R: Classes and Methods for a Compound Poisson Linear Model...

class-methods {cplm} | R Documentation

## Classes and Methods for a Compound Poisson Linear Model Object

### Description

Documented here are the `"cplm"` class and its derived classes `"cpglm"`, `"cpglmm"`, `"bcplm"` and `"zcpglm"`. Several primitive methods and statistical methods are created to facilitate the extraction of specific slots and further statistical analysis. `"gini"` is a class that stores the Gini indices and associated standard errors that could be used to perform model comparison involving the compound Poisson distribution. `"NullNum"`, `"NullList"`, `"NullFunc"` and `"ListFrame"` are virtual classes for `c("NULL", "numeric")`, `c("NULL","list")`, `c("NULL","function")` and `c("list","data.frame")`, respectively.

### Objects from the Class

`"cplm"`

  Objects can be created by calls of the form `new("cplm", ...)`.

`"cpglm"`

  Objects can be created by calls from `new("cpglm", ...)` or `cpglm`.

`"cpglmm"`

  Objects can be created by calls of the form `new("cpglmm", ...)`, or a call to `cpglmm`.

`"summary.cpglmm"`

  Objects can be created by calls of the form `new("summary.cpglmm", ...)`, or a call to `summary` on a `cpglmm` object.

`"bcplm"`

  Objects can be created by calls from `new("bcplm", ...)` or `bcplm`.

`"zcpglm"`

  Objects can be created by calls from `new("zcpglm", ...)` or `zcpglm`.

`"gini"`

  Objects can be created by calls from `new("gini", ...)` or `gini`.

`"NullNum"`, `"NullList"`, `"NullFunc"`

  These are virtual classes and no objects may be created from them.

### Slots

The `"cplm"` class defines the slots common in all the model classes in the `cplm` package, and thus the utility methods defined on the `"cplm"` class such as `[`, `names` and so on are applicable to all of the derived classes.

`call`:

  the matched call.

`formula`:

  the formula supplied, class `"formula"`

`contrasts`:

  the contrasts used, class `"NullList"`

`link.power`:

  index of power link function, class `"numeric"`. See `tweedie`.

`model.frame`:

  the data frame used. class `"ListFrame"`.

`inits`:

  initial values used, class `"NullList"`.

The `"cpglm"` class extends `"cplm"` directly. Most of the slots have the same definition as those in `glm`. The following slots are in addition to those in `"cplm"`:

`coefficients`:

  estimated mean parameters, class `"numeric"`.

`residuals`:

  the working residuals, that is the residuals in the final iteration of the IWLS fit, class `"numeric"`

`fitted.values`:

  the fitted mean values, obtained by transforming the linear predictors by the inverse of the link function, class `"numeric"`

`linear.predictors`:

  the fitted linear predictors, class `"numeric"`

`weights`:

  working weights from the last iteration of the iterative least square, class `"numeric"`

`df.residual`:

  residual degrees of freedom, class `"integer"`

`deviance`:

  up to a constant, minus twice the maximized log-likelihood. Where sensible, the constant is chosen so that a saturated model has deviance zero. This is computed using `tweedie.dev`.

`aic`:

  a version of Akaike's Information Criterion, minus twice the maximized log-likelihood plus twice the number of mean parameters. This is computed using the tweedie density approximation as in `dtweedie`.

`offset`:

  the offset vector used, class `"NullNum"`,

`prior.weights`:

  the weights initially supplied, a vector of `1`s if none were, class `"NullNum"`

`y`:

  the response vector used.

`control`:

  the value of the control argument used, class `"list"`

`p`:

  the maximum likelihood estimate of the index parameter.

`phi`:

  the maximum likelihood estimate of the dispersion parameter.

`vcov`:

  estimated variance-covariance matrix, class `"matrix"`

`iter`:

  the number of Fisher's scoring iterations in the final GLM.

`converged`:

  indicating whether the algorithm has converged, class `"logical"`.

`na.action`:

  method of handling `NA`'s, class `"NullFunc"`.

