| Title: | Weighted Smooth Backfitting for Structured Models |
|---|---|
| Description: | Non- and semiparametric regression for generalized additive, partial linear, and varying coefficient models as well as their combinations via smoothed backfitting. Based on Roca-Pardinas J and Sperlich S (2010) <doi:10.1007/s11222-009-9130-2>; Mammen E, Linton O and Nielsen J (1999) <doi:10.1214/aos/1017939138>; Lee YK, Mammen E, Park BU (2012) <doi:10.1214/12-AOS1026>. |
| Authors: | Javier Roca-Pardinas [aut, cre], Maria Xose Rodriguez-Alvarez [aut], Stefan Sperlich [aut], Alan Miller (FORTRAN code lsq.f90: weighted least-squares module) [ctb] |
| Maintainer: | Javier Roca-Pardinas <[email protected]> |
| License: | GPL |
| Version: | 1.0-5 |
| Built: | 2024-08-25 06:25:56 UTC |
| Source: | CRAN |
Non- and semiparametric regression for generalized additive, partial linear, and varying coefficient models as well as their combinations. Specifically, the package provides estimation procedures for a large class of regression models common in applied statistics. The regression models belong to the class of the so-called generalized structured models, i.e.,
Note that, up to identification restrictions specified e.g. in Park and Mammen (2006), several of the and can refer to the same variable. For example, all may be the same but all different.
The estimation procedure is based on smoothed backfitting which to our knowledge is the statistically most efficient existing procedure for this model class. Additional weights allow sampling weights, trimming, or efficient estimation under heteroscedasticity. This package also allows to either set the bandwidths or automatically select them using k-fold cross-validation. The option 'offset' facilitates the application of smooth backfitting on aggregated data.
| Package: | wsbackfit |
| Type: | Package |
| Version: | 1.0-5 |
| Date: | 2021-04-30 |
| License: | GPL |
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez, Stefan Sperlich
Maintainer: Javier Roca-Pardinas <[email protected]>
Han, K. and Park B.U. (2018). Smooth backfitting for errors-in-variables additive models. Annals of Statistics, 46, 2216-2250.
Lee, Y.K., Mammen, E. and Park, B.U. (2012). Flexible generalized varying coefficient regression models. The Annals of Statistics, 40(3), 1906-1933.
Mammen, E. and Nielsen, J. (2003). Generalised structured models. Biometrika, 90, 551-566.
Mammen, E. Linton, O. and Nielsen, J. (1999). The existence and asymptotic properties of a backfitting projection algorithm under weak conditions. Annals of Statistics, 27 (5), 1443-1490.
Mammen, E. and Park, B.U. (2006). A simple smooth backfitting method for additive models. Annals of Statistics, 34 (5), 2252-2271.
Nielsen. J. and Sperlich, S. (2005). Smooth backfitting in practice. Journal of the Royal Statistical Society, B, 67, 43-61.
Roca-Pardinas, J. and Sperlich, S. (2010). Feasible Estimation in Generalized Structured Models. Statistics and Computing, 20, 367-379.
Data from a prospective study conducted at the University Hospital of Santiago de Compostela (Spain). A total of 2318 patients who underwent surgery at this center between January 1996 and March 1997 were characterized post-operatively, in respect of whether they suffered or not post-operative infection.
data(infect)data(infect)
A data frame with 2318 observations on the following 6 variables.
agepatient's age.
sexpatient's sex. Coded as 1 = Man and 2 = Woman.
linflymphocytes (expressed as relative counts (in %) of the white blood cell count)
glucplasma glucose concentration (measured in mg/dl)
diabdiabetes. Coded as 1 = presence and 2 = absence.
infvariable indicating whether the patient suffered (inf = 1) or not (inf = 0) a post-operative infection.
data(infect) summary(infect)data(infect) summary(infect)
Takes a fitted object produced by sback() and plots the estimates of the nonparametric functions on the scale of their respective covariates, no matter whether a particular nonparametric function is an additive component or a varying coefficient.
