(rnorm(20), ncol = 2) y4 = x4[, 1] + x4[, 2] + rlaplace(10, 0, 20) x5 = matrix(rnorm(20), ncol = 2) y5 = x5[, 1] + x5[, 2] + rlaplace(10, 0, 30) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,10),rep(2,10),rep(3,10),rep(4,10),rep(5,10)) bt1 = boot_het.regL1(x, y, group_index, 1000) bt1$lambda_mle_het
This function can be used to construct standard errors, confidence intervals and tests of hypotheses regarding linear L1 regression models. The bootstrap method used compute xypairs bootstrap for linear L1 regression.
boot.regL1(x, y, R = 1000)boot.regL1(x, y, R = 1000)
x |
the regression design matrix. |
y |
the regression response vector. |
R |
the number of bootstrap replications. |
A list consisting of four elements: a vector of lambda mle estimate for each bootstrap sample and another vector with empirical quantiles. A matrix B of dimension R by p is returned with the R resampled estimates of the vector of L1 linear regression parameters. A matrix U of sampled indices.
boot.rq Bootstrapping Quantile Regression from package quantreg.
data(stackloss) bt1 = boot.regL1(stack.x, stack.loss, 1000) plot(bt1$lambda_mle)data(stackloss) bt1 = boot.regL1(stack.x, stack.loss, 1000) plot(bt1$lambda_mle)
Changing the object's class from "rq" to "regL1" allows you to use functions from the 'diagL1' package normally.
class_to_regL1(object)class_to_regL1(object)
object |
Object from "rq" class. |
Object with class "regL1".
regL1 for fitting linear L1 models.
rq for fitting linear L1 models.
Changing the object's class from "regL1" to "rq" allows you to use functions from the 'quantreg' package normally.
class_to_rq(object)class_to_rq(object)
object |
Object from "regL1" class. |
Object with class "rq".
regL1 for fitting linear L1 models.
rq for fitting linear L1 models.
Calculate Cook Distance
CookDistance(model)CookDistance(model)
model |
Object returned from regL1 representing the fit of the L1 model. |
Cook Distance |
A vector with Cook Distance for each observation. |
.
Sun, R.-B. and Wei, B.-C. (2004). On influence assessment for lad regression. Statistics & Probability Letters, 67, 97-110. doi:10.1016/j.spl.2003.08.018.
set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) CookDistance(mod1)set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) CookDistance(mod1)
Probability density function (PDF) of the Laplace distribution
dlaplace(x, location = 0, scale = 1)dlaplace(x, location = 0, scale = 1)
x |
Values for which to calculate the probability density. |
location |
Location parameter of the Laplace distribution (default = 0). |
scale |
Scale parameter of the Laplace distribution (default = 1). |
Vector of calculated probability densities.
dlaplace(0, 0, 1)dlaplace(0, 0, 1)
F Distance
FD(model, norm = 2)FD(model, norm = 2)
model |
Object returned from regL1 representing the fit of the L1 model. |
norm |
Type of norm, there are two types, 1 (norm L1) and 2 (norm L2). The default is norm L2. |
F Distance |
A vector with F Distance for each observation. |
.
Sun, R.-B. and Wei, B.-C. (2004). On influence assessment for lad regression. Statistics & Probability Letters, 67, 97-110. doi:10.1016/j.spl.2003.08.018.
set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) FD(mod1)set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) FD(mod1)
A dataset containing incidence of fire data for 47 residential areas in Chicago for the year 1975.
data(Fire)data(Fire)
A data frame with 47 rows and 6 variables.
Fire: fires per 1000 housing units
log_Fire: log of variable Fire
Theft: thefts per 1000 residents
Age: percent of housing units built in or before 1940
Income: median family income as a multiple of $1000
Birkes, D.and Dodge, Y. (1993). Alternative Methods of Regression. Jonh Wiley & Sons.
