| Type: | Package |
| Title: | Quantile Regression Mixture Models |
| Version: | 0.9.0 |
| Date: | 2017-04-24 |
| Author: | Maria de los Angeles Resa, Birol Emir, Javier Cabrera |
| Maintainer: | Maria de los Angeles Resa <maria@stat.columbia.edu> |
| Description: | Implements the robust algorithm for fitting finite mixture models based on quantile regression proposed by Emir et al., 2017 (unpublished). |
| License: | LGPL-2 | LGPL-2.1 | LGPL-3 [expanded from: LGPL] |
| LazyData: | TRUE |
| Imports: | MASS, quantreg |
| RoxygenNote: | 6.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2017-05-03 17:29:11 UTC; Angeles |
| Repository: | CRAN |
| Date/Publication: | 2017-05-03 21:49:24 UTC |
Tukey's Bisquare Loss
Description
"Bisquare" evaluates Tukey's Bisquare function defined as
f(r) = \left\{
\begin{array}{ll}
1-(1-(\frac{r}{c})^2)^3) & |r| \le c \\
1 & |r| > c
\end{array}
\right.
Usage
Bisquare(r, c = 4.685)
Arguments
r |
a real number or vector. |
c |
a positive number. If the value is negative, it's absolute value will be used. |
Examples
set.seed(1)
x = rnorm(200, mean = 3)
y = Bisquare(x)
plot(x, y)
Huber Loss
Description
Evaluates the Huber loss function defined as
f(r) = \left\{
\begin{array}{ll}
\frac{1}{2}|r|^2 & |r| \le c \\
c(|r|-\frac{1}{2}c) & |r| > c
\end{array}
\right.
Usage
Huber(r, c = 1.345)
Arguments
r |
a real number or vector. |
c |
a positive number. If the value is negative, it's absolute value will be used. |
Examples
set.seed(1)
x = rnorm(200, mean = 1)
y = Huber(x)
plot(x, y)
abline(h = (1.345)^2/2)
Blood Pressure Data for qrmix
Description
Simulated blood pressure data created for usage in qrmix examples.
Usage
blood.pressureFormat
A data frame with 500 observations on the following 7 variables.
bmia numeric vector referring to body mass index
agea numeric vector
systolica numeric vector referring to systolic blood pressure
diastolica numeric vector referring to diastolic blood pressure
gendera factor with levels
femaleandmaleracea factor with levels
white,black, andothersmokinga factor with levels
yesandno
Note
This data does not include any real patient information.
Plot Method for a qrmix Object
Description
Three types of plots (chosen with type) are currently available: density of the response variable by cluster, plots of the response variable against each covariate included in the model (scatterplots with the k fitted lines for continues variables and boxplots by cluster for the categorical variables), and boxplots of the residuals by cluster.
Usage
## S3 method for class 'qrmix'
plot(x, data = NULL, type = c(1,2,3), lwd = 2, bw = "SJ", adjust = 2, ...)
Arguments
x |
a fitted object of class |
data |
the data used to fit the model |
type |
a numeric vector with values chosen from 1:3 to specify a subset of types of plots required. |
lwd |
the line width for the first type of plot (density plot), a positive number. If a negative number is given, |
bw |
the smoothing bandwidth to be used to obtain the density for the first type of plot. See |
adjust |
the bandwidth used is adjust*bw. See |
... |
other argumets passed to other methods. |
Examples
data(blood.pressure)
#qrmix model using default function values:
mod1 = qrmix(bmi ~ ., data = blood.pressure, k = 3)
plot(mod1)
plot(mod1, type = c(1,3), lwd = 1)
Predict Method for qrmix Fits
Description
Obtains clusters, predictions, or residuals from a fitted qrmix object.
Usage
## S3 method for class 'qrmix'
predict(object, newdata = NULL, type = "clusters", ...)