## S3 method for class 'sback' plot(x, composed = TRUE, ask = TRUE, select = NULL, ...)## S3 method for class 'sback' plot(x, composed = TRUE, ask = TRUE, select = NULL, ...)
x |
an object of class |
composed |
a logical value. If |
ask |
a logical value. If |
select |
Allows the plot for a single model term to be selected for printing. e.g. if you just want the plot for the second smooth term set select = 2. |
... |
other graphics parameters to pass on to plotting commands. |
For identifiability purposes, the estimating algorithm implemented in the wsbackfit package decomposes each nonparametric function in two components: a linear (parametric) component and a nonlinear (nonparametric) component. For plotting, the user can choose to plot these components either separately in one graph (composed = FALSE), or to only plot the resulting composed function (composed = TRUE). Also, for the varying coefficient terms, the plots show the estimated surface spanned by .
None
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez and Stefan Sperlich
library(wsbackfit) ################################################ # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.13) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) plot(m0)library(wsbackfit) ################################################ # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.13) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) plot(m0)
Predicted smooth functions and values based on an sback object
## S3 method for class 'sback' predict(object, newdata, newoffset = NULL, ...)## S3 method for class 'sback' predict(object, newdata, newoffset = NULL, ...)
object |
an object of class |
newdata |
a data frame containing the values of the covariates at which predictions are wanted. If not provided then the predictions correspond to the original data. |
newoffset |
an optional numerical vector containing an a priori known component to be included in the linear predictor for the predictions (offset associated with the newdata). |
... |
not yet implemented. |
A list with the following components:
pdata |
the original supplied |
poffset |
the original supplied |
coeff |
a numeric vector with the estimated coefficients. This vector includes both the parametric effects as well as the coefficients associated with the linear component of the nonparametric functions. |
peffects |
matrix with the estimated nonparametric functions (only the nonlinear component) for each covariate value in the original supplied newdata. |
pfitted.values |
a numeric vector with the fitted values for the supplied newdata. |
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez and Stefan Sperlich
library(wsbackfit) data(infect) # Generalized varying coefficient model with binary response m3 <- sback(formula = inf ~ sb(gluc, h = 10) + sb(gluc, by = linf, h = 10), data = infect, family = "binomial", kbin = 15) summary(m3) # Plot both linear and non linear # components of nonparametric functions: composed = FALSE op <- par(no.readonly = TRUE) par(mfrow = c(1,3)) plot(m3, composed = FALSE) # Personalized plots # First obtain predictions in new data # Create newdata for prediction ngrid <- 30 gluc0 <- seq(50, 190, length = ngrid) linf0 <- seq(0, 45, length = ngrid) df <- expand.grid(gluc = gluc0, linf = linf0) m3p <- predict(m3, newdata = df) par(mfrow = c(1,2)) ii <- order(df[,"gluc"]) ## Parametric coefficients names(m3p$coeff) # Nonlinear components colnames(m3p$peffects) # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10)"], type = 'l', xlab = "Glucose (mg/dl)", ylab = "f_1(gluc)", main = "Nonparametric effect of Glucose") # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc:linf"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10, by = linf)"], type= 'l', xlab = "Glucose (mg/dl)", ylab = "f_2(gluc)", main = "Varying coefficients as a function of Glucose") # Countour plot of the probability of post-opererational infection n <- sqrt(nrow(df)) Z <- matrix(m3p$pfitted.values, n, n) filled.contour(z = Z, x = gluc0, y = linf0, xlab = "Glucose (mg/dl)", ylab = "Lymphocytes (%)", main = "Probability of post-opererational infection") par(op)library(wsbackfit) data(infect) # Generalized varying coefficient model with binary response m3 <- sback(formula = inf ~ sb(gluc, h = 10) + sb(gluc, by = linf, h = 10), data = infect, family = "binomial", kbin = 15) summary(m3) # Plot both linear and non linear # components of nonparametric functions: composed = FALSE op <- par(no.readonly = TRUE) par(mfrow = c(1,3)) plot(m3, composed = FALSE) # Personalized plots # First obtain predictions in new data # Create newdata for prediction ngrid <- 30 gluc0 <- seq(50, 190, length = ngrid) linf0 <- seq(0, 45, length = ngrid) df <- expand.grid(gluc = gluc0, linf = linf0) m3p <- predict(m3, newdata = df) par(mfrow = c(1,2)) ii <- order(df[,"gluc"]) ## Parametric coefficients names(m3p$coeff) # Nonlinear components colnames(m3p$peffects) # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10)"], type = 'l', xlab = "Glucose (mg/dl)", ylab = "f_1(gluc)", main = "Nonparametric effect of Glucose") # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc:linf"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10, by = linf)"], type= 'l', xlab = "Glucose (mg/dl)", ylab = "f_2(gluc)", main = "Varying coefficients as a function of Glucose") # Countour plot of the probability of post-opererational infection n <- sqrt(nrow(df)) Z <- matrix(m3p$pfitted.values, n, n) filled.contour(z = Z, x = gluc0, y = linf0, xlab = "Glucose (mg/dl)", ylab = "Lymphocytes (%)", main = "Probability of post-opererational infection") par(op)
sback object.
