| Type: | Package |
| Title: | Copula-Based Mixed Regression Models |
| Version: | 0.6.5 |
| Description: | Estimation of 2-level factor copula-based regression models for clustered data where the response variable can be either discrete or continuous. |
| Depends: | R (≥ 3.5.0), stats, statmod, matrixStats |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | yes |
| Packaged: | 2025-04-24 15:45:37 UTC; 49009427 |
| Author: | Pavel Krupskii [aut, ctb, cph], Bouchra R. Nasri [aut, ctb, cph], Bruno N Remillard [aut, cre, cph] |
| Maintainer: | Bruno N Remillard <bruno.remillard@hec.ca> |
| Repository: | CRAN |
| Date/Publication: | 2025-04-24 16:00:02 UTC |
Copula-based estimation of mixed regression models for continuous response
Description
This function computes the estimation of a copula-based 2-level hierarchical model.
Usage
EstContinuous(
y,
model,
family,
rot = 0,
clu,
xc = NULL,
xm = NULL,
start = NULL,
LB = NULL,
UB = NULL,
nq = 31,
dfC = NULL,
dfM = NULL,
prediction = TRUE
)
Arguments
y |
n x 1 vector of response variable (assumed continuous). |
model |
function for margins: "gaussian" (normal), "t" (Student with known df=dfM), "laplace" , "exponential", "weibull". |
family |
copula family: "gaussian" (normal), "t" , "clayton" , "frank" , "fgm", "gumbel". |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
clu |
variable of size n defining the clusters; can be a factor |
xc |
covariates of size n for the estimation of the copula, in addition to the constant; default is NULL. |
xm |
covariates of size n for the estimation of the mean of the margin, in addition to the constant; default is NULL. |
start |
starting point for the estimation; default (NULL) are the ones associated with a Gaussian-copula model defined by lme. |
LB |
lower bound for the parameters. |
UB |
upper bound for the parameters. |
nq |
number of nodes and weighted for Gaussian quadrature of the product of conditional copulas; default is 25. |
dfC |
degrees of freedom for a Student margin; default is 5. |
dfM |
degrees of freedom for a Student margin; default is NULL for non-t distribution. |
prediction |
logical variable for prediction of latent variables V; default is TRUE. |
Value
coefficients |
List of estimated parameters: copula, margin, size |
sd |
Standard deviations of the estimated parameters |
tstat |
T statistics for the estimated parameters |
pval |
P-values of the t statistics for the estimated parameters |
gradient |
Gradient of the log-likelihood |
loglik |
Log-likelihood |
aic |
AIC coefficient |
bic |
BIC coefficient |
cov |
Covariance matrix of the estimations |
grd |
Gradients by clusters |
clu |
Cluster values |
Matxc |
Matrix of covariates defining the copula parameters, including a constant |
Matxm |
Matrix of covariates defining the margin parameters, including a constant |
V |
Estimated value of the latent variable by clusters (if prediction=TRUE) |
cluster |
Unique values of clusters |
family |
Copula family |
tau |
Kendall's tau by observation |
thC0 |
Estimated parameters of the copula by observation |
thF |
Estimated parameters of the margins by observation |
pcond |
Conditional copula cdf |
fcpdf |
Margin functions (cdf and pdf) |
dfM |
Degrees of freedom for Student margin (default is NULL) |
dfC |
Degrees of freedom for the Student copula (default is NULL) |
Author(s)
Pavel Krupskii, Bouchra R. Nasri and Bruno N. Remillard
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
data(normal) #simulated data with normal margins
start=c(0,0,0,1); LB=c(rep(-10,3),0.001);UB=c(rep(10,3),10)
y=normal$y; clu=normal$clu;xm=normal$xm
out=EstContinuous(y,model="gaussian",family="clayton",rot=90,clu=clu,xm=xm,start=start,LB=LB,UB=UB)
Copula-based estimation of mixed regression models for continuous or discrete response
Description
This function computes the estimation of a copula-based 2-level hierarchical model.
