summary.pblm: Summarizing methods for bivariate additive logistic regression

Description

Summarizing methods anf functions for objects of class pblm.

Usage

# S3 method for pblm
summary(object,...)
 
# S3 method for pblm
print(x,digits = max(3, getOption("digits") - 3),...)
# S3 method for summary.pblm
print(x,digits = max(3, getOption("digits") - 3),...) 
 
# S3 method for pblm
AIC(object,...,k=2) 
# S3 method for pblm
logLik(object, penalized=FALSE,...)
# S3 method for pblm
vcov(object,...)
# S3 method for pblm
coef(object, digits = max(3, getOption("digits") - 3), ...)
# S3 method for pblm
coefficients(object, digits = max(3, getOption("digits") - 3), ...)
# S3 method for pblm
residuals(object, type = c("working", "pearson"),...)
# S3 method for pblm
resid(object, type = c("working", "pearson"),...)
# S3 method for pblm
fitted(object,...)
# S3 method for pblm
predict(object, newdata, type=c("link","response","terms","count"), 
                  se.fit=FALSE, digits= max(6, getOption("digits") - 3),...)
# S3 method for pblm
deviance(object, penalized=FALSE,...)
edf.pblm(object, which.eq=1, which.var=1 )
chisq.test.pblm(obj)
se.smooth.pblm(object)
Rsq.pblm(object, type = c("McFadden", "Cox Snell", "Cragg Uhler", "all"))

Value

print.pblm return an object of class "pblm". print.summary.pblm return an object of class "summary.pblm". summary.pblm returns a list with the following components:

results: A \(p \times 4\) data frame with columns for the estimated coefficient, its standard error, z-statistic, and corresponding (two-sided) p-value.
convergence: Logical flag indicating whether the algorithm converged.
iter: Number of iterations performed in the model fitting.
logLik: Log-likelihood value at convergence.
logLikp: Penalized log-likelihood of the fitted model.
AIC: Akaike Information Criterion of the fitted model.
gAIC: Generalized AIC of the fitted model.
BIC: Bayesian Information Criterion of the fitted model.
gaic.m: Penalty coefficient used in the gAIC.
np1, np2: Number of parameters estimated in the first and second marginal, respectively.
deviance: Model deviance.
names: A character vector of length two containing the names of the response variables.
df.res: Residual degrees of freedom.
df.tot: Total degrees of freedom of the model.
df.fix: Degrees of freedom associated with the fixed part of the model.
df.smooth: Effective degrees of freedom of the smoothers in the model, if any.
res.smooth: A data frame reporting an approximate chi-squared test for the smooth terms. If the effective degrees of freedom are far from the fixed ones, consider re-fitting the model by reducing pgtol.df in pblm.control, via the control argument.
smoother: Logical. TRUE if smooth terms were used in the model.
pnl.type: Penalty type as specified in the fitted object.
PR: A matrix with residuals summarized by row, one per model equation.
which.term: A list. For internal use.
respStr: A matrix. For internal use.
label1, label2: Names of the two response variables, respectively.
call: Matched call from the fitted object.

coef.pblm, coefficients.pblm return a numeric vector of estimated coefficient.

edf.pblm returns a scalar with the effective degrees of freedom for a specified smooth term.

vcov.pblm returns the variance-covariance matrix.

If se.fit = FALSE, the method predict.pblm returns a data frame with predicted values according to the specified prediction type. If se.fit = TRUE, a list of length two is returned with the following components:

fit: Data frame of predicted values for each linear predictor, according to the specified prediction type.
se.fit: Associated data frame of standard errors.

resid.pblm, residuals.pblm return a data frame with the specified type of residuals.

se.smooth.pblm returns a list of length three, containing the standard errors and the lower and upper bounds of the 95% confidence intervals for the smooth terms.

chisq.test.pblm returns a list of length two containing the results of the \(\chi^2\) and \(G^2\) tests.

Rsq.pblm returns a scalar, or a list if type="both" is selected.

AIC.pblm returns a scalar with several attributes, with printed AIC and df. If more objects are passed as arguments, it returns a data frame.

logLik, deviance return a scalar.

Arguments

object, obj: An object of class pblm.
digits: Integer controlling the number of digits printed in the output.
x: An object produced by pblm or summary.pblm to be printed.
k: Numeric; the penalty per parameter to be used. By default k = 2, corresponding to the classical AIC.
penalized: Logical indicating whether the value of the penalized log-likelihood is required.
which.var: Index indicating the position of the smoother as it appears in the model formula.
which.eq: Equation index for the smoothers.
newdata: Optional data frame with new values of the model covariates.
type: The type of residuals, predictions, or pseudo R-squared desired.
se.fit: Logical. Should prediction standard errors be returned? Currently available only for type = "link" or type = "terms" when newdata is not specified, and only for type = "link" when newdata is specified.
...: Further arguments passed to or from other methods.

Author

Marco Enea

Details

fitted.pblm is equivalent to predict.pblm specifying type="response". chisq.test.pblm performs the \(\chi^2\) and \(G^2\) tests. Rsq.pblm calculates pseudo R-squared.

Examples

Run this code


#NOT RUN 
## Example 1
#The Dale's model 
data(ulcer)
m1 <- pblm(fo1=cbind(pain,medication)~1, fo12=~I(operation=="vh"), RC.fo=~Col,
           data=ulcer, weights=freq,  contrasts=list(Col="contr.SAS"))
summary(m1)
deviance(m1)
predict(m1,type="response")


#the same data but in another format
#compare with Dale (1986), Table 3
dat <- multicolumn(freq~medication+pain+operation,data=ulcer)
fo <- as.formula(paste(attributes(dat)$"resp","~1",sep=""))
m1bis <- pblm(fo1=fo, fo12=~I(operation=="vh"), RC.fo=~Col, verbose=TRUE,
              data=dat, ncat1=3, contrasts=list(Col="contr.SAS"))
deviance(m1bis)
chisq.test.pblm(m1bis)
Rsq.pblm(m1bis)

# Example 2. An artificial data set: 
set.seed(10)
da <- expand.grid("Y1"=1:3,"Y2"=1:3,"fat1"=0:4,"fat2"=0:1)
da$Freq <- sample(1:20,3*3*5*2,replace=TRUE)
da$x1 <- rnorm(90)

#the bivariate additive proportional-odds model
m2 <- pblm(fo1=cbind(Y1,Y2) ~ fat1 + pb(x1), data=da, weights=Freq)
summary(m2)

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