The default print method for a sback object.
## S3 method for class 'sback' print(x, ...)## S3 method for class 'sback' print(x, ...)
x |
an object of class |
... |
further arguments passed to or from other methods. Not yet implemented. |
None
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez and Stefan Sperlich
sback, summary.sback, plot.sback
library(wsbackfit) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) m0library(wsbackfit) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) m0
Returns residuals for a fitted sback object. Deviance, pearson, working and response residuals are available.
## S3 method for class 'sback' residuals(object, type = c("deviance", "pearson", "working", "response"), ...)## S3 method for class 'sback' residuals(object, type = c("deviance", "pearson", "working", "response"), ...)
object |
an object of class |
type |
the type of residuals which should be returned: "deviance" (default), "pearson", "working" and "response". |
... |
further arguments passed to or from other methods. Not yet implemented. |
For details see residuals.glm.
Numeric vector with the residuals.
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez and Stefan Sperlich
sback, summary.sback, plot.sback.
library(wsbackfit) data(infect) # Generalized varying coefficient model with binary response m3 <- sback(formula = inf ~ sb(gluc, h = 10) + sb(gluc, by = linf, h = 10), data = infect, family = "binomial", kbin = 15) summary(m3) # Deviance summary(residuals(m3)) # Pearson summary(residuals(m3, type = "pearson"))library(wsbackfit) data(infect) # Generalized varying coefficient model with binary response m3 <- sback(formula = inf ~ sb(gluc, h = 10) + sb(gluc, by = linf, h = 10), data = infect, family = "binomial", kbin = 15) summary(m3) # Deviance summary(residuals(m3)) # Pearson summary(residuals(m3, type = "pearson"))
Function used to indicate nonparametric terms and varying coefficient terms in a sback formula.
sb(x1 = NULL, by = NULL, h = -1)sb(x1 = NULL, by = NULL, h = -1)
x1 |
the univariate predictor |
by |
numeric predictor of the same dimension as |
h |
bandwidth (on the scale of the predictor) for this term. If |
A list with the following components:
cov |
character vector with the name(s) of the involved predictor(s). |
h |
numeric value with the specified smoothing parameter. |
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez and Stefan Sperlich
sback, summary.sback, plot.sback
library(wsbackfit) set.seed(123) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) summary(m0) op <- par(no.readonly = TRUE) par(mfrow = c(2,2)) plot(m0) # Fit the model with the bandwidths selected by k-fold cross-validation. m1 <- sback(formula = y ~ x5 + sb(x1, h = -1) + sb(x2, h = -1) + sb(x3, h = -1) + sb(x4, h = -1), kbin = 30, bw.grid = seq(0.01, 0.99, length = 30), data = df) summary(m1) par(mfrow = c(2,2)) plot(m1) par(op)library(wsbackfit) set.seed(123) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) summary(m0) op <- par(no.readonly = TRUE) par(mfrow = c(2,2)) plot(m0) # Fit the model with the bandwidths selected by k-fold cross-validation. m1 <- sback(formula = y ~ x5 + sb(x1, h = -1) + sb(x2, h = -1) + sb(x3, h = -1) + sb(x4, h = -1), kbin = 30, bw.grid = seq(0.01, 0.99, length = 30), data = df) summary(m1) par(mfrow = c(2,2)) plot(m1) par(op)
Main function for fitting generalized structured models by using smooth backfitting.
