Help for package DiSSMod

Type:

Package

Title:

Fitting Sample Selection Models for Discrete Response Variables

Version:

1.0.0

Date:

2019-04-15

Author:

Sang Kyu Lee <lsk0816@gmail.com>, Adelchi Azzalini <adelchi.azzalini@unipd.it>, Hyoung-Moon Kim <hmk966a@gmail.com>

Maintainer:

Sang Kyu Lee <lsk0816@gmail.com>

Description:

Tools to fit sample selection models in case of discrete response variables, through a parametric formulation which represents a natural extension of the well-known Heckman selection model are provided in the package. The response variable can be of Bernoulli, Poisson or Negative Binomial type. The sample selection mechanism allows to choose among a Normal, Logistic or Gumbel distribution.

Depends:

R (≥ 2.10)

Imports:

sfsmisc, matrixcalc, psych, MASS

License:

GPL-2

Encoding:

UTF-8

LazyData:

true

RoxygenNote:

6.1.1

NeedsCompilation:

Packaged:

2019-04-15 10:14:28 UTC; user

Repository:

CRAN

Date/Publication:

2019-04-15 10:42:40 UTC

Credit cards derogatory reports data

Description

Data is originally from Greene (1992), used for studying statistical credit scoring methods.

Usage

data(CreditMDR)

Format

A data frame with 13444 observations of 8 variables as below;

MAJORDRG: count of major derogatory reports (numeric)
CARDHLDR: 1 for cardholders, 0 for denied applicants (categorical)
AGE: age in years and twelfths of a year (numeric)
INCOME: primary income, divided by 10,000 (numeric)
OWNRENT: ownRent, individual owns (1) or rents (0) home (categorical)
ADEPCNT: not classified yet (numeric)
SELFEMPL: self employed; 1=yes, 0=no (categorical)
EXP_INC: average expenditure for 12 months/average monthly income (numeric)

Source

Greene, W. H. (1992) A Statistical Model for Credit Scoring. Working Paper No. EC-92-29, Department of Economics, Stern School of Business, New York University, 1992.

http://pages.stern.nyu.edu/~wgreene/Text/Edition7/tablelist8new.htm

References

Greene, W. H. (2012) Econometric Analysis, 7th Edition. Pearson education.

Azzalini, A., Kim, H.-M. and Kim, H.-J. (2019) Sample selection models for discrete and other non-Gaussian response variables. Statistical Methods & Applications, 28, 27–56. First online 30 March 2018. https://doi.org/10.1007/s10260-018-0427-1

Fitting Sample Selection Models for Discrete Response Variables

Description

Function DiSSMod fits sample selection models for discrete random variables, by suitably extending the formulation of the classical Heckman model to the case of a discrete response, but retaining the original conceptual framework. Maximum likelihood estimates are obtained by Newton-Raphson iteration combined with use of profile likelihood.

Usage

DiSSMod(response, selection, data, resp.dist, select.dist, alpha,
  trunc.num, standard = FALSE, verbose = 1, eps = 1e-07,
  itmax = 1000)

Arguments

response

a formula for the response equation.

selection

a formula for the selection equation.

data

a data frame and data has to be included with the form of data.frame.

resp.dist

a character for the distribution choice of the response variable, "bernoulli" for Bernoulli distribution, "poisson" for Poisson distribution, and "negbinomial" for Negative binomial distribution. Also, the character strings can be abbreviated and can be upper or lower case as preferred.

select.dist

a character for the distribution choice of the selection variable, "gumbel" for Gumbel distribution, "normal" for Normal distribution, and "logistic" for Logistic distribution. Also, the character strings can be abbreviated and can be upper or lower case as preferred.

alpha

a vector of alpha values on which the profile log-likelihood function is evaluated; if the argument is missing, a set of values in the interval (-10, 10) is used for the initial search, followed by a second search on a revised interval which depends on the outcome from the first search.

trunc.num

an integer numeric constant used as the truncation point of an infine summation of probabilities involved when resp.dist equals "Poisson" or "NegBinomial"; if the argument is missing, a default choice is made, as described in the ‘Details’ section. Notice: this default choice of trunc.num may be subject to revision in some future version of the package, and the argument trunc.num itselt may possibly be replaced by some other ingredient.

