Kernel Modal Regression with Mixed Data Types

npconmode performs kernel modal regression on mixed data, and finds the conditional mode given a set of training data, consisting of explanatory data and dependent data, and possibly evaluation data. Automatically computes various in sample and out of sample measures of accuracy.

Usage

npconmode(bws, ...)

# S3 method for class 'formula'
npconmode(bws, data = NULL, newdata = NULL, ...)

# S3 method for class 'call'
npconmode(bws, ...)

# Default S3 method
npconmode(bws, txdat, tydat, ...)

# S3 method for class 'conbandwidth'
npconmode(bws,
          txdat = stop("invoked without training data 'txdat'"),
          tydat = stop("invoked without training data 'tydat'"),
          exdat,
          eydat,
          ...)

Arguments

bws: a bandwidth specification. This can be set as a conbandwidth object returned from an invocation of npcdensbw
...: additional arguments supplied to specify the bandwidth type, kernel types, and so on, detailed below. This is necessary if you specify bws as a \(p+q\)-vector and not a conbandwidth object, and you do not desire the default behaviours.
data: an optional data frame, list or environment (or object coercible to a data frame by as.data.frame) containing the variables in the model. If not found in data, the variables are taken from environment(bws), typically the environment from which npcdensbw was called.
newdata: An optional data frame in which to look for evaluation data. If omitted, the training data are used.
txdat: a \(p\)-variate data frame of explanatory data (conditioning data) used to calculate the regression estimators. Defaults to the training data used to compute the bandwidth object.
tydat: a one (1) dimensional vector of unordered or ordered factors, containing the dependent data. Defaults to the training data used to compute the bandwidth object.
exdat: a \(p\)-variate data frame of points on which the regression will be estimated (evaluation data). By default, evaluation takes place on the data provided by txdat.
eydat: a one (1) dimensional numeric or integer vector of the true values (outcomes) of the dependent variable. By default, evaluation takes place on the data provided by tydat.

Value

npconmode returns a conmode object with the following components:

conmode: a vector of type factor (or ordered factor) containing the conditional mode at each evaluation point
condens: a vector of numeric type containing the modal density estimates at each evaluation point
xeval: a data frame of evaluation points
yeval: a vector of type factor (or ordered factor) containing the actual outcomes, or NA if not provided
confusion.matrix: the confusion matrix or NA if outcomes are not available
CCR.overall: the overall correct classification ratio, or NA if outcomes are not available
CCR.byoutcome: a numeric vector containing the correct classification ratio by outcome, or NA if outcomes are not available
fit.mcfadden: the McFadden-Puig-Kerschner performance measure or NA if outcomes are not available

The functions mode, and fitted may be used to extract the conditional mode estimates, and the conditional density estimates at the conditional mode, respectively, from the resulting object. Also, summary supports conmode objects.

References

Aitchison, J. and C.G.G. Aitken (1976), “Multivariate binary discrimination by the kernel method,” Biometrika, 63, 413-420.

Hall, P. and J.S. Racine and Q. Li (2004), “Cross-validation and the estimation of conditional probability densities,” Journal of the American Statistical Association, 99, 1015-1026.

Li, Q. and J.S. Racine (2007), Nonparametric Econometrics: Theory and Practice, Princeton University Press.

McFadden, D. and C. Puig and D. Kerschner (1977), “Determinants of the long-run demand for electricity,” Proceedings of the American Statistical Association (Business and Economics Section), 109-117.

Pagan, A. and A. Ullah (1999), Nonparametric Econometrics, Cambridge University Press.

Scott, D.W. (1992), Multivariate Density Estimation. Theory, Practice and Visualization, New York: Wiley.

Silverman, B.W. (1986), Density Estimation, London: Chapman and Hall.

Wang, M.C. and J. van Ryzin (1981), “A class of smooth estimators for discrete distributions,” Biometrika, 68, 301-309.

Author

Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca

Usage Issues

If you are using data of mixed types, then it is advisable to use the data.frame function to construct your input data and not cbind, since cbind will typically not work as intended on mixed data types and will coerce the data to the same type.

Examples

if (FALSE) { # \dontrun{
# EXAMPLE 1 (INTERFACE=FORMULA): For this example, we use the
# birthweight data taken from the MASS library, and compute a parametric
# logit model and a nonparametric conditional mode model. We then
# compare their confusion matrices and summary measures of
# classification ability.

library("MASS")
data("birthwt")
attach(birthwt)

# Fit a parametric logit model with low (0/1) as the dependent
# variable and age, lwt, and smoke (0/1) as the covariates

# From ?birthwt
# 'low' indicator of birth weight less than 2.5kg
# 'smoke' smoking status during pregnancy
# 'race' mother's race ('1' = white, '2' = black, '3' = other)
# 'ht' history of hypertension
# 'ui' presence of uterine irritability
# 'ftv' number of physician visits during the first trimester
# 'age' mother's age in years
# 'lwt' mother's weight in pounds at last menstrual period

model.logit <- glm(low~factor(smoke)+
                   factor(race)+
                   factor(ht)+
                   factor(ui)+
                   ordered(ftv)+
                   age+
                   lwt, 
                   family=binomial(link=logit))

# Generate the confusion matrix and correct classification ratio

cm <- table(low, ifelse(fitted(model.logit)>0.5, 1, 0))
ccr <- sum(diag(cm))/sum(cm)

# Now do the same with a nonparametric model.  Note - this may take a
# few minutes depending on the speed of your computer... 

bw <- npcdensbw(formula=factor(low)~factor(smoke)+
                factor(race)+
                factor(ht)+
                factor(ui)+
                ordered(ftv)+
                age+
                lwt)

model.np <- npconmode(bws=bw)

# Compare confusion matrices from the logit and nonparametric model

# Logit

cm
ccr

# Nonparametric
summary(model.np)

detach(birthwt)

# EXAMPLE 1 (INTERFACE=DATA FRAME): For this example, we use the
# birthweight data taken from the MASS library, and compute a parametric
# logit model and a nonparametric conditional mode model. We then
# compare their confusion matrices and summary measures of
# classification ability.

library("MASS")
data("birthwt")
attach(birthwt)

# Fit a parametric logit model with low (0/1) as the dependent
# variable and age, lwt, and smoke (0/1) as the covariates

# From ?birthwt
# 'low' indicator of birth weight less than 2.5kg
# 'smoke' smoking status during pregnancy
# 'race' mother's race ('1' = white, '2' = black, '3' = other)
# 'ht' history of hypertension
# 'ui' presence of uterine irritability
# 'ftv' number of physician visits during the first trimester
# 'age' mother's age in years
# 'lwt' mother's weight in pounds at last menstrual period

model.logit <- glm(low~factor(smoke)+
                   factor(race)+
                   factor(ht)+
                   factor(ui)+
                   ordered(ftv)+
                   age+
                   lwt, 
                   family=binomial(link=logit))

# Generate the confusion matrix and correct classification ratio

cm <- table(low, ifelse(fitted(model.logit)>0.5, 1, 0))
ccr <- sum(diag(cm))/sum(cm)

# Now do the same with a nonparametric model...

X <- data.frame(factor(smoke), 
                factor(race), 
                factor(ht), 
                factor(ui), 
                ordered(ftv), 
                age, 
                lwt)

y <- factor(low)

# Note - this may take a few minutes depending on the speed of your
# computer... 

bw <- npcdensbw(xdat=X, ydat=y)

model.np <- npconmode(bws=bw)

# Compare confusion matrices from the logit and nonparametric model

# Logit

cm
ccr

# Nonparametric
summary(model.np)

detach(birthwt)
} # }