sback(formula, data, offset = NULL, weights = NULL, kernel = c("Gaussian", "Epanechnikov"), bw.grid = seq(0.01, 0.99, length = 30), c.bw.factor = FALSE, KfoldCV = 5, kbin = 30, family = c("gaussian", "binomial", "poisson"))sback(formula, data, offset = NULL, weights = NULL, kernel = c("Gaussian", "Epanechnikov"), bw.grid = seq(0.01, 0.99, length = 30), c.bw.factor = FALSE, KfoldCV = 5, kbin = 30, family = c("gaussian", "binomial", "poisson"))
formula |
a |
data |
data frame representing the data and containing all needed variables |
offset |
an optional numerical vector containing priori known components to be included in the linear predictor during fitting. Default is zero. |
weights |
an optional numeric vector of ‘prior weights’ to be used in the fitting process. By default, the weights are set to one. |
kernel |
a character specifying the kernel function. Implemented are: Gaussian and Epanechnikov. By default ‘Gaussian’. |
bw.grid |
numeric vector; a grid for for searching the bandwidth factor |
c.bw.factor |
logical; indicates whether the common factor scheme for bandwidth selection proposed by Han and Park (2018) is performed. If TRUE, and provided the user has specified the (marginal) bandwidths for all nonparametric functions, say |
KfoldCV |
number of cross-validation folds to be used for either (1) automatically selecting the optimal bandwidth (in the sequence given in argument |
kbin |
an integer value specifying the number of binning knots. Default is 30. |
family |
a character specifying the distribution family. Implemented are: Gaussian, Binomial and Poisson. In all cases, the link function is the canonical one (logit for binomial, identity for Gaussian and logarithm for Poisson). By default ‘gaussian’. |
The argument formula corresponds to the model for the conditional mean function, i.e.,
This formula is similar to that used for the glm function, except that nonparametric functions can be added to the additive predictor by means of function sb. For instance, specification y ~ x1 + sb(x2, h = -1) assumes a parametric effect of x1 (with x1 either numerical or categorical), and a nonparametric effect of x2. h = -1 indicates that the bandwidth should be selected using k-fold cross-validation. Varying coefficient terms get incorporated similarly. For example, y ~ sb(x1, by = x2) indicates that the coefficients of x2 depend, nonparametrically, on x1. In this case both, x1 and x2, should be numerical predictors.
With respect to the bandwidths associated with each nonparametric function specified using function sb, the user has two options: a) to specify in the formula the desired bandwidth - on the scale of the predictor - through argument h of function sb (followed or not by the common bandwidth factor scheme proposed by Han and Park (2018); see argument c.bw.factor); or, b) to allow the bandwidths to be automatically and data adaptively selected via cross-validation. In the latter case, the estimation procedure tests each of the bandwidth factors supplied in argument bw.grid, and selects the one that minimizes the deviance via (k-fold) cross-validation. The number k of cross-validation folds is specified through argument KfoldCV, with 5 by default. We note that when using cross-validation, to ensure that the bandwidths associated with the nonparametric functions are on the scale of the predictors, the finally used bandwidth is with being the standard deviation of . That is, before fitting the model, each bandwidth factor provided in bw.grid is multiplied by the standard deviation of the corresponding predictor. Note that the user has also the possibility to specify the bandwidths for some nonparametric function (through argument h), while letting for the remaining nonparametric functions the procedure select the bandwidths by cross-validation. For these functions, argument h should be set to -1. In this case, the common bandwidth factor scheme proposed by Han and Park (2018) cannot be used as it requires that all bandwidths are specified.
Finally, it is worth noting that for identifiability purposes, the estimating algorithm implemented in the wsbackfit package decomposes each nonparametric function in two components: a linear (parametric) component and a nonlinear (nonparametric) component. Note that it implies that for a varying coefficient term ~ sb(x1, by = x2), the parametric part includes the linear component associated with x1, as well as the linear interaction between x1 and x2.
A list with the following components:
call |
the matched call. |
formula |
the original supplied |
data |
the original supplied |
offset |
the original supplied |
weights |
the original supplied |
kernel |
the original supplied |
kbin |
the original supplied |
family |
the original supplied |
effects |
matrix with the estimated nonparametric functions (only the nonlinear component) for each covariate value in the original supplied data. |
fitted.values |
a numeric vector with the fitted values for the supplied data. |
residuals |
a numeric vector with the deviance residuals for the supplied data. |
h |
a numeric vector of the same length as the number of nonparametric functions, with the bandwidths actually used in the estimation (scaled. See Details). |
coeff |
a numeric vector with the estimated coefficients. This vector includes both the parametric effects as well as the coefficients associated with the linear component of the nonparametric functions. |
err.CV |
matrix with the cross-validated error (deviance) associated with the sequence of tested (unscaled) bandwidths. Each line corresponds to a particular bandwidth (unscaled. See Details). |
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez and Stefan Sperlich
Han, K. and Park B.U. (2018). Smooth backfitting for errors-in-variables additive models. Annals of Statistics, 46, 2216-2250.