Usage
EstCopulaGAMM(
y,
model,
family = "clayton",
rot = 0,
clu,
xc = NULL,
xm = NULL,
start,
LB,
UB,
nq = 25,
dfC = NULL,
dfM = NULL,
offset = NULL,
prediction = TRUE
)
Arguments
y |
n x 1 vector of response variable (assumed continuous). |
model |
margins: "binomial" or "bernoulli","poisson", "nbinom" (Negative Binomial), "geometric", "multinomial", "gaussian" or "normal", "t", "laplace" , "exponential", "weibull". |
family |
copula family: "gaussian" (normal), "t" , "clayton" , "frank" , "fgm", gumbel". |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
clu |
variable of size n defining the clusters; can be a factor |
xc |
covariates of size n for the estimation of the copula, in addition to the constant; default is NULL. |
xm |
covariates of size n for the estimation of the mean of the margin, in addition to the constant; default is NULL. |
start |
starting point for the estimation; could be the ones associated with a Gaussian-copula model defined by lmer. |
LB |
lower bound for the parameters. |
UB |
upper bound for the parameters. |
nq |
number of nodes and weighted for Gaussian quadrature of the product of conditional copulas; default is 25. |
dfC |
degrees of freedom for a Student margin; default is NULL. |
dfM |
degrees of freedom for a Student margin; default is NULL for non-t distribution, |
offset |
offset (default is NULL) |
prediction |
logical variable for prediction of latent variables V (default is TRUE). |
Value
coefficients |
Estimated parameters |
sd |
Standard deviations of the estimated parameters |
tstat |
T statistics for the estimated parameters |
pval |
P-values of the t statistics for the estimated parameters |
gradient |
Gradient of the log-likelihood |
loglik |
Log-likelihood |
aic |
AIC coefficient |
bic |
BIC coefficient |
cov |
Covariance matrix of the estimations |
grd |
Gradients by clusters |
clu |
Cluster values |
Matxc |
Matrix of covariates defining the copula parameters, including a constant |
Matxm |
Matrix of covariates defining the margin parameters, including a constant |
V |
Estimated value of the latent variable by clusters (if prediction=TRUE) |
cluster |
Unique clusters |
family |
Copula family |
thC0 |
Estimated parameters of the copula by observation |
thF |
Estimated parameters of the margins by observation |
rot |
rotation |
dfC |
Degrees of freedom for the Student copula |
model |
Name of the margins |
disc |
Discrete margin number |
Author(s)
Pavel Krupskii, Bouchra R. Nasri and Bruno N. Remillard
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
data(sim.poisson) #simulated data with Poisson margins
start=c(2,8,3,-1); LB = c(-3, 3, -7, -6);UB=c( 7, 13, 13, 4)
y=sim.poisson$y; clu=sim.poisson$clu;
xc=sim.poisson$xc; xm=sim.poisson$xm
model = "poisson"; family="frank"
out.poisson=EstCopulaGAMM(y,model,family,rot=0,clu,xc,xm,start,LB,UB,nq=31,prediction=TRUE)
Copula-based estimation of mixed regression models for discrete response
Description
This function computes the estimation of a copula-based 2-level hierarchical model.
Usage
EstDiscrete(
y,
model,
family,
rot = 0,
clu,
xc = NULL,
xm = NULL,
start,
LB,
UB,
nq = 25,
dfC = NULL,
offset = NULL,
prediction = TRUE
)
Arguments
y |
n x 1 vector of response variable (assumed continuous). |
model |
margins: "binomial" or "bernoulli","poisson", "nbinom" (Negative Binomial), "geometric", "multinomial". |
family |
copula family: "gaussian" , "t" , "clayton" , "frank" , "fgm", gumbel". |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
clu |
variable of size n defining the clusters; can be a factor |
xc |
covariates of size n for the estimation of the copula, in addition to the constant; default is NULL. |
xm |
covariates of size n for the estimation of the mean of the margin, in addition to the constant; default is NULL. |
start |
starting point for the estimation; could be the ones associated with a Gaussian-copula model defined by lmer. |
LB |
lower bound for the parameters. |
UB |
upper bound for the parameters. |
nq |
number of nodes and weighted for Gaussian quadrature of the product of conditional copulas; default is 25. |
dfC |
degrees of freedom for a Student margin; default is NULL. |
offset |
offset (default is NULL) |
prediction |
logical variable for prediction of latent variables V (default is TRUE). |
Value
coefficients |
List of estimated parameters: copula, margin, size |
sd |
Standard deviations of the estimated parameters |
tstat |
T statistics for the estimated parameters |
pval |
P-values of the t statistics for the estimated parameters |
gradient |
Gradient of the log-likelihood |
loglik |
Log-likelihood |
aic |
AIC coefficient |
bic |
BIC coefficient |
cov |
Covariance matrix of the estimations |
grd |
Gradients by clusters |
clu |
Cluster values |
Matxc |
Matrix of covariates defining the copula parameters, including a constant |
Matxm |
Matrix of covariates defining the margin parameters, including a constant |
V |
Estimated value of the latent variable by clusters (if prediction=TRUE) |
cluster |
Unique clusters |
family |
Copula family |
thC0 |
Estimated parameters of the copula by observation |
thF |
Estimated parameters of the margins by observation |
rot |
rotation |
dfC |
Degrees of freedom for the Student copula |
model |
Name of the margins |
disc |
Discrete margin number |
Author(s)
Pavel Krupskii, Bouchra R. Nasri and Bruno N. Remillard
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
data(sim.poisson) #simulated data with Poisson margins
start=c(2,8,3,-1); LB = c(-3, 3, -7, -6);UB=c( 7, 13, 13, 4)
y=sim.poisson$y; clu=sim.poisson$clu;
xc=sim.poisson$xc; xm=sim.poisson$xm
model = "poisson"; family="frank"
out.poisson=EstDiscrete(y,model,family,rot=0,clu,xc,xm,start,LB,UB,nq=31,prediction=TRUE)
Estimation of latent variables in the continuous case
Description
This function computes the estimation of a latent variables for each cluster using the conditional a posteriori median.