This function applies the forward search approach to robust analysis in linear L1 models. This function is based on function fwdlm of package 'forward'.
forwardSearch_regL1( formula, data, nsamp = "best", intercept = TRUE, trace = TRUE, subset, weights, na.action, method = "br", model = TRUE, contrasts = NULL, ... )forwardSearch_regL1( formula, data, nsamp = "best", intercept = TRUE, trace = TRUE, subset, weights, na.action, method = "br", model = TRUE, contrasts = NULL, ... )
formula |
a formula object, with the response on the left of a ~ operator, and the terms, separated by + operators, on the right. |
data |
a data.frame in which to interpret the variables named in the formula, or in the subset and the weights argument. If this is missing, then the variables in the formula should be on the search list. This may also be a single number to handle some special cases – see below for details. |
nsamp |
the initial subset for the forward search in linear regression is found by fitting the regression model with the R function |
intercept |
logical for the inclusion of the intercept (if no formula is provided). |
trace |
logical, if TRUE a message is printed for every ten iterations completed during the forward search. |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
weights |
vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the absolute residuals. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous. |
na.action |
a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.omit, which deletes observations that contain one or more missing values. |
method |
the algorithmic method used to compute the fit. There are several options: "br", "fn", "pfn", "sfn", "fnc", "conquer", "pfnb", "qfnb", "ppro" and "lasso". See |
model |
if TRUE then the model frame is returned. This is essential if one wants to call summary subsequently. |
contrasts |
a list giving contrasts for some or all of the factors default = NULL appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels. |
... |
additional arguments for the fitting routines (see |
A fitted forward search in linear L1 regression model object.
Atkinson, A.C. and Riani, M. (2000). Robust Diagnostic Regression Analysis. New York: Springer.
# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile)# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile)
Homogeneity of Variance Tests for Linear L1 Models
HV_test(y, x, groups, alpha = 0.05, tolerance = 0.001, max_iteration = 2000)HV_test(y, x, groups, alpha = 0.05, tolerance = 0.001, max_iteration = 2000)
y |
A vector with response variables. |
x |
A matrix with a single explanatory variable. |
groups |
Vector containing the group index to which the observation belongs. |
alpha |
Significance level of the test, must be between 0 and 1. |
tolerance |
threshold that determines when the iterative algorithm should stop (for |
max_iteration |
maximum number of iterations (for |
The 3 statistics to test homogeneity of variance are discussed in Rodrigues (2024), for more details see this reference. In practice, use the HV_LRT statistic results. If possible, use the HV_LRT statistic with a critical value obtained via bootstrap simulation.
A list with results from 3 homogeneity of variance tests
alpha |
alpha argument. |
asymptotic_critical_value |
asymptotic alpha-based test critical value. |
HV_LRT |
LF1 statistic value using MLE (Maximum Likelihood Estimator). |
HV_max_lambda_ratio |
p-value of LF1 statistic using MLE. |
HV_max_log_lambda_ratio |
LF1 statistic value using ROS (Residuals Order Statistics). |
number_of_groups |
number of groups. |
N |
overall sample size. |
lambda_heteroscedastic |
heteroscedastic estimation of the scaling parameters. |
lambda_homocedastic |
homoscedastic estimation of the scale parameter. |
Rodrigues, K. A. S. (2024). Analysis of the adjustment of the L1 regression model. Phd dissertation, University of São Paulo, BR.
