| Type: | Package |
| Title: | Multiple Ordinal Tobit (MOT) Model |
| Version: | 0.1.4 |
| Date: | 2017-05-10 |
| Author: | Marvin N. Wright |
| Maintainer: | Marvin N. Wright <marv@wrig.de> |
| Description: | Fit right censored Multiple Ordinal Tobit (MOT) model. |
| License: | GPL-3 |
| Depends: | maxLik, MASS |
| RoxygenNote: | 5.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2017-05-10 12:56:23 UTC; wright |
| Repository: | CRAN |
| Date/Publication: | 2017-05-10 15:37:47 UTC |
Multiple Ordinal Tobit Model
Description
Fit right censored Multiple Ordinal Tobit (MOT) model.
Usage
lmmot(formula, data = sys.frame(sys.parent()), threshold, stdEr = "fisher",
...)
Arguments
formula |
Object of class formula describing the model. |
data |
Optional data frame or environment containing the variables in the model. |
threshold |
Vector of thresholds in the model. |
stdEr |
Method for standard error estimation. Use "fisher" for estimation using the inverse of the Fisher information matrix or "hessian" for estimation using the Hessian matrix. |
... |
Further arguments passed to the maximum likelihood estimation function maxLik. |
Details
Fit right censored Multiple Ordinal Tobit (MOT) model. The model is a right censored Tobit model with multiple ordinal categories for latent values above the threshold, the threshold is therefore replaced by a threshold vector.
For the latent variable a linear model with independent and identically distributed non-systematic and homoscedastic errors is assumed.
If the threshold is of length 1, the model is equivalent to the standard right censored Tobit model.
The data is fitted with the Maximum Likelihood method.
Value
lmmot object: maxLik object with additional fields:
censoring: Number of obeservations in the censoring intervals.
fisherInfo: Fisher information matrix.
stdEr: Standard errors for estimated coefficients.
tval: Value for t statistic in Wald test.
pval: p-value in Wald test.
fitted.values: Fitted values of the estimated model.
residuals: Residuals of the estimated model.
Author(s)
Marvin N. Wright
See Also
Examples
# Random data for x
N <- 100
x <- rnorm(N, 25, 10)
# Simulate data for latent variable ystar with simple linear model
beta_0 <- 60
beta_1 <- 1
sigma <- 8
ystar <- beta_0 + beta_1*x + rnorm(N, 0, sigma)
# Simulate censoring for observed variable y
y <- ystar
y[y >= 100] <- 100
y[(y >= 90) & (y < 100)] <- 90
y[(y >= 80) & (y < 90)] <- 80
# MOT regression with observed variable y
mot.fit <- lmmot(y ~ x, threshold = c(80, 90, 100))
# Show details
summary(mot.fit)
# Compare real data with model fit
plot(x, ystar)
abline(coefficients(mot.fit)[1:2])
Fisher information for mot model
Description
Fisher information matrix for right censored Multiple Ordinal Tobit (MOT) model.
Usage
motFisher(param, xx, tau)
Arguments
param |
parameter vector: (beta_0, beta_1, ... , beta_m, sigma). |
xx |
design matrix of the model. |
tau |
threshold vector from tau_1 to tau_K. |
Value
fisher information matrix, summarized over all observations.
Author(s)
Marvin Wright
See Also
Gradient of log-Likelihood for mot model
Description
Gradient of log-Likelihood for right censored Multiple Ordinal Tobit (MOT) model.
Usage
motGradient(param, xx, y, tau)
Arguments
param |
parameter vector: (beta_0, beta_1, ... , beta_m, sigma). |
xx |
design matrix of the model. |
y |
observation vector. |
tau |
threshold vector from tau_1 to tau_K. |
Value
gradient of log-likelihood, vector with all observations.
Author(s)
Marvin Wright
See Also
Hessian matrix of log-Likelihood for mot model
Description
Hessian matrix of log-Likelihood for right censored Multiple Ordinal Tobit (MOT) model.
Usage
motHessian(param, xx, y, tau)
Arguments
param |
parameter vector: (beta_0, beta_1, ... , beta_m, sigma). |
xx |
design matrix of the model. |
y |
observation vector. |
tau |
threshold vector from tau_1 to tau_K. |
Value
hessian matrix, summarized over all observations.
Author(s)
Marvin Wright
See Also
log-likelihood for mot model
Description
Log-Likelihood for multiple ordinal right censored Multiple Ordinal Tobit (MOT) model.
Usage
motLogLik(param, xx, y, tau)
Arguments
param |
parameter vector: (beta_0, beta_1, ... , beta_m, sigma). |
xx |
design matrix of the model. |
y |
observation vector. |
tau |
threshold vector from tau_1 to tau_K. |
Value
log-likelihood, vector with all observations.
Author(s)
Marvin Wright
See Also
Print lmmot object
Description
Print lmmot object.
Usage
## S3 method for class 'lmmot'
print(x, digits = max(3, getOption("digits") - 3), ...)
Arguments
x |
lmmot object to print. |
digits |
number of decimal digits to print. |
... |
further arguments passed to or from other methods. |
Author(s)
Marvin Wright
See Also
Summary if lmmot object
Description
Print details about lmmot object.
Usage
## S3 method for class 'lmmot'
summary(object, digits = max(3, getOption("digits") - 3), ...)
Arguments
object |
lmmot object to print. |
digits |
number of decimal digits to print. |
... |
further arguments passed to or from other methods. |
Author(s)
Marvin Wright