Usage
MAP.continuous(u, family, rot, thC0k, dfC = NULL, nq = 35)
Arguments
u |
vector of values in (0,1) |
family |
copula family: "gaussian" , "t" , "clayton" , "joe", "frank" , "fgm", gumbel", "plackett", "galambos", "huesler-reiss" |
rot |
rotation: 0 (default), 90, 180 (survival), or 270. |
thC0k |
vector of copula parameters |
dfC |
degrees of freedom for the Student copula (default is NULL) |
nq |
number of nodes and weighted for Gaussian quadrature of the product of conditional copulas; default is 31. |
Value
condmed |
Conditional a posteriori median. |
Author(s)
Pavel Krupskii, Bouchra R. Nasri and Bruno N. Remillard
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
u = c(0.5228155, 0.3064417, 0.2789849, 0.5176489, 0.3587144)
thC0k=rep(17.54873,5)
MAP.continuous(u,"clayton",rot=90,thC0k,nq=35)
Estimation of latent variable in the dicrete case
Description
This function computes the estimation of a latent variables foe=r each cluster using the conditional a posteriori median.
Usage
MAP.discrete(vv, uu, family, rot, thC0k, dfC = NULL, nq = 35)
Arguments
vv |
vector of values in (0,1) |
uu |
vector of values in (0,1) |
family |
copula family "gaussian" , "t" , "clayton" , "joe", "frank" , "fgm", gumbel", "plackett", "galambos", "huesler-reiss" |
rot |
rotation: 0 (default), 90, 180 (survival), or 270. |
thC0k |
vector of copula parameters |
dfC |
degrees of freedom for the Student copula (default is NULL) |
nq |
number of nodes and weighted for Gaussian quadrature of the product of conditional copulas; default is 31. |
Value
condmed |
Conditional a posteriori median. |
Author(s)
Pavel Krupskii, Bouchra R. Nasri and Bruno N. Remillard
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
uu = c(0.5228155, 0.3064417, 0.2789849, 0.5176489, 0.3587144)
vv = c(0.7816627, 0.6688788, 0.6351364, 0.7774917, 0.7264787)
thC0k=rep(17.54873,5)
MAP.discrete(vv,uu,"clayton",rot=90,thC0k,nq=35)
Simulation of clustered data
Description
Generate a random sample of observations from a copula-based mixed regression model.
Usage
SimGenCluster(
parC,
parM,
clu,
xc = NULL,
xm = NULL,
family,
rot = 0,
dfC = NULL,
model,
dfM = NULL,
offset = NULL
)
Arguments
parC |
vector of copula parameters; k1 is the number of covariates + constant for the copula |
parM |
vector of margin parameters; k2 is the number of covariates + constant for the margins |
clu |
vector of clusters (can be a factor) |
xc |
matrix (N x k1) of covariates for the copula, not including the constant (can be NULL) |
xm |
matrix (N x k2) of covariates for the margins, not including the constant (can be NULL) |
family |
copula family: "gaussian" , "t" , "clayton" , "joe", "frank" , "gumbel", "plackett" |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
dfC |
degrees of freedom for the Student copula (default is NULL) |
model |
marginal distribution: "binomial" (bernoulli), "poisson", "nbinom" (mean is the parameter),"nbinom1" (p is the parameter), "geometric", "multinomial", exponential", "weibull", "normal" (gaussian),"t", "laplace" |
dfM |
degrees of freedom for the Student margins (default is NULL) |
offset |
offset for the margins (default is NULL) |
Value
out |
List of simulated responses (y) and cluster factors (V) |
y |
Simulated values |
Author(s)
Bruno N. Remillard
Examples
K=50 #number of clusters
n=5 #size of each cluster
N=n*K
set.seed(1)
clu=rep(c(1:K),each=n)
parC = 0 # yields tau = 0.5 for Clayton
parM= c(1,-1,4)
xm = runif(N)
y=SimGenCluster(parC,parM,xm,family="clayton",rot=90,clu=clu,model="gaussian")$y
Simulation of multinomial clustered data
Description
Generate a random sample of multinomial observations from a copula-based mixed regression model.