set.seed(123) x1 = matrix(rnorm(20), ncol = 1) y1 = x1 + rlaplace(20, 0, 1) x2 = matrix(rnorm(20), ncol = 1) y2 = x2 + rlaplace(20, 0, 1.5) x3 = matrix(rnorm(20), ncol = 1) y3 = x3 + rlaplace(20, 0, 2) x4 = matrix(rnorm(20), ncol = 1) y4 = x4 + rlaplace(20, 0, 2.5) x5 = matrix(rnorm(20), ncol = 1) y5 = x5 + rlaplace(20, 0, 3) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,20),rep(2,20),rep(3,20),rep(4,20),rep(5,20)) # Application of the homogeneity of variance test test_result = HV_test(y, x, group_index) test_resultset.seed(123) x1 = matrix(rnorm(20), ncol = 1) y1 = x1 + rlaplace(20, 0, 1) x2 = matrix(rnorm(20), ncol = 1) y2 = x2 + rlaplace(20, 0, 1.5) x3 = matrix(rnorm(20), ncol = 1) y3 = x3 + rlaplace(20, 0, 2) x4 = matrix(rnorm(20), ncol = 1) y4 = x4 + rlaplace(20, 0, 2.5) x5 = matrix(rnorm(20), ncol = 1) y5 = x5 + rlaplace(20, 0, 3) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,20),rep(2,20),rep(3,20),rep(4,20),rep(5,20)) # Application of the homogeneity of variance test test_result = HV_test(y, x, group_index) test_result
Function to estimate lambda via MLE
lambda_mle(model)lambda_mle(model)
model |
A linear model L1 fitted with the |
lambda MLE (Maximum Likelihood Estimator) estimator.
data(stackloss) model_L1 = regL1(stack.loss ~ stack.x) lambda_mle(model_L1)data(stackloss) model_L1 = regL1(stack.loss ~ stack.x) lambda_mle(model_L1)
Function to compute a robust lambda estimator, which is based on the residuals order statistics.
lambda_ros(model)lambda_ros(model)
model |
A linear model L1 fitted with the |
Robust lambda estimator, which is based on the residuals order statistics.
data(stackloss) model_L1 = regL1(stack.loss ~ stack.x) lambda_ros(model_L1)data(stackloss) model_L1 = regL1(stack.loss ~ stack.x) lambda_ros(model_L1)
This function is a wrapper for the 'laplace.test' function from the 'lawstat' package. The advantage of using this function instead of the 'laplace.test' function of the 'lawstat' package is that this function shows the tables with the critical values of the statistics provided by Puig and Stephens (2000). This makes interpretation of the results easier.
laplace.dist.test(y, print_tables = TRUE)laplace.dist.test(y, print_tables = TRUE)
y |
A numeric vector containing the sample data. |
print_tables |
A boolean variable that indicates whether tables with critical values will be printed or not. |
The result of the laplace.test function.
Puig, P. and Stephens, M. A. (2000). Tests of fit for the Laplace distribution, with applications. Technometrics, 42(4), 417-424. doi:10.2307/1270952.
laplace.test Goodness-of-fit Test Statistics for the Laplace Distribution from package lawstat.
normal_sample = rnorm(100, 0, 10) laplace_sample = rlaplace(100, 0, 10) laplace.dist.test(normal_sample) laplace.dist.test(laplace_sample)normal_sample = rnorm(100, 0, 10) laplace_sample = rlaplace(100, 0, 10) laplace.dist.test(normal_sample) laplace.dist.test(laplace_sample)
Lack of Fit Tests for Linear L1 Models
LF_test(y, x, groups, alpha = 0.05)LF_test(y, x, groups, alpha = 0.05)
y |
A vector with response variables. |
x |
A matrix with a single explanatory variable. |
groups |
Vector containing the group index to which the observation belongs. |
alpha |
Significance level of the test, must be between 0 and 1. |
The 3 statistics to test lack of fit are discussed in Rodrigues (2024), for more details see this reference. In practice, use the LF1_MLE statistic results. These tests were developed with just one explanatory variable in mind, which is why we include an error if there is more than one explanatory variable.