standard

a logical value for the standardizing explanatory variables, if TRUE two types of values (standardized and not) will be returned.

verbose

an integer value for the level of printed details (values: 0|1|2); the default value is 1 which stands for shortly printed details. If the value is 2, more details are viewed such as values of the log likelihood functions and iteration numbers. If the value is 0, there is no printed detail.

eps

a numeric value for the estimating parameters, which is needed for the step of the optimization. If the sum of absolute differences between present step estimated parameters and former step estimated parameters is smaller than eps, we assume that estimated parameters are optimized.

itmax

an integer stands for maximum number for the iteration of optimizing the parameters.

Details

The specification of the two linear models regulating the response variable and the selection mechanism, as indicated in the ‘Background’ section, is accomplished by two arguments of formula type, denoted response and selection, respectively. Each formula is specified with the same syntax of similar arguments in standard functions such as lm and glm, with the restriction that the intercept term (which is automatically included) must not be removed.

The distributional assumptions associated to the response and selection components are specified by the arguments resp.dist and select.dist, respectively. Argument select.dist refers to the unobservable continuous variable of which we observe only the dichotomous outcome Yes-No.

In this respect, a remark is appropriate about the option "Gumbel" for select.dist. This choice is equivalent to the adoption of an Exponential distribution of the selection variables combined an exponential transformation of the linear predictor of the selection argument, as it is presented in Section 3.2 of Azzalini et al. (2019). Also, it corresponds to work with the log-transformation of an Exponential variable, which is essentially a Gumbel type of variable, up to a linear transformation with respect to its more commonly employed parameterization.

When resp.dist is "Poisson" or "NegBinomial" and trunc.num is missing, a default choice is made; this equals 1.5*m or 2*m in the two respective cases, where m denotes the maximum observed value of the response variable.

Function DiSSMOd calls lower level functions, nr.bin, nr.nbinom, nr.pois and the others for the actual numerical maximization of the log-likelihood via a Newton-Raphson iteration.

Notice that the automatic initialization of the alpha search interval, when this argument is missing, may change in future versions of the package.

Value

DiSSMod returns an object of class "DiSSMod", which is a list containing following components:

call

a matched call.

standard

a logical value, stands for standardization or not.

st_loglik

a vector containing the differences between log likelihoods and maximized log likelihood.

max_loglik

a maximized log likelihood value.

mle_alpha

a maximized likelihood estimator of alpha.

alpha

a vector containing grids of the alpha

Nalpha

a vector containing proper alpha, which does not have NA value for corresponding log likelihood.

num_NA

a number of NA values of log likelihoods.

n_select

a number of selected response variables.

n_all

a number of all response variables.

estimate_response

estimated values for the response model.

std_error_response

estimated standard errors for the response model.

estimate_selection

estimated values for the selection model.

std_error_selection

estimated standard errors for the selection model.

Background

Function DiSSMod fits sample selection models for discrete random variables, by suitably extending the formulation of the classical Heckman model to the case of a discrete response, but retaining the original conceptual framework. This logic involves the following key ingredients: (1) a linear model indicating which explanatory variables influence the response variable; (2) a linear model indicating which (possibly different) explanatory variables, besides the response variable itself, influence a ‘selection variable’, which is intrinsically continuous but we only observe a dichotomous outcome from it, of type Yes-No, which selects which are the observed response cases; (3) distributional assumptions on the response and the selection variable.

The data fitting method is maximum likelihood estimation (MLE), which operates in two steps: (i) for each given value of parameter alpha which regulates the level of selection, MLE is performed for all the remaining parameters, using a Newton-Raphson iteration; (ii) a scan of the alpha axis builds the profile log-likelihood function and its maximum point represents the overall MLE.

A detailed account of the underlying theory and the operational methodology is provided by Azzalini et al. (2019).