Usage
SimMultinomial(
parC,
parM,
clu,
xc = NULL,
xm = NULL,
family,
rot = 0,
dfC = NULL,
offset = NULL
)
Arguments
parC |
copula parameters |
parM |
matrix of dimension (L-1)x k2 of margin parameters; L is the number of levels and k2 is the number of covariates+constant for the margins |
clu |
vector of clusters (can be a factor) |
xc |
matrix of covariates for the copula, not including the constant (can be NULL) |
xm |
matrix of covariates for the margins, not including the constant (can be NULL) |
family |
copula family: "gaussian" (normal), "t" , "clayton" , "joe", "frank" , "gumbel", "plackett" |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
dfC |
degrees of freedom for student copula (default is NULL) |
offset |
offset for the margins (default is NULL) |
Value
out |
List of simulated factors (y) and cluster factors (V) |
Author(s)
Bruno N. Remillard
Examples
K=50 #number of clusters
n=5 #size of each cluster
N=n*K
set.seed(1)
clu=rep(c(1:K),each=n)
parC = 2
parM=matrix(c(1,-1,0.5,2),byrow=TRUE,ncol=2)
xm = runif(N)
y=SimMultinomial(parC,parM,clu,xm=xm,family="clayton",rot=90)$y
Bernoulli with p = 1/(1+exp(-th)) cdf/pdf and derivatives
Description
This function computes the cdf, pdf, and associated derivatives
Usage
berncpdf(z, th)
Arguments
z |
vector of responses |
th |
linear combination of covariates (can be negative) |
Value
out |
Matrix of conditional cdf and pdf with derivative with respect to parameters |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = berncpdf(0,2.5)
Copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
coplik(u, v, family, rot = 0, cpar, dfC = NULL, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
family |
copula family: "gaussian", "t", "clayton", "frank", "fgm", "gumbel", "joe", "plackett". |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
cpar |
copula parameter |
dfC |
degrees of freedom for the Student copula (default is NULL) |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameters |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = coplik(0.3,0.5,"clayton",cpar=2,du=TRUE)
Normal density
Description
Density at (x1,x2)
Usage
dbvn(x1, x2, rh)
Arguments
x1 |
vector of values |
x2 |
vector of values |
rh |
correlation parameter, -1< rh <1 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dbvn(0.3,0.5,-0.6)
Normal density (version 2)
Description
Density at (x1,x2)
Usage
dbvn2(x1, x2, rh)
Arguments
x1 |
vector of values |
x2 |
vector of values |
rh |
correlation parameter, -1< rh <1 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dbvn2(0.3,0.5,-0.4)
Normal copula density
Description
Density at (u,v)
Usage
dbvncop(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter, -1< cpar<1 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dbvncop(0.3,0.5,-0.5)
Student copula density
Description
Density at (u,v)
Usage
dbvtcop(u, v, cpar, dfC)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter, -1< cpar<1 |
dfC |
degrees of freedom |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dbvtcop(0.3,0.5,-0.7,25)
Copula pdf
Description
Evaluates the copula density at given points (u,v)#'
Usage
dcop(u, v, family, rot = 0, cpar, dfC = NULL)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
family |
copula family: "gaussian" ("normal), "t", "clayton", "frank", "fgm", "galambos", "gumbel", "joe", "huesler-reiss", "plackett". |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
cpar |
copula parameter |
dfC |
degrees of freedom for the Student copula (default is NULL) |
Value
out |
Copula density |
out |
Vector of pdf values |
Author(s)
Pavel Krupskii and Bruno Remillard, May 1, 2023
Examples
out = dcop(0.3,0.7,"clayton",270,2)
Farlie-Gumbel-Morgenstern copula density, -1<= cpar<=
Description
Density at (u,v)
Usage
dfgm(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter > 0 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dfgm(0.3,0.5,0.2)
B3 bivariate Frank copula density
Description
Density at (u,v)
Usage
dfrk(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter, cpar>0 or cpar<0 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dfrk(0.3,0.5,2)
B7 Galambos copula density, cpar>0
Description
Density at (u,v)
Usage
dgal(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter > 0 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dgal(0.3,0.5,2)
B6 Gumbel copula density, cpar>1
Description
Density at (u,v)
Usage
dgum(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter > 0 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dgum(0.3,0.5,2)
B8 Huesler-Reiss copula density, cpar>0
Description
Density at (u,v)
Usage
dhr(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter > 0 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dhr(0.3,0.5,2)
B5 Joe copula density
Description
Density at (u,v)
Usage
djoe(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter > 1 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = djoe(0.3,0.5,2)
B4 MTCJ copula density, cpar>0
Description
Density at (u,v)
Usage
dmtcj(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter > 0 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dmtcj(0.3,0.5,2)
B2 Plackett copula density
Description
Density at (u,v)
Usage
dpla(u, v, cpar)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
cpar |
copula parameter > 0 |
Value
out |
Vector of densities |
Author(s)
Pavel Krupskii
Examples
out = dpla(0.3,0.5,2)
Conditional expectation
Description
This function computes the conditional expectation for a given copula family and a given margin variables for a clustered data model. The clusters ar3e independent but the observations with clusters are dependent, according to a one-factor copula model.