A list with results from 3 lack of fit tests
alpha |
alpha argument. |
critical_value |
alpha-based test critical value. |
LF1_MLE |
LF1 statistic value using MLE (Maximum Likelihood Estimator). |
LF1_MLE |
p-value of LF1 statistic using MLE. |
LF1_ROS |
LF1 statistic value using ROS (Residuals Order Statistics). |
LF2 |
LF2 statistic value. |
modelo_H0 |
model fitted under H0. |
modelo_Ha |
model fitted under Ha. |
MLE |
estimation of the scale parameter of the estimator model via MLE. |
ROS |
estimation of the scale parameter of the estimator model via ROS. |
SAE_H0 |
SAE (Sum of Absolute Errors) of the adjusted model under H0. |
SAE_Ha |
SAE (Sum of Absolute Errors) of the adjusted model under Ha. |
matrix_mean_x |
average of the explanatory variable per group of observations. |
number_of_groups |
number of groups. |
Rodrigues, K. A. S. (2024). Analysis of the adjustment of the L1 regression model. Phd dissertation, University of São Paulo, BR.
set.seed(123) x1 = matrix(rnorm(20), ncol = 1) y1 = x1 + rlaplace(20, 0, 5) x2 = matrix(rnorm(20), ncol = 1) y2 = x2 + rlaplace(20, 1, 5) x3 = matrix(rnorm(20), ncol = 1) y3 = x3 + rlaplace(20, 2, 5) x4 = matrix(rnorm(20), ncol = 1) y4 = x4 + rlaplace(20, 3, 5) x5 = matrix(rnorm(20), ncol = 1) y5 = x5 + rlaplace(20, 4, 5) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,20),rep(2,20),rep(3,20),rep(4,20),rep(5,20)) # Application of the lack of fit test test_result = LF_test(y, x, group_index) test_resultset.seed(123) x1 = matrix(rnorm(20), ncol = 1) y1 = x1 + rlaplace(20, 0, 5) x2 = matrix(rnorm(20), ncol = 1) y2 = x2 + rlaplace(20, 1, 5) x3 = matrix(rnorm(20), ncol = 1) y3 = x3 + rlaplace(20, 2, 5) x4 = matrix(rnorm(20), ncol = 1) y4 = x4 + rlaplace(20, 3, 5) x5 = matrix(rnorm(20), ncol = 1) y5 = x5 + rlaplace(20, 4, 5) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,20),rep(2,20),rep(3,20),rep(4,20),rep(5,20)) # Application of the lack of fit test test_result = LF_test(y, x, group_index) test_result
Calculate Conditional Likelihood Displacement
likelihoodCD(model)likelihoodCD(model)
model |
Object returned from regL1 representing the fit of the L1 model. |
Likelihood Displacement |
A vector with Likelihood Displacement for each observation. |
.
Elian, S. N., André, C. D. S. and Narula, S. C. (2000). Influence Measure for the L1 regression. Communications in Statistics - Theory and Methods, 29(4), 837-849. doi:10.1080/03610920008832518.
set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) likelihoodCD(mod1)set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) likelihoodCD(mod1)
Calculate Likelihood Displacement
likelihoodD(model)likelihoodD(model)
model |
Object returned from regL1 representing the fit of the L1 model. |
Likelihood Displacement |
A vector with Likelihood Displacement for each observation. |
.
Elian, S. N., André, C. D. S. and Narula, S. C. (2000). Influence Measure for the L1 regression. Communications in Statistics - Theory and Methods, 29(4), 837-849. doi:10.1080/03610920008832518.
set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) likelihoodD(mod1)set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x) likelihoodD(mod1)
Predictive Influence Function
PIF(y, x, w, num_cores = 2)PIF(y, x, w, num_cores = 2)
y |
A vector with response variables. |
x |
A matrix with a single explanatory variable. |
w |
Explanatory variables vector for z, usually explanatory variables averages. |
num_cores |
Number of cores you want to use for parallel processing (default = 2). |
Please, install and load the "foreach" package to use this function. For more details see Rodrigues (2024).
A vector with predictive influence function value for each observation.
Rodrigues, K. A. S. (2024). Analysis of the adjustment of the L1 regression model. Phd dissertation, University of São Paulo, BR.