Arguments
object |
a fitted object of class |
newdata |
optional data frame for which clusters, predictions, or residuals will be obtained from the qrmix fitted object. If omitted, the training values will be used. |
type |
the type of prediction. |
... |
other argumets passed to other methods. |
Value
A vector with predicted clusters, responses, or residuals, depending on type.
Examples
data(blood.pressure)
set.seed(8)
sampleInd = sort(sample(1:500, 400))
bpSample1 = blood.pressure[sampleInd,]
bpSample2 = blood.pressure[-sampleInd,]
mod1 = qrmix(bmi ~ ., data = bpSample1, k = 3)
#Cluster assigned to the training values
predict(mod1)
#Residuals corresponding to the response predicted values from mod1 for new data
predict(mod1, newdata = bpSample2, type = "residuals")
Quantile Regression Classification
Description
qrmix estimates the components of a finite mixture model by using quantile regression to select a group of quantiles that satisfy an optimality criteria chosen by the user.
Usage
qrmix(formula, data, k, Ntau=50, alpha=0.03, lossFn="Squared", fitMethod="lm",
xy=TRUE, ...)
Arguments
formula |
an object of class |
data |
an optional data frame that contains the variables in |
k |
number of clusters. |
Ntau |
an optional value that indicates the number of quantiles that will be considered for quantile regression comparison. |
alpha |
an optional value that will determine the minimum separation between the k quantiles that represent each of the k clusters. |
lossFn |
the loss function to be used to select the best combination of k quantiles. The available functions are |
fitMethod |
the method to be used for the final fitting. Use |
xy |
logical. If |
... |
additional arguments to be passed to the function determined in |
Details
The optimality criteria is determined by the lossFn parameter. If, for example, the default value is used (lossFn = "Squared"), the k quantiles selected will minimize the sum of squared residuals. Use "Bisquare" or "Huber" to make the method less sensitive to outliers.
Value
qrmix returns an object of class "qrmix"
coefficients |
a matrix with k columns that represent the coefficients for each cluster. |
clusters |
cluster assignment for each observation. |
quantiles |
the set of k quantiles that minimize the mean loss. |
residuals |
the residuals, response minus fitted values. |
fitted.values |
the fitted values. |
call |
the matched call. |
xy |
the data used if xy is set to |
References
Emir, B., Willke, R. J., Yu, C. R., Zou, K. H., Resa, M. A., and Cabrera, J. (2017), "A Comparison and Integration of Quantile Regression and Finite Mixture Modeling" (submitted).
Examples
data(blood.pressure)
#qrmix model using default function values:
mod1 = qrmix(bmi ~ ., data = blood.pressure, k = 3)
summary(mod1)
#qrmix model using Bisquare loss function and refitted with robust regression:
mod2 = qrmix(bmi ~ age + systolic + diastolic + gender, data = blood.pressure, k = 3,
Ntau = 25, alpha = 0.1, lossFn = "Bisquare", fitMethod = "rlm")
summary(mod2)
Summarizing qrmix Fits
Description
summary method for class "qrmix"
Usage
## S3 method for class 'qrmix'
summary(object, fitMethod=NULL, data=NULL, ...)
Arguments
object |
an object of class |
fitMethod |
an optional refitting method if the user wants a method different than the one used to obtain |
data |
data used to fit |
... |
other argumets passed to other methods. |
Value
residuals |
the residuals, response minus fitted values. |
clusters |
cluster assignment for each observation. |
call |
the matched call. |
fitMethod |
the fitting method used to obtain |
quantiles |
the set of k quantiles that minimize the mean loss. |
clusters# |
generic summary from function |
Examples
data(blood.pressure)
#qrmix model using default function values:
mod1 = qrmix(bmi ~ ., data = blood.pressure, k = 3)
#summary using fitMethod = "rlm" instead of the one used when fitting the model mod1
summary1 = summary(mod1, fitMethod = "rlm")
#Are the quantiles selected in this case the same as in the original model?
summary1$quantiles
mod1$quantiles