The `"cpglmm"` class extends `"cplm"` and the old version of `"mer"` class from `lme4` directly, and has the following additional slots:

`p`:

  estimated value of the index parameter, class `"numeric"`

`phi`:

  estimated value of the dispersion parameter, class `"numeric"`

`bound.p`:

  the specified bounds of the index parameter, class `"numeric"`

`vcov`:

  estimated variance-covariance matrix, class `"matrix"`

`smooths`:

  a list of smooth terms

The slots it used from the old `"mer"` class has the following slots (copied from `lme4_0.999999-2`):

`env`:

  An environment (class `"environment"`) created for the evaluation of the nonlinear model function.

`nlmodel`:

  The nonlinear model function as an object of class `"call"`.

`frame`:

  The model frame (class `"data.frame"`).

`call`:

  The matched call to the function that created the object. (class `"call"`).

`flist`:

  The list of grouping factors for the random effects.

`X`:

  Model matrix for the fixed effects.

`Zt`:

  The transpose of model matrix for the random effects, stored as a compressed column-oriented sparse matrix (class `"dgCMatrix"`).

`pWt`:

  Numeric prior weights vector. This may be of length zero (0), indicating unit prior weights.

`offset`:

  Numeric offset vector. This may be of length zero (0), indicating no offset.

`y`:

  The response vector (class `"numeric"`).

`Gp`:

  Integer vector of group pointers within the random effects vector. The elements of `Gp` are 0-based indices of the first element from each random-effects term. Thus the first element is always 0. The last element is the total length of the random effects vector.

`dims`:

  A named integer vector of dimensions. Some of the dimensions are n, the number of observations, p, the number of fixed effects, q, the total number of random effects, s, the number of parameters in the nonlinear model function and nt, the number of random-effects terms in the model.

`ST`:

  A list of S and T factors in the TSST' Cholesky factorization of the relative variance matrices of the random effects associated with each random-effects term. The unit lower triangular matrix, T, and the diagonal matrix, S, for each term are stored as a single matrix with diagonal elements from S and off-diagonal elements from T.

`V`:

  Numeric gradient matrix (class `"matrix"`) of the nonlinear model function.

`A`:

  Scaled sparse model matrix (class `"dgCMatrix"`) for the the unit, orthogonal random effects, U.

`Cm`:

  Reduced, weighted sparse model matrix (class `"dgCMatrix"`) for the unit, orthogonal random effects, U. .

`Cx`:

  The `"x"` slot in the weighted sparse model matrix (class `"dgCMatrix"`) for the unit, orthogonal random effects, U, in generalized linear mixed models. For these models the matrices A and C have the same sparsity pattern and only the `"x"` slot of C needs to be stored.

`L`:

  The sparse lower Cholesky factor of P(AA'+I)P' (class `"dCHMfactor"`) where P is the fill-reducing permutation calculated from the pattern of nonzeros in A.

`deviance`:

  Named numeric vector containing the deviance corresponding to the maximum likelihood (the `"ML"` element) and `"REML"` criteria and various components. The `"ldL2"` element is twice the logarithm of the determinant of the Cholesky factor in the `L` slot. The `"usqr"` component is the value of the random-effects quadratic form.

`fixef`:

  Numeric vector of fixed effects.

`ranef`:

  Numeric vector of random effects on the original scale.

`u`:

  Numeric vector of orthogonal, constant variance, random effects.

`eta`:

  The linear predictor at the current values of the parameters and the random effects.

`mu`:

  The means of the responses at the current parameter values.

`muEta`:

  The diagonal of the Jacobian of mu by eta. Has length zero (0) except for generalized mixed models.

`var`:

  The diagonal of the conditional variance of Y given the random effects, up to prior weights. In generalized mixed models this is the value of the variance function for the `glm` family.

`resid`:

  The residuals, y-mu, weighted by the `sqrtrWt` slot (when its length is >0).

`sqrtXWt`:

  The square root of the weights applied to the model matrices X and Z. This may be of length zero (0), indicating unit weights.