sb, print.sback, summary.sback, plot.sback
library(wsbackfit) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) summary(m0) op <- par(no.readonly = TRUE) par(mfrow = c(2,2)) plot(m0) # Fit the model with bandwidths selectec using K-fold cross-validation ## Not run: m0cv <- sback(formula = y ~ x5 + sb(x1) + sb(x2) + sb(x3) + sb(x4), kbin = 30, bw.grid = seq(0.01, 0.99, length = 30), KfoldCV = 5, data = df) summary(m0cv) par(mfrow = c(2,2)) plot(m0cv) ## End(Not run) # Estimate Variance as a function of x5 (which is binary) resid <- y - m0$fitted.values sig0 <- var(resid[x5 == 0]) sig1 <- var(resid[x5 == 1]) w <- x5/sig1 + (1-x5)/sig0 m1 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), weights = w, kbin = 30, data = df) summary(m1) par(mfrow = c(2,2)) plot(m1) ############################################### # Poisson Simulated Data ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n,-1,1) x2 <- runif(n,-1,1) eta <- 2 + 3*x1^2 + 5*x2^3 exposure <- round(runif(n, 50, 500)) y <- rpois(n, exposure*exp(eta)) df <- data.frame(y = y, x1 = x1, x2 = x2) # Fit the model m2 <- sback(formula = y ~ sb(x1, h = 0.1) + sb(x2, h = 0.1), data = df, offset = log(exposure), kbin = 30, family = "poisson") summary(m2) par(mfrow = c(1,2)) plot(m2) # Dataframe and offset for prediction n.p <- 100 newoffset <- rep(0, n.p) df.pred <- data.frame(x1 = seq(-1, 1,l = n.p), x2 = seq(-1, 1,l = n.p)) m2p <- predict(m2, newdata = df.pred, newoffset = newoffset) ############################################### # Postoperative Infection Data ############################################### data(infect) # Generalized varying coefficient model with binary response m3 <- sback(formula = inf ~ sb(gluc, h = 10) + sb(gluc, by = linf, h = 10), data = infect, family = "binomial", kbin = 15) summary(m3) # Plot both linear and non linear # components of nonparametric functions: composed = FALSE par(mfrow = c(1,3)) plot(m3, composed = FALSE) # Personalized plots # First obtain predictions in new data # Create newdata for prediction ngrid <- 30 gluc0 <- seq(50, 190, length = ngrid) linf0 <- seq(0, 45, length = ngrid) df <- expand.grid(gluc = gluc0, linf = linf0) m3p <- predict(m3, newdata = df) par(mfrow = c(1,2)) ii <- order(df[,"gluc"]) ## Parametric coefficients names(m3p$coeff) # Nonlinear components colnames(m3p$peffects) # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10)"], type = 'l', xlab = "Glucose (mg/dl)", ylab = "f_1(gluc)", main = "Nonparametric effect of Glucose") # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc:linf"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10, by = linf)"], type= 'l', xlab = "Glucose (mg/dl)", ylab = "f_2(gluc)", main = "Varying coefficients as a function of Glucose") # Countour plot of the probability of post-opererational infection n <- sqrt(nrow(df)) Z <- matrix(m3p$pfitted.values, n, n) filled.contour(z = Z, x = gluc0, y = linf0, xlab = "Glucose (mg/dl)", ylab = "Lymphocytes (%)", main = "Probability of post-opererational infection") par(op)library(wsbackfit) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) summary(m0) op <- par(no.readonly = TRUE) par(mfrow = c(2,2)) plot(m0) # Fit the model with bandwidths selectec using K-fold cross-validation ## Not run: m0cv <- sback(formula = y ~ x5 + sb(x1) + sb(x2) + sb(x3) + sb(x4), kbin = 30, bw.grid = seq(0.01, 0.99, length = 30), KfoldCV = 5, data = df) summary(m0cv) par(mfrow = c(2,2)) plot(m0cv) ## End(Not run) # Estimate Variance as a function of x5 (which is binary) resid <- y - m0$fitted.values sig0 <- var(resid[x5 == 0]) sig1 <- var(resid[x5 == 1]) w <- x5/sig1 + (1-x5)/sig0 m1 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.1) + sb(x3, h = 0.1) + sb(x4, h = 0.1), weights = w, kbin = 30, data = df) summary(m1) par(mfrow = c(2,2)) plot(m1) ############################################### # Poisson Simulated Data ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n,-1,1) x2 <- runif(n,-1,1) eta <- 2 + 3*x1^2 + 5*x2^3 exposure <- round(runif(n, 50, 500)) y <- rpois(n, exposure*exp(eta)) df <- data.frame(y = y, x1 = x1, x2 = x2) # Fit the model m2 <- sback(formula = y ~ sb(x1, h = 0.1) + sb(x2, h = 0.1), data = df, offset = log(exposure), kbin = 30, family = "poisson") summary(m2) par(mfrow = c(1,2)) plot(m2) # Dataframe and offset for prediction n.p <- 100 newoffset <- rep(0, n.p) df.pred <- data.frame(x1 = seq(-1, 1,l = n.p), x2 = seq(-1, 1,l = n.p)) m2p <- predict(m2, newdata = df.pred, newoffset = newoffset) ############################################### # Postoperative Infection Data ############################################### data(infect) # Generalized varying coefficient model with binary response m3 <- sback(formula = inf ~ sb(gluc, h = 10) + sb(gluc, by = linf, h = 10), data = infect, family = "binomial", kbin = 15) summary(m3) # Plot both linear and non linear # components of nonparametric functions: composed = FALSE par(mfrow = c(1,3)) plot(m3, composed = FALSE) # Personalized plots # First obtain predictions in new data # Create newdata for prediction ngrid <- 30 gluc0 <- seq(50, 190, length = ngrid) linf0 <- seq(0, 45, length = ngrid) df <- expand.grid(gluc = gluc0, linf = linf0) m3p <- predict(m3, newdata = df) par(mfrow = c(1,2)) ii <- order(df[,"gluc"]) ## Parametric coefficients names(m3p$coeff) # Nonlinear components colnames(m3p$peffects) # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10)"], type = 'l', xlab = "Glucose (mg/dl)", ylab = "f_1(gluc)", main = "Nonparametric effect of Glucose") # Include the linear component plot(df[ii,"gluc"], m3p$coeff[["gluc:linf"]]*df[ii,"gluc"] + m3p$peffects[ii,"sb(gluc, h = 10, by = linf)"], type= 'l', xlab = "Glucose (mg/dl)", ylab = "f_2(gluc)", main = "Varying coefficients as a function of Glucose") # Countour plot of the probability of post-opererational infection n <- sqrt(nrow(df)) Z <- matrix(m3p$pfitted.values, n, n) filled.contour(z = Z, x = gluc0, y = linf0, xlab = "Glucose (mg/dl)", ylab = "Lymphocytes (%)", main = "Probability of post-opererational infection") par(op)
sback fitted object
Takes a fitted object produced by sback() and produces various useful summaries from it.
## S3 method for class 'sback' summary(object, ...)## S3 method for class 'sback' summary(object, ...)
object |
an object of class |
... |
other arguments (not implemented) |
An object of class summary.sback with the information needed to print the results.
Javier Roca-Pardinas, Maria Xose Rodriguez-Alvarez, Stefan Sperlich
library(wsbackfit) set.seed(123) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.13) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) summary(m0)library(wsbackfit) set.seed(123) ############################################### # Gaussian Simulated Sample ############################################### set.seed(123) # Define the data generating process n <- 1000 x1 <- runif(n)*4-2 x2 <- runif(n)*4-2 x3 <- runif(n)*4-2 x4 <- runif(n)*4-2 x5 <- as.numeric(runif(n)>0.6) f1 <- 2*sin(2*x1) f2 <- x2^2 f3 <- 0 f4 <- x4 f5 <- 1.5*x5 mu <- f1 + f2 + f3 + f4 + f5 err <- (0.5 + 0.5*x5)*rnorm(n) y <- mu + err df <- data.frame(x1 = x1, x2 = x2, x3 = x3, x4 = x4, x5 = as.factor(x5), y = y) # Fit the model with a fixed bandwidth for each covariate m0 <- sback(formula = y ~ x5 + sb(x1, h = 0.1) + sb(x2, h = 0.13) + sb(x3, h = 0.1) + sb(x4, h = 0.1), kbin = 30, data = df) summary(m0)