Usage
expcond(w, family, rot = 0, cpar, margin, dfC = NULL, subs = 1000)
Arguments
w |
value of the conditioning random variable |
family |
copula model: "gaussian" , "t" , "clayton" ,"joe", "frank" , "gumbel", "plackett" |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
cpar |
copula parameter |
margin |
marginal distribution function |
dfC |
degrees of freedom for the Student copula (default is NULL) |
subs |
number of subdivisions for the integrals (default=1000) |
Value
mest |
Conditional expectations |
Author(s)
Pavel Krupskii and Bruno N. Remillard
Examples
margin = function(x){ppois(x,10)}
expcond(0.4,'clayton',cpar=2,margin=margin)
Inverse conditional expectation for a vector of probabilities
Description
This function computes the inverse conditional expecatation for a given copula family and a given margin variables for a clustered data model. The clusters ar3e independent but the observations with clusters are dependent, according to a one-factor copula model.
Usage
expcondinv(u, family, cpar, rot = 0, margin, subs = 1000, eps = 1e-04)
Arguments
u |
conditional expectation |
family |
copula model: "gaussian" , "t" , "clayton" "joe", "frank" , "gumbel", "plackett" |
cpar |
copula parameter |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
margin |
marginal distribution function of the response |
subs |
number of subdivisions for the integrals (default=1000) |
eps |
precision required |
Value
minv |
Inverse conditional expectation |
Author(s)
Pavel Krupskii and Bruno N. Remillard
Inverse conditional expectation for a single value
Description
Inverse conditional expectation for a single value
Usage
expcondinv1(u, family, cpar, rot = 0, margin, subs = 1000, eps = 1e-04)
Arguments
u |
conditional expectation |
family |
copula model: "gaussian" , "t" , "clayton" "joe", "frank" , "gumbel", "plackett" |
cpar |
copula parameter |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
margin |
marginal distribution function of the response |
subs |
number of subdivisions for the integrals (default=1000) |
eps |
precision required |
Value
minv |
Inverse conditional expectation |
Exponential cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
expcpdf(z, th)
Arguments
z |
vector of responses |
th |
th is rate > 0 |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = expcpdf(2,3)
Farlie-Gumbel-Morgenstern copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
ffgmders(u, v, cpar, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter in [-1,1] |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = ffgmders(0.3,0.5,2,TRUE)
Frank copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
ffrkders(u, v, cpar, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = ffrkders(0.3,0.5,2,TRUE)
Gumbel copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
fgumders(u, v, cpar, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter > 1 |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = fgumders(0.3,0.5,2,TRUE)
Joe copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
fjoeders(u, v, cpar, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter > 1 |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = fjoeders(0.3,0.5,2,TRUE)
Clayton copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
fmtcjders(u, v, cpar, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter > 0 |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = fmtcjders(0.3,0.5,2,TRUE)
Farlie-Gumbel-Morgenstern copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
fnorders(u, v, cpar, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter in (-1,1) |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = fnorders(0.3,0.5,0.6,TRUE)
Plackett copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
fpladers(u, v, cpar, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter > 0 |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = fpladers(0.3,0.5,2,TRUE)
Student copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
ftders(u, v, cpar, nu, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter in (-1,1) |
nu |
degrees of freedom >0 |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = ftders(0.3,0.5,2,25)
Student copula cdf/pdf and ders
Description
Derivatives C(u|v), C'_dl(u|v), c(u,v), c'_dl(u,v), c'_u(u,v) for the linking copula
Usage
ftdersP(u, v, cpar, dfC, du = FALSE)
Arguments
u |
vector of values in (0,1) |
v |
conditioning variable in (0,1) |
cpar |
copula parameter in (-1,1) |
dfC |
degrees of freedom |
du |
logical value (default = FALSE) for the derivative of the copula density with respect to u |
Value
out |
Matrix of conditional cdf, pdf, and derivatives with respect to parameter |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = ftdersP(0.3,0.5,2,25,TRUE)
Geometric with p = 1/(1+exp(-th)) cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
geomcpdf(z, th)
Arguments
z |
vector of responses |
th |
linear combination of covariates (can be negative) |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = geomcpdf(0,-3)
Inverse function
Description
This function is used to get the inverse of a monotonic function on (0,1), depending on parameters, and using the bisection method
Usage
invfunc(q, func, th, lb = 1e-12, ub = 1 - 1e-12, tol = 1e-08, nbreak = 40)
Arguments
q |
Function value (can be a vector if func() supports a vector argument) |
func |
Function of one argument to be inverted |
th |
Function parameters |
lb |
Lower bound for the possible values |
ub |
Upper bound for the possible values |
tol |
Tolerance for the inversion |
nbreak |
Maximum number of iterations (default is 40) |
Value
out |
Inverse values |
Author(s)
Pavel Krupskii
Laplace cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
lapcpdf(z, th)
Arguments
z |
vector of responses |
th |
th[,1] is mean, th[,2] is standard deviation > 0 |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = lapcpdf(2,c(-3,4))
Link to copula parameter
Description
Computes the copula parameters given a linear combination of covariates.