References

Examples

set.seed(45)
data(DoctorRWM, package = "DiSSMod")
n0 <- 600
set.n0 <- sample(1:nrow(DoctorRWM), n0)
reduce_DoctorRWM <- DoctorRWM[set.n0,]
result0 <- DiSSMod(response = as.numeric(DOCVIS > 0) ~ AGE + INCOME_SCALE + HHKIDS + EDUC + MARRIED,
                   selection = PUBLIC ~ AGE + EDUC + FEMALE,
                   data = reduce_DoctorRWM, resp.dist="bernoulli", select.dist = "normal",
                   alpha = seq(-5.5, -0.5, length.out = 21), standard = TRUE)

print(result0)

data(CreditMDR, package = "DiSSMod")
n1 <- 600
set.n1 <- sample(1:nrow(CreditMDR), n1)
reduce_CreditMDR <- CreditMDR[set.n1,]
result1 <- DiSSMod(response = MAJORDRG ~ AGE + INCOME + EXP_INC,
                   selection = CARDHLDR ~ AGE + INCOME + OWNRENT + ADEPCNT + SELFEMPL,
                   data = reduce_CreditMDR, resp.dist="poi", select.dist = "logis",
                   alpha = seq(-0.3, 0.3,length.out = 21), standard = FALSE, verbose = 1)

print(result1)

German doctor first visits data

Description

Data is from Riphahn, Wambach and Million (2003), used for studying longitudinal analysis concerning the usage of the German health insurance system. The original data contain a few years data for patients, but we have only for first year.

Usage

data(DoctorRWM)

Format

A data frame with 7293 observations of 26 variables as below;

ID: identification number (numeric)
FEMALE: female or not (categorical)
YEAR: year (categorical)
AGE: age (numeric)
HSAT: health satisfaction coded 0 (low) to 10 (high) (numeric)
HANDDUM: person is handicappe or not (categorical)
HANDPER: percentage degree of handicap (numeric)
HHNINC: monthly household net income (numeric)
HHKIDS: child (ren) below age 16 in household (numeric)
EDUC: years of schooling (numeric)
MARRIED: person is married or not (categorical)
HAUPTS: level of schooling (categorical)
REALS: level of schooling (categorical)
FACHHS: level of schooling (categorical)
ABITUR: level of schooling (categorical)
UNIV: level of schooling (categorical)
WORKING: employed or not (categorical)
BLUEC: person is blue collar worker or not (categorical)
WHITEC: person is white collar worker or not (categorical)
SELF: person is self-employed or not (categorical)
BEAMT: civil servant or not (categorical)
DOCVIS: number of doctor visits in last 3 months (numeric)
HOSPVIS: number of hospital visits last year (numeric)
PUBLIC: person is insured in public health insurance or not (categorical)
ADDON: person is insured in add-on insurance or not (categorical)
INCOME_SCALE: scaled income; original income/1000 (numeric)

Source

Riphahn, R. T., Wambach, A. and Million, A. (2003) Incentive Effects in the Demand for Health Care: A Bivariate Panel Count Data Estimation, Journal of Applied Econometrics, 18, 4, 387–405. Published online 8 October 2002. https://doi.org/10.1002/jae.680

http://qed.econ.queensu.ca/jae/2003-v18.4/riphahn-wambach-million/

References

Greene, W. H. (2012) Econometric Analysis, 7th Edition. Pearson education.

Getting Coefficients of Discrete Sample Selection Model Fits

Description

coef method for a class "DiSSMod".

Usage

## S3 method for class 'DiSSMod'
coef(object, only = NULL, ...)

Arguments

object

an object of class "DiSSMod" made by the function DiSSMod.

only

a character value for choosing specific variable's coefficients. Initial value is

...

not used, but exists because of the compatibility. NULL, which shows all variable's coefficients. If "response" is written, only coefficients for response variables will be returned, and if "selection" is written, only coefficients for selection variables will be returned.

Details

It looks as similar as the generic function coef, but this case there are two equations. Therefore, there exist little differences.

Value

a numeric vector or a list is given.