`sqrtrWt`:

  The square root of the weights applied to the residuals to obtain the weighted residual sum of squares. This may be of length zero (0), indicating unit weights.

`RZX`:

  The dense solution (class `"matrix"`) to L RZX = ST'Z'X = AX.

`RX`:

  The upper Cholesky factor (class `"matrix"`) of the downdated X'X.

The `"summary.cpglmm"` class contains the `"cpglmm"` class and has the following additional slots:

`methTitle`:

  character string specifying a method title

`logLik`:

  the same as `logLik(object)`.

`ngrps`:

  the number of levels per grouping factor in the `flist` slot.

`sigma`:

  the scale factor for the variance-covariance estimates

`coefs`:

  the matrix of estimates, standard errors, etc. for the fixed-effects coefficients

`REmat`:

  the formatted Random-Effects matrix

`AICtab`:

  a named vector of values of AIC, BIC, log-likelihood and deviance

The `"bcplm"` class extends `"cplm"` directly, and has the following additional slots:

`dims`:

  a named integer vector of dimensions.

`sims.list`:

  an object of class `"mcmc.list"`. It is a list of `n.chains` `mcmc` objects, each `mcmc` object storing the simulation result from a Markov chain. See `mcmc` and `mcmc.convert`. Since this is an `"mcmc.list"` object, most methods defined in the `coda` package can be directly applied to it.

`Zt`:

  the transpose of model matrix for the random effects, stored as a compressed column-oriented sparse matrix (class `"dgCMatrix"`).

`flist`:

  the list of grouping factors for the random effects.

`prop.var`:

  a named list of proposal variance-covariance matrix used in the Metropolis-Hasting update.

The `"zcpglm"` class extends `"cplm"` directly and has the following additional slots:

`coefficients`:

  a list of estimated mean parameters for the zero-inflation and the compound Poisson parts, respectively

`residuals`:

  raw residuals, class `"numeric"`

`fitted.values`:

  the fitted mean values, that is (1 - probability of zero state) * compound Poisson mean, class `"numeric"`

`df.residual`:

  residual degrees of freedom, class `"integer"`

`offset`:

  a list of the offset vectors used in each model

`prior.weights`:

  the weights initially supplied, a vector of `1`s if none were, class `"numeric"`

`y`:

  the response vector used.

`control`:

  the value of the control argument used, class `"list"`

`p`:

  the maximum likelihood estimate of the index parameter.

`phi`:

  the maximum likelihood estimate of the dispersion parameter.

`vcov`:

  estimated variance-covariance matrix, class `"matrix"`

`converged`:

  indicating whether the algorithm has converged, class `"logical"`.

`na.action`:

  method of handling `NA`'s, class `"NullFunc"`.

`llik`:

  loglikelihood, class `numeric`.

The `"gini"` class has the following slots:

`call`:

  the matched call.

`gini`:

  a matrix of the Gini indices. The row names are corresponding to the base while the column names are corresponding to the scores.

`sd`:

  a matrix of standard errors for each computed Gini index.

`lorenz`:

  a list of matrices that determine the graph of the ordered Lorenz curve associated with each base and score combination. For each base, there is an associated matrix.

### Extends

Class `"cpglm"` extends class `"cplm"`, directly.

Class `"cpglmm"` extends class `"cplm"`, directly;

Class `"summary.cpglmm"` extends class `"cpglmm"`, directly; class `"cplm"`, by class `"cpglmm"`, distance 2.

Class `"bcplm"` extends class `"cplm"`, directly.

Class `"zcpglm"` extends class `"cplm"`, directly.

### Methods

The following methods are defined for the class `"cplm"`, which are also applicable to all of the derived classes:

$

  `signature(x = "cplm")`: extract a slot of `x` with a specified slot name, just as in list.

[[

  `signature(x = "cplm", i = "numeric", j = "missing")`: extract the i-th slot of a `"cpglm"` object, just as in list.

[[

  `signature(x = "cplm", i = "character", j = "missing")`: extract the slots of a `"cpglm"` object with names in `i`, just as in list.