Usage
linkCop(th, family = "clayton")
Arguments
th |
vector of linear combinations |
family |
copula family: "gaussian" , "t" , "clayton" , "claytonR" , "frank" , "gumbel", "gumbelR". |
Value
cpar |
Associated copula parameters |
hder |
Derivative of link function |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2023
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
out = linkCop(-1,"gaussian")
Margins cdf/pdf and their derivatives
Description
This function computes the cdf, pdf, and associated derivatives
Usage
margins(z, th, model, x = NULL, dfM = NULL)
Arguments
z |
vector of responses |
th |
linear combination of covariates (can be negative) |
model |
model for margin: "binomial" (bernoulli), "poisson", "nbinom" (mean is the parameter),"nbinom1" (p is the parameter), "geometric", "multinomial", "exponential", "weibull", "normal","t", "laplace" |
x |
covariates for the multinomial margin (default is NULL) |
dfM |
degrees of freedom for the Student margin (default is NULL) |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = margins(0,2.5,"binomial")
Estimation of the parameter of a bivariate copula (Clayton, Frank, Gumbel)
Description
Computes the MLE estimation for a bivariate copula using gradient. The likelihood is likelihood is c(u,v;theta)
Usage
mlecop(u, v, fcopders, start = 2, LB = 1.01, UB = 7)
Arguments
u |
vector of values in (0,1) |
v |
vector of values in (0,1) |
fcopders |
ffrkders, fgumders or fmtcjders |
start |
starting value for the parameter (default =2) |
LB |
lower bound for the parameter (default is 1.01) |
UB |
upper bound for the parameter (default is 7) |
Value
mle |
List of outputs from nlm function |
Author(s)
Pavel Krupskii
Examples
set.seed(2)
v = runif(250)
w = runif(250)
u = 1/sqrt(1+(w^(-2/3)-1)/v^2) # Clayton copula with parameter 2 (tau=0.5)
out = mlecop(u,v,fmtcjders)
Estimation of the parameter of a bivariate copula (Clayton, Frank, Gumbel) when the first observation is 0 or 1
Description
Computes the MLE estimation for a bivariate copula using gradient. The likelihood is likelihood is C(1-p|v;theta) if y=0 and 1-C(1-p|v;theta) if y=1
Usage
mlecop.disc(y, v, fcopders, start = 2, LB = 1.01, UB = 7)
Arguments
y |
vector of binary values 0 or 1 |
v |
vector of values in (0,1) |
fcopders |
ffrkders, fgumders or fmtcjders |
start |
starting value for the parameter (default =2) |
LB |
lower bound for the parameter (default is 1.01) |
UB |
upper bound for the parameter (default is 7) |
Value
mle |
List of outputs from nlm function |
Author(s)
Pavel Krupskii
Examples
set.seed(2)
v = runif(250)
w = runif(250)
u = 1/sqrt(1+(w^(-2/3)-1)/v^2) #Clayton with parameter 2
y = as.numeric(u>0.6) # if one takes (u<4), one obtains a rotation of the Clayton!
out = mlecop.disc(y,v,fmtcjders)
Multinomial with p = 1/(1+exp(-th)) cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
multinomcpdf(z, th, x)
Arguments
z |
vector of responses taking values in 1,...,nL: as.number(z) if z is a factor! |
th |
th is a n x (L-1) matrix of parameters, i.e., mpar = a=[a_1,1,...a_1,k2,a_2,1,...a_2,k2,... a_L-1,1... a_L-1,k2], and first level is the baseline. |
x |
matrix of covariates (including the constant) |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
x=matrix(c(1,1,-1,-1,0,2),nrow=2)
z = c(1,3)
th = matrix(c(1,2,3,4,5,6),nrow=2)
out = multinomcpdf(z,th,x = x)
Simulated data
Description
Simulated clustered data from a Clayton copula with parameter 2, and multinomial margins with 3 levels and parameters 1.0,-1 for level 2 and 0.5, 2 for level 3. Clusters and covariates are included.
Usage
data(multinomial)Format
Data frame of numerical values
Examples
data(multinomial)
Negative binomial cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
nbinom1cpdf(z, th)
Arguments
z |
vector of responses |
th |
th[,1] is size > 0 and th[,2] is mean > 0; size does not have to be integer |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = nbinom1cpdf(0,c(1,0.5))
Negative binomial cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
nbinomcpdf(z, th)
Arguments
z |
vector of responses |
th |
th[,1] is size > 0 and th[,2] is p, with 0<p<1; size does not have to be integer |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = nbinomcpdf(0,c(1,0.5))
Simulated data
Description
Simulated clustered data from a Clayton copula with parameter 2, rotation = 90, and normal margins with 1,-1 for the mean, and sd = 4. Clusters and covariates are included.
Usage
data(normal)Format
List of simulated values (y, clu, xm)
Examples
data(normal)
normal cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
normcpdf(z, th)
Arguments
z |
vector of responses |
th |
th[,1] is mean, th[,2] is standard deviation > 0; |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = normcpdf(2,c(-3,4))
EstContinuous object
Description
Output of EstContinuous for the simulated clustered data normal.