Examples

# example continued from DiSSMod
set.seed(45)
data(DoctorRWM, package = "DiSSMod")
n0 <- 600
set.n0 <- sample(1:nrow(DoctorRWM), n0)
reduce_DoctorRWM <- DoctorRWM[set.n0,]
result0 <- DiSSMod(response = as.numeric(DOCVIS > 0) ~ AGE + INCOME_SCALE + HHKIDS + EDUC + MARRIED,
                   selection = PUBLIC ~ AGE + EDUC + FEMALE,
                   data = reduce_DoctorRWM, resp.dist="bernoulli", select.dist = "normal",
                   alpha = seq(-5.5, -0.5, length.out = 21), standard = TRUE)

coef(result0)

data(CreditMDR, package = "DiSSMod")
n1 <- 600
set.n1 <- sample(1:nrow(CreditMDR), n1)
reduce_CreditMDR <- CreditMDR[set.n1,]
result1 <- DiSSMod(response = MAJORDRG ~ AGE + INCOME + EXP_INC,
                   selection = CARDHLDR ~ AGE + INCOME + OWNRENT + ADEPCNT + SELFEMPL,
                   data = reduce_CreditMDR, resp.dist="poi", select.dist = "logis",
                   alpha = seq(-0.3, 0.3,length.out = 21), standard = FALSE, verbose = 1)

coef(result1)

Getting Confidence Intervals for Parameters of Discrete Sample Selection Model Fits

Description

confint method for a class "DiSSMod".

Usage

## S3 method for class 'DiSSMod'
confint(object, parm, level = 0.95, ...)

Arguments

object

an object of class "DiSSMod" made by the function DiSSMod.

parm

not used, but it exists for compatibility reasons.

level

a numeric value between 0 and 1 for controlling the significance level of confidence interval; default value is 0.95.

...

not used, but it exists for compatibility reasons.

Value

a list, containing level and confidence intervals for parameters, is given.

Examples

# example continued from DiSSMod
set.seed(45)
data(DoctorRWM, package = "DiSSMod")
n0 <- 600
set.n0 <- sample(1:nrow(DoctorRWM), n0)
reduce_DoctorRWM <- DoctorRWM[set.n0,]
result0 <- DiSSMod(response = as.numeric(DOCVIS > 0) ~ AGE + INCOME_SCALE + HHKIDS + EDUC + MARRIED,
                   selection = PUBLIC ~ AGE + EDUC + FEMALE,
                   data = reduce_DoctorRWM, resp.dist="bernoulli", select.dist = "normal",
                   alpha = seq(-5.5, -0.5, length.out = 21), standard = TRUE)

confint(result0, level = 0.90)

data(CreditMDR, package = "DiSSMod")
n1 <- 600
set.n1 <- sample(1:nrow(CreditMDR), n1)
reduce_CreditMDR <- CreditMDR[set.n1,]
result1 <- DiSSMod(response = MAJORDRG ~ AGE + INCOME + EXP_INC,
                   selection = CARDHLDR ~ AGE + INCOME + OWNRENT + ADEPCNT + SELFEMPL,
                   data = reduce_CreditMDR, resp.dist="poi", select.dist = "logis",
                   alpha = seq(-0.3, 0.3,length.out = 21), standard = FALSE, verbose = 1)

confint(result1)

Relative Log Likelihood Plot for Discrete Sample Selection Model Fits

Description

plot method for a class "DiSSMod".

Usage

## S3 method for class 'DiSSMod'
plot(x, ...)

Arguments

x

an object of class "DiSSMod" made by the function DiSSMod.

...

additional control argument is as follows.

level: an option for controlling the significance level of confidence interval. It has to be given in probability between 0 and 1. Initial level is set to 1 - \alpha = 0.95.

Details

Function plot draws a convex line due to the values of twice relative log likelihoods by using the profile likelihood approach with following the grids of alpha. If confidence interval created from the function confint exists between the maximum and minimum value of the alpha, there will be two points drawn with the color red. Also, the Maximum Likelihood Estimator (MLE) of alpha can be seen easily, if it exists between the maximum and minimum value of the alpha.

