Covariance: R6 Class representing a covariance function and data

In samuel-watson/glmmr: Design and analysis for generalised linear mixed models in R

R6 Class representing a covariance function and data

Description

R6 Class representing a covariance function and data

R6 Class representing a covariance function and data

Details

For the generalised linear mixed model

Y \sim F(μ,σ)

μ = h^-1(Xβ + Zγ)

γ \sim MVN(0,D)

where h is the link function, this class defines Z and D. The covariance is defined by a covariance function, data, and parameters. A new instance can be generated with $new(). The class will generate the relevant matrices Z and D automatically.

**Intitialisation** A covariance function is specified as an additive formula made up of components with structure (1|f(j)). The left side of the vertical bar specifies the covariates in the model that have a random effects structure. The right side of the vertical bar specify the covariance function 'f' for that term using variable named in the data 'j'. If there are multiple covariates on the left side, it is assumed their random effects are correlated, e.g. (1+x|f(j)). Additive functions are assumed to be independent, for example, (1|f(j))+(x|f(j)) would create random effects with zero correlation for the intercept and the parameter on covariate x. Covariance functions on the right side of the vertical bar are multiplied together, i.e. (1|f(j)*g(t)).

There are several common functions included for a named variable in data x: * gr(x): Indicator function (1 parameter) * fexp(x): Exponential function (2 parameters) * ar1(x): AR1 function (1 parameter) * sqexp(x): Squared exponential (1 parameter) * matern(x): Matern function (2 parameters) * bessel(x): Modified Bessel function of the 2nd kind (1 parameter)

Parameters are provided to the covariance function as a vector. The parameters in the vector for each function should be provided in the order the covariance functions are written are written. For example, * Formula: '~(1|gr(j))+(1|gr(j*t))'; parameters: 'c(0.25,0.1)' * Formula: '~(1|gr(j)*fexp(t))'; parameters: 'c(0.25,1,0.5)' Note that it is also possible to specify a group membership with two variable alternatively as '(1|gr(j)*gr(t))', for example, but this will require two parameters to be specified, so it is recommended against.

Public fields

data

Data frame with data required to build covariance

formula

Covariance function formula. See 'help(Covariance$new())' for details.

parameters

List of lists holding the model parameters. See 'help(Covariance$new())' for details.

Z

Design matrix

D

Covariance matrix of the random effects

Methods

Public methods

• Covariance$n()

• Covariance$new()

• Covariance$check()

• Covariance$print()

• Covariance$subset()

• Covariance$sampleD()

• Covariance$clone()

---

Method n()

Return the size of the design

Usage

Covariance$n()

Returns

Scalar

---

Method new()

Create a new Covariance object

Usage

Covariance$new(formula = NULL, data = NULL, parameters = NULL, verbose = TRUE)

Arguments

formula

Formula describing the covariance function. See Details

data

Data frame with data required for constructing the covariance.

parameters

List of lists with parameter values for the functions in the model formula. See Details.

verbose

Logical whether to provide detailed output.

Returns

A Covariance object

Examples

df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = c(0.25,0.7),
                      data= df)

---

Method check()

Check if anything has changed and update matrices if so.

Usage

Covariance$check(verbose = TRUE)

Arguments

verbose

Logical whether to report if any changes detected.

Returns

NULL

Examples

df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)
cov$parameters <- list(list(0.01,0.1))
cov$check(verbose=FALSE)

---

Method print()

Show details of Covariance object

Usage

Covariance$print()

Arguments

...

ignored

Examples

df <- nelder(~(cl(5)*t(5)) > ind(5))
Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)

---

Method subset()

Keep specified indices and removes the rest

Usage

Covariance$subset(index)

Arguments

index

vector of indices to keep

Examples

df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)
cov$subset(1:100)                     

---

Method sampleD()

Generate a new D matrix

D is the covariance matrix of the random effects terms in the generalised linear mixed model. This function will return a matrix D for a given set of parameters.

Usage

Covariance$sampleD(parameters)

Arguments

parameters

list of lists, see initialize()

Returns

matrix

Examples

df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)
cov$sampleD(list(list(0.01,0.1)))

---

Method clone()

The objects of this class are cloneable with this method.

Usage

Covariance$clone(deep = FALSE)

Arguments

deep

Whether to make a deep clone.

Examples

## ------------------------------------------------
## Method `Covariance$new`
## ------------------------------------------------

df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = c(0.25,0.7),
                      data= df)

## ------------------------------------------------
## Method `Covariance$check`
## ------------------------------------------------

df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)
cov$parameters <- list(list(0.01,0.1))
cov$check(verbose=FALSE)

## ------------------------------------------------
## Method `Covariance$print`
## ------------------------------------------------

df <- nelder(~(cl(5)*t(5)) > ind(5))
Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)

## ------------------------------------------------
## Method `Covariance$subset`
## ------------------------------------------------

df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)
cov$subset(1:100)                     

## ------------------------------------------------
## Method `Covariance$sampleD`
## ------------------------------------------------

df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(j)*ar1(t)),
                      parameters = list(list(0.05,0.8)),
                      data= df)
cov$sampleD(list(list(0.01,0.1)))

samuel-watson/glmmr documentation built on July 27, 2022, 10:30 p.m.