Usage
data(out.normal)Format
Data frame of numerical values
Examples
data(out.normal)
EstDiscrete object
Description
Output of EstDiscrete for the simulated clustered data poisson.
Usage
data(out.poisson)Format
Data frame of numerical values
Examples
data(out.poisson)
Conditional cdf
Description
This function computes the conditional cdf C(U|V) for a copula C
Usage
pcond(U, V, family, rot = 0, cpar, dfC = NULL)
Arguments
U |
values at which the cdf is evaluated |
V |
value of the conditioning variable in (0,1) |
family |
"gaussian" , "t" , "clayton" , "joe", "frank" , "fgm", gumbel", "plackett", "galambos", "huesler-reiss" |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
cpar |
copula parameter (vector) |
dfC |
degrees of freedom of the Student copula (default is NULL) |
Value
p |
Conditional cdf |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
p = pcond(0.1,0.2,"clayton",rot=270,cpar=0.87)
Conditional Clayton
Description
Conditional Clayton
Usage
pcondcla(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter |
Value
ccdf |
Conditional cdf |
Examples
pcondcla(0.5,0.6,2)
Conditional FGM (B10)
Description
Conditional FGM (B10)
Usage
pcondfgm(u, v, cpar)
Arguments
u |
probability |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter -1<=cpar<=1 |
Value
ccdf |
Conditional cdf |
Examples
pcondfgm(0.5,0.6,0.9)
Conditional Frank (B3)
Description
Conditional Frank (B3)
Usage
pcondfrk(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter |
Value
ccdf |
Conditional cdf |
Examples
pcondfrk(0.5,0.6,2)
Conditional Galambos (B7)
Description
Conditional Galambos (B7)
Usage
pcondgal(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter |
Value
ccdf |
Conditional cdf |
Examples
pcondgal(0.5,0.6,2)
Conditional Gumbel (B6)
Description
Conditional Gumbel (B6)
Usage
pcondgum(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter >1 |
Value
ccdf |
Conditional cdf |
Examples
pcondgum(0.5,0.6,2)
Conditional Huesler-Reiss (B8)
Description
Conditional Huesler-Reiss (B8)
Usage
pcondhr(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter >0 |
Value
ccdf |
Conditional cdf |
Examples
pcondhr(0.5,0.6,2)
Conditional Joe (B5)
Description
Conditional Joe (B5)
Usage
pcondjoe(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter |
Value
ccdf |
Conditional cdf |
Examples
pcondjoe(0.5,0.6,2)
Conditional Gaussian
Description
Conditional Gaussian
Usage
pcondnor(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter |
Value
ccdf |
Conditional cdf |
Examples
pcondnor(0.5,0.6,0.6)
Conditional Plackett (B2)
Description
Conditional Plackett (B2)
Usage
pcondpla(u, v, cpar)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter >1 |
Value
ccdf |
Conditional cdf |
Examples
pcondpla(0.5,0.6,2)
Conditional Student
Description
Conditional Student is Y2|Y1=y1 ~ t(nu+1,location=rho*y1, sigma(y1)), where here sigma^2 = (1-rho^2)(nu+y1^2)/(nu+1)
Usage
pcondt(u, v, cpar, dfC)
Arguments
u |
values at which the cdf is evaluated |
v |
value of the conditioning variable in (0,1) |
cpar |
copula parameter |
dfC |
degrees of freedom |
Value
ccdf |
Conditional cdf |
Examples
pcondt(0.5,0.6,0.6,15)
Poisson cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
poiscpdf(z, th)
Arguments
z |
vector of responses |
th |
values of lambda >0 |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = poiscpdf(0,2.5)
Conditional expectation for a copula-based estimation of mixed regression models for continuous response
Description
Compute the conditional expectation of a copula-based 2-level hierarchical model for continuous response.
Usage
predictContinuous(object, newdata = NULL, nq = 25)
Arguments
object |
Object of class “EstContinuous“ generated by EstContinuous. |
newdata |
List of variables for be predicted (“clu“ for clusters, “xc“ for the copula covariates, and “xm“ for the margins covariates). The covariates can be NULL. |
nq |
number of nodes and weighted for Gaussian quadrature of the product of conditional copulas; default is 25. |
Value
mest |
Conditional expectations |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2023
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
data(out.normal)
newdata=list(clu=c(1:50),xm=rep(0.4,50))
pred= predictContinuous(out.normal,newdata)
Conditional expectation for a copula-based estimation of mixed regression models for continuous or discrete response
Description
Compute the conditional expectation of a copula-based 2-level hierarchical model for disctrete response.