Cumulative distribution function (CDF) of the Laplace distribution
plaplace(q, location = 0, scale = 1)plaplace(q, location = 0, scale = 1)
q |
Values for which to calculate the cumulative distribution. |
location |
Location parameter of the Laplace distribution (default = 0). |
scale |
Scale parameter of the Laplace distribution (default = 1). |
Vector of calculated cumulative distributions.
plaplace(0, 0, 1)plaplace(0, 0, 1)
This function plots the results of a forward search in linear L1 models.
## S3 method for class 'forwardSearch_regL1' plot( x, type.plot = 1:5, squared = FALSE, scaled = FALSE, ylim = NULL, xlim = NULL, th.Res = 2, th.Lev = 0.25, sig.Tst = 2.58, labels.in.plot = TRUE, ... )## S3 method for class 'forwardSearch_regL1' plot( x, type.plot = 1:5, squared = FALSE, scaled = FALSE, ylim = NULL, xlim = NULL, th.Res = 2, th.Lev = 0.25, sig.Tst = 2.58, labels.in.plot = TRUE, ... )
x |
a "forwardSearch_regL1" object. |
type.plot |
select which plots to draw, by default all. Each graph is addressed by an integer:
|
squared |
logical, if TRUE plots squared residuals. |
scaled |
logical, if TRUE plots scaled coefficient estimates. |
ylim |
a two component vector for the min and max of the y axis. |
xlim |
a two component vector for the min and max of the x axis. |
th.Res |
numerical, a threshold for labelling the residuals. |
th.Lev |
numerical, a threshold for labelling the leverages. |
sig.Tst |
numerical, a value (on the scale of the t statistics) used to draw the confidence interval on the plot of the t statistics. |
labels.in.plot |
logical, if TRUE units are labelled in the plots when required. |
... |
additional arguments. |
No return value, just plots the results of a forward search in linear L1 models.
forwardSearch_regL1 for apply forward search in linear L1 regression model.
# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) plot(mod, 1)# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) plot(mod, 1)
Print an object generated by forwardSearch_regL1
## S3 method for class 'forwardSearch_regL1' print(x, ...)## S3 method for class 'forwardSearch_regL1' print(x, ...)
x |
Object returned from forwardSearch_regL1. |
... |
Optional arguments. |
No return value, called for side effects.
forwardSearch_regL1 for apply forward search in linear L1 regression model.
# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) mod # or print(mod)# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) mod # or print(mod)
Print an object generated by regL1
## S3 method for class 'regL1' print(x, ...)## S3 method for class 'regL1' print(x, ...)
x |
Object returned from regL1 representing the fit of the L1 model. |
... |
Optional arguments. |
No return value, called for side effects.
regL1 for fitting linear L1 models.
Print summary of forward search in linear L1 model object.
## S3 method for class 'summary.forwardSearch_regL1' print(x, digits = 4, ...)## S3 method for class 'summary.forwardSearch_regL1' print(x, digits = 4, ...)
x |
This is an object of class " |
digits |
Significant digits reported in the printed table. |
... |
Optional arguments. |
No return value, called for side effects.
forwardSearch_regL1 for apply forward search in linear L1 regression model.
# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) summary(mod)# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) summary(mod)
Print summary of linear L1 regression object.
## S3 method for class 'summary.regL1' print(x, digits = max(5, .Options$digits - 2), ...)## S3 method for class 'summary.regL1' print(x, digits = max(5, .Options$digits - 2), ...)
x |
This is an object of class " |
digits |
Significant digits reported in the printed table. |
... |
Optional arguments. |
No return value, called for side effects.
Quantile function (inverse of the CDF) of the Laplace distribution
qlaplace(p, location = 0, scale = 1)qlaplace(p, location = 0, scale = 1)
p |
Values for which to calculate quantiles. |
location |
Location parameter of the Laplace distribution (default = 0). |
scale |
Scale parameter of the Laplace distribution (default = 1). |
Vector of calculated quantiles.
qlaplace(0.5, 0, 1)qlaplace(0.5, 0, 1)
This function fits an L1 regression model using the rq function from the 'quantreg' package. L1 regression allows dealing with outliers and non-normal distributions in the data.