[

  `signature(x = "cplm", i = "numeric", j = "missing", drop="missing")`: extract the i-th slot of a `"cpglm"` object, just as in list. `i` could be a vector.

[

  `signature(x = "cplm", i = "character", j = "missing", drop="missing")`: extract the slots of a `"cpglm"` object with names in `i`, just as in list. `i` could be a vector.

names

  `signature(x = "cplm")`: return the slot names.

terms

  `signature(x = "cplm")`: extract the `terms` object from the model frame. See `terms`.

formula

  `signature(x = "cplm")`: extract the `formula` slot. See `formula`.

model.matrix

  `signature(object = "cplm")`: extract the design matrix.

show

  `signature(object = "cplm")`: method for `show`.

vcov

  `signature(object = "cplm")`: extract the variance-covariance matrix of a `"cplm"` object.

The following methods are defined for the `"cpglm"` class:

coef

  `signature(object = "cpglm")`: extract the estimated coefficients.

fitted

  `signature(object = "cpglm")`: return the fitted values.

residuals

  `signature(object = "cpglm")`: extract residuals from a `cpglm` object. You can also specify a `type` argument to indicate the type of residuals to be computed. See `glm.summaries`.

resid

  `signature(object = "cpglm")`: same as `residuals`.

AIC

  `signature(object = "cpglm",k="missing")`: extract the AIC information from the `"cpglm"` object. See `AIC`.

deviance

  `signature(object = "cpglm")`: extract the deviance from the `"cpglm"` object. See `deviance`.

summary

  `signature(object = "cpglm")`: the same as `glm.summaries` except that both the dispersion and the index parameter are estimated using maximum likelihood estimation.

predict

  `signature(object = "cpglm")`: generate predictions for new data sets

The following are written for `"cpglmm"`:

print

  `signature(x = "cpglmm")`: print the object

summary

  `signature(object = "cpglmm")`: summary results

predict

  `signature(object = "cpglmm")`: generate predictions for new data sets

VarCorr

  `signature(x = "cpglmm")`: estimation for the variance components

vcov

  `signature(object = "cpglmm")`: variance-covariance matrix for fixed effects

The following methods are available for the class `"bcplm"`:

plot

  `signature(x = "bcplm", y = "missing")`: summarize the `"bcplm"` object with a trace of the sampled output and a density estimate for each variable in the chain. See `plot.mcmc`.

summary

  `signature(object = "bcplm")`: produce two sets of summary statistics. See `summary.mcmc`.

VarCorr

  `signature(x = "bcplm")`: estimation for the variance components if the random effects are present

fixef

  `signature(object = "bcplm")`: extract fixed effects. Additional arguments include: `sd = FALSE`: extract standard errors; `quantiles = NULL`: compute empirical quantiles. These additional statistics are stored as attributes in the returned results.

The following methods are defined for the `"zcpglm"` class:

coef

  `signature(object = "zcpglm")`: extract the estimated coefficients.

fitted

  `signature(object = "zcpglm")`: return the fitted values.

residuals

  `signature(object = "zcpglm")`: extract raw residuals.

resid

  `signature(object = "zcpglm")`: same as `residuals`.

summary

  `signature(object = "zcpglm")`: summary statistics using Z-test.

predict

  `signature(object = "zcpglm")`: generate predicted values for a new data set. Argument `type = c("response", "zero", "tweedie")`

specifies which component of the fitted values should be computed.

The following methods are defined for the `"gini"` class:

plot

  `signature(x = "gini", y = "missing")`: plot the ordered Lorenz curve from each model comparison. If `overlay = TRUE` (the default), different curves are plotted on the same graph for each base.

show

  `signature(object = "gini")`: print the computed Gini indices and standard errors.

### Author(s)

Wayne Zhang actuary_zhang@hotmail.com

### See Also

See also `cpglm`, `cpglmm`, `bcplm`, `zcpglm`, `glm`.

[Package cplm version 0.7-8 Index]