Usage
predictCopulaGAMM(object, newdata, m = 100)
Arguments
object |
Object of class “CopulaGAMM“ generated by EstCopulaGAMM. |
newdata |
List of variables for be predicted (“clu“ for clusters, “xc“ for the copula covariates, and “xm“ for the margins covariates). The covariates can be NULL. |
m |
Number of points for the numerical integration in the discrete case (default is 100). |
Value
mest |
Conditional expectations (conditional probabilities for the multinomial case |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2023
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
data(out.poisson)
newdata = list(clu=c(1:50),xc=rep(0.2,50),xm=rep(0.5,50))
pred= predictCopulaGAMM(out.poisson,newdata,m=100)
Conditional expectation for a copula-based estimation of mixed regression models for discrete response
Description
Compute the conditional expectation of a copula-based 2-level hierarchical model for disctrete response.
Usage
predictDiscrete(object, newdata, m = 100)
Arguments
object |
Object of class “EstDiscrete“ generated by EstDiscrete. |
newdata |
List of variables for be predicted (“clu“ for clusters, “xc“ for the copula covariates, and “xm“ for the margins covariates). The covariates can be NULL. |
m |
Number of points for the numerical integration (default is 100). |
Value
mest |
Conditional expectations (conditional probabilities for the multinomial case |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2023
References
Krupskii, Nasri & Remillard (2023). On factor copula-based mixed regression models
Examples
data(out.poisson)
newdata = list(clu=c(1:50),xc=rep(0.2,50),xm=rep(0.5,50))
pred= predictDiscrete(out.poisson,newdata,m=100)
Estimation cdf, left-continuous cdf, and pseudo-observations
Description
This function estimates the empirical cdf, its left limit, and pseudo-observations for a univatiate vector y
Usage
pseudosC(y)
Arguments
y |
univariate data |
Value
Fn |
Emprirical cdf |
Fm |
Left-contniuous cdf |
U |
Pseudo-obsevations |
Author(s)
Bruno N. Remillard, January 20, 2022
Examples
y = rpois(100,2)
out=pseudosC(y)
Inverse conditional cdf
Description
This function computes the quantile of conditional cdf C(U|v) for a copula C
Usage
qcond(w, v, family, cpar, rot = 0)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
family |
"gaussian" , "t" , "clayton" , "fgm", "frank" , "gumbel", "plackett", "galambos", "huesler-reiss" |
cpar |
copula parameter (vector) |
rot |
rotation: 0 (default), 90, 180 (survival), or 270 |
Value
U |
Conditional quantile |
U |
Conditional quantile |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
U = qcond(0.1,0.2,"gaussian",0.87)
Inverse clayton
Description
Inverse clayton
Usage
qcondcla(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter |
Value
out |
Conditional quantile |
Inverse FGM (B10)
Description
Inverse FGM (B10)
Usage
qcondfgm(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter -1<=th<=1 |
Value
out |
Conditional quantile |
Inverse Frank
Description
Inverse Frank
Usage
qcondfra(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter |
Value
out |
Conditional quantile |
Inverse Galambos
Description
Inverse Galambos
Usage
qcondgal(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter >0 |
Value
out |
Conditional quantile |
Inverse Gumbel
Description
Inverse Gumbel
Usage
qcondgum(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter |
Value
out |
Conditional quantile |
Inverse Huesler-Reiss
Description
Inverse Huesler-Reiss
Usage
qcondhr(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter >0 |
Value
out |
Conditional quantile |
Inverse Joe
Description
Inverse Joe
Usage
qcondjoe(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter >-1 |
Value
out |
Conditional quantile |
Inverse Gaussian
Description
Inverse Gaussian
Usage
qcondnor(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter (correlation) |
Value
out |
Conditional quantile |
Inverse Plackett
Description
Inverse Plackett
Usage
qcondpla(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter |
Value
out |
Conditional quantile |
Inverse Student
Description
Inverse Student
Usage
qcondt(w, v, th)
Arguments
w |
probability |
v |
value of the conditioning variable in (0,1) |
th |
copula parameter |
Value
out |
Conditional quantile |
Simulated data
Description
Simulated clustered data from a Frank copula with parC=c(2,8), and Poisson margins with parM=c(3.0,-0.1). Clusters and covariates (both uniform) are included.
Usage
data(sim.poisson)Format
List of simulated values (y, clu,xc,xm) together with true parameters
Examples
data(sim.poisson)
Student cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
tcpdf(z, th, df)
Arguments
z |
vector of responses |
th |
th[,1] is mean, th[,2] is standard deviation > 0 |
df |
degrees of freedom |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = tcpdf(2,c(-3,4),25)
Weibul cdf/pdf and ders
Description
This function computes the cdf, pdf, and associated derivatives
Usage
weibcpdf(z, th)
Arguments
z |
vector of responses |
th |
th[,1] is rate>0, th[,2] is shape > 0; |
Value
out |
Matrix of conditional cdf, derivative with respect to parameter, pdf, |
Author(s)
Pavel Krupskii and Bruno N. Remillard, January 20, 2022
Examples
out = weibcpdf(2,c(2,3))