regL1( formula, data, subset, weights, na.action, method = "br", model = TRUE, contrasts = NULL, ... )regL1( formula, data, subset, weights, na.action, method = "br", model = TRUE, contrasts = NULL, ... )
formula |
a formula object, with the response on the left of a ~ operator, and the terms, separated by + operators, on the right. |
data |
a data.frame in which to interpret the variables named in the formula, or in the subset and the weights argument. If this is missing, then the variables in the formula should be on the search list. This may also be a single number to handle some special cases – see below for details. |
subset |
an optional vector specifying a subset of observations to be used in the fitting process. |
weights |
vector of observation weights; if supplied, the algorithm fits to minimize the sum of the weights multiplied into the absolute residuals. The length of weights must be the same as the number of observations. The weights must be nonnegative and it is strongly recommended that they be strictly positive, since zero weights are ambiguous. |
na.action |
a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.omit, which deletes observations that contain one or more missing values. |
method |
the algorithmic method used to compute the fit. There are several options: "br", "fn", "pfn", "sfn", "fnc", "conquer", "pfnb", "qfnb", "ppro" and "lasso". See |
model |
if TRUE then the model frame is returned. This is essential if one wants to call summary subsequently. |
contrasts |
a list giving contrasts for some or all of the factors default = NULL appearing in the model formula. The elements of the list should have the same name as the variable and should be either a contrast matrix (specifically, any full-rank matrix with as many rows as there are levels in the factor), or else a function to compute such a matrix given the number of levels. |
... |
additional arguments for the fitting routines (see |
L1 regression is an important particular case of quantile regression, so this function inherits from the "rq" class of the quantreg package.
A fitted L1 linear regression model object.
set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x)set.seed(123) x = matrix(rnorm(100), ncol = 2) y = x[, 1] + x[, 2] + rlaplace(50, 0, 5) # Fits a linear regression L1 model mod1 = regL1(y ~ x)
This function fits an groupwise heteroscedastic L1 regression model using the rq function from the 'quantreg' package.
regL1_het( x, y, groups, na.action = stats::na.omit, method = "br", model = TRUE, tolerance = 0.001, max_iteration = 2000, ... )regL1_het( x, y, groups, na.action = stats::na.omit, method = "br", model = TRUE, tolerance = 0.001, max_iteration = 2000, ... )
x |
the regression design matrix. |
y |
the regression response vector. |
groups |
vector with the group index associated with the observation, observations with the same index belong to the same group. |
na.action |
a function to filter missing data. This is applied to the model.frame after any subset argument has been used. The default (with na.fail) is to create an error if any missing values are found. A possible alternative is na.omit, which deletes observations that contain one or more missing values. |
method |
the algorithmic method used to compute the fit. There are several options: "br", "fn", "pfn", "sfn", "fnc", "conquer", "pfnb", "qfnb", "ppro" and "lasso". See |
model |
if TRUE then the model frame is returned. This is essential if one wants to call summary subsequently. |
tolerance |
threshold that determines when the iterative algorithm should stop. |
max_iteration |
maximum number of iterations. |
... |
additional arguments for the fitting routines (see |
L1 regression is an important particular case of quantile regression, so this function inherits from the "rq" class of the quantreg package.
A fitted heteroscedastic L1 linear regression model object.