Examples

# example continued from DiSSMod
set.seed(45)
data(DoctorRWM, package = "DiSSMod")
n0 <- 600
set.n0 <- sample(1:nrow(DoctorRWM), n0)
reduce_DoctorRWM <- DoctorRWM[set.n0,]
result0 <- DiSSMod(response = as.numeric(DOCVIS > 0) ~ AGE + INCOME_SCALE + HHKIDS + EDUC + MARRIED,
                   selection = PUBLIC ~ AGE + EDUC + FEMALE,
                   data = reduce_DoctorRWM, resp.dist="bernoulli", select.dist = "normal",
                   alpha = seq(-5.5, -0.5, length.out = 21), standard = TRUE)

plot(result0, level = 0.90)

data(CreditMDR, package = "DiSSMod")
n1 <- 600
set.n1 <- sample(1:nrow(CreditMDR), n1)
reduce_CreditMDR <- CreditMDR[set.n1,]
result1 <- DiSSMod(response = MAJORDRG ~ AGE + INCOME + EXP_INC,
                   selection = CARDHLDR ~ AGE + INCOME + OWNRENT + ADEPCNT + SELFEMPL,
                   data = reduce_CreditMDR, resp.dist="poi", select.dist = "logis",
                   alpha = seq(-0.3, 0.3,length.out = 21), standard = FALSE, verbose = 1)

plot(result1)

Summarizing Discrete Sample Selection Model Fits

Description

summary method for a class "DiSSMod".

Usage

## S3 method for class 'DiSSMod'
summary(object, ...)

## S3 method for class 'summary.DiSSMod'
print(x, digits = max(3, getOption("digits") -
  3), ...)

Arguments

object

an object of class "DiSSMod" made by the function DiSSMod.

...

additional control argument is as follows.

level: an option for controlling the significance level of confidence interval. It has to be given in probability between 0 and 1. Initial level is set to 1 - \alpha = 0.95.

x

an object of class "summary.DiSSMod".

digits

a numeric number of significant digits.

Details

If standard equals TRUE, summary also additionally returns summary statistics of standardized results. Otherwise, it just returns summary statistics as similar statistics as the generic function summary.

Value

The function summary.DiSSMod returns a list of summary statistics of the fitted discrete sample selection model given in object.

The components, which are not duplicated from the object, are as follows:

z.value_response

Z statistics (normal distribution) for coefficients of response equation.

z.value_selection

Z statistics (normal distribution) for coefficients of selection equation.

CI_alpha

confidence interval of the parameter alpha.

level

a numeric value between 0 and 1 for controlling the significance level of confidence interval. Initial level is set to 1 - \alpha = 0.95.

Examples

# example continued from DiSSMod
set.seed(45)
data(DoctorRWM, package = "DiSSMod")
n0 <- 600
set.n0 <- sample(1:nrow(DoctorRWM), n0)
reduce_DoctorRWM <- DoctorRWM[set.n0,]
result0 <- DiSSMod(response = as.numeric(DOCVIS > 0) ~ AGE + INCOME_SCALE + HHKIDS + EDUC + MARRIED,
                   selection = PUBLIC ~ AGE + EDUC + FEMALE,
                   data = reduce_DoctorRWM, resp.dist="bernoulli", select.dist = "normal",
                   alpha = seq(-5.5, -0.5, length.out = 21), standard = TRUE)

summary(result0, level = 0.90)

data(CreditMDR, package = "DiSSMod")
n1 <- 600
set.n1 <- sample(1:nrow(CreditMDR), n1)
reduce_CreditMDR <- CreditMDR[set.n1,]
result1 <- DiSSMod(response = MAJORDRG ~ AGE + INCOME + EXP_INC,
                   selection = CARDHLDR ~ AGE + INCOME + OWNRENT + ADEPCNT + SELFEMPL,
                   data = reduce_CreditMDR, resp.dist="poi", select.dist = "logis",
                   alpha = seq(-0.3, 0.3,length.out = 21), standard = FALSE, verbose = 1)

summary(result1)

Credit cards derogatory reports data

Description

Usage

Format

Source

References

Fitting Sample Selection Models for Discrete Response Variables

Description

Usage

Arguments

Details

Value

Background

References

See Also

Examples

German doctor first visits data

Description

Usage

Format

Source

References

Getting Coefficients of Discrete Sample Selection Model Fits

Description

Usage

Arguments

Details

Value

See Also

Examples

Getting Confidence Intervals for Parameters of Discrete Sample Selection Model Fits

Description

Usage

Arguments

Value

See Also

Examples

Relative Log Likelihood Plot for Discrete Sample Selection Model Fits

Description

Usage

Arguments

Details

See Also

Examples

Summarizing Discrete Sample Selection Model Fits

Description

Usage

Arguments

Details

Value

See Also

Examples