set.seed(123) x1 = matrix(rnorm(20), ncol = 2) y1 = x1[, 1] + x1[, 2] + rlaplace(10, 0, 5) x2 = matrix(rnorm(20), ncol = 2) y2 = x2[, 1] + x2[, 2] + rlaplace(10, 0, 10) x3 = matrix(rnorm(20), ncol = 2) y3 = x3[, 1] + x3[, 2] + rlaplace(10, 0, 15) x4 = matrix(rnorm(20), ncol = 2) y4 = x4[, 1] + x4[, 2] + rlaplace(10, 0, 20) x5 = matrix(rnorm(20), ncol = 2) y5 = x5[, 1] + x5[, 2] + rlaplace(10, 0, 30) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,10),rep(2,10),rep(3,10),rep(4,10),rep(5,10)) # Fits a heteroscedastic linear regression L1 model mod1 = regL1_het(x, y, group_index)set.seed(123) x1 = matrix(rnorm(20), ncol = 2) y1 = x1[, 1] + x1[, 2] + rlaplace(10, 0, 5) x2 = matrix(rnorm(20), ncol = 2) y2 = x2[, 1] + x2[, 2] + rlaplace(10, 0, 10) x3 = matrix(rnorm(20), ncol = 2) y3 = x3[, 1] + x3[, 2] + rlaplace(10, 0, 15) x4 = matrix(rnorm(20), ncol = 2) y4 = x4[, 1] + x4[, 2] + rlaplace(10, 0, 20) x5 = matrix(rnorm(20), ncol = 2) y5 = x5[, 1] + x5[, 2] + rlaplace(10, 0, 30) y = c(y1, y2, y3, y4, y5) x = rbind(x1, x2, x3, x4, x5) group_index = c(rep(1,10),rep(2,10),rep(3,10),rep(4,10),rep(5,10)) # Fits a heteroscedastic linear regression L1 model mod1 = regL1_het(x, y, group_index)
Function to generate random values from the Laplace distribution
rlaplace(n, location = 0, scale = 1)rlaplace(n, location = 0, scale = 1)
n |
Number of values to generate. |
location |
Location parameter of the Laplace distribution (default = 0). |
scale |
Scale parameter of the Laplace distribution (default = 1). |
Vector of generated random values.
rlaplace(10, 0, 1)rlaplace(10, 0, 1)
Function to calculate SAE (Sum of Absolute Errors) of the adjusted model.
SAE(model)SAE(model)
model |
A linear model L1 fitted with the |
SAE (Sum of Absolute Errors).
data(stackloss) model_L1 = regL1(stack.loss ~ stack.x) SAE(model_L1)data(stackloss) model_L1 = regL1(stack.loss ~ stack.x) SAE(model_L1)
Returns a summary list for a forward search in linear L1 regression fit.
## S3 method for class 'forwardSearch_regL1' summary(object, steps = "auto", ...)## S3 method for class 'forwardSearch_regL1' summary(object, steps = "auto", ...)
object |
Object returned from forwardSearch_regL1. |
steps |
the number of forward steps to show. |
... |
Optional arguments. |
No return value, called for side effects.
Atkinson, A.C. and Riani, M. (2000). Robust Diagnostic Regression Analysis. New York: Springer.
forwardSearch_regL1 for apply forward search in linear L1 regression model.
# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) summary(mod)# applies the forward search approach to robust analysis in a linear L1 model mod = forwardSearch_regL1(Concentration ~ Age, data = bile) summary(mod)
Returns a summary list for a L1 regression fit. A null value will be returned if printing is invoked.
## S3 method for class 'regL1' summary( object, se = NULL, covariance = FALSE, hs = TRUE, U = NULL, gamma = 0.7, ... )## S3 method for class 'regL1' summary( object, se = NULL, covariance = FALSE, hs = TRUE, U = NULL, gamma = 0.7, ... )
object |
Object returned from regL1 representing the fit of the L1 model. |
se |
specifies the method used to compute standard standard errors. There are currently seven available methods: "rank", "iid", "nid", "ker", "boot", "BLB", "conquer" and "extreme". |
covariance |
logical flag to indicate whether the full covariance matrix of the estimated parameters should be returned. |
hs |
Use Hall Sheather bandwidth for sparsity estimation If false revert to Bofinger bandwidth. |
U |
Resampling indices or gradient evaluations used for bootstrap, see |
gamma |
parameter controlling the effective sample size of the'bag of little bootstrap samples that will be b = n^gamma where n is the sample size of the original model. |
... |
Optional arguments. See |
No return value, called for side effects.
regL1 for fitting linear L1 models.
summary.rq summary methods for Quantile Regression.