Covariance: R6 Class representing a covariance function and data
In glmmrBase: Generalised Linear Mixed Models in R
Covariance R Documentation
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(\mu,\sigma)
\mu = h^-1(X\beta + Z\gamma)
\gamma \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 $new(). The class will generate the
relevant matrices Z and D automatically. See glmmrBase for a
detailed guide on model specification.
**Intitialisation**
A covariance function is specified as an additive formula made up of
components with structure (1|f(j)). The left side of the vertical bar
specifies the covariates in the model that have a random effects structure.
The right side of the vertical bar specify the covariance function 'f' for
that term using variable named in the data 'j'.
Covariance functions on the right side of the vertical bar are multiplied
together, i.e. (1|f(j)*g(t)).
There are several common functions included for a named variable in data x.
A non-exhaustive list (see glmmrBase for a full list):
* gr(x): Indicator function (1 parameter)
* fexp(x): Exponential function (2 parameters)
* ar(x): AR function (2 parameters)
* sqexp(x): Squared exponential (1 parameter)
* matern(x): Matern function (2 parameters)
* bessel(x): Modified Bessel function of the 2nd kind (1 parameter)
For many 2 parameter functions, such as 'ar' and 'fexp', alternative one parameter
versions are also available as 'ar0' and 'fexp0'. These function omit the variance
parameter and so can be used in combination with 'gr' functions such as 'gr(j)*ar0(t)'.
Parameters are provided to the covariance function as a vector.
The parameters in the vector for each function should be provided
in the order the covariance functions are written are written.
For example,
* Formula: '~(1|gr(j))+(1|gr(j*t))'; parameters: 'c(0.05,0.01)'
* Formula: '~(1|gr(j)*fexp0(t))'; parameters: 'c(0.05,0.5)'
Updating of parameters is automatic if using the 'update_parameters()' member function.
Using 'update_parameters()' is the preferred way of updating the parameters of the
mean or covariance objects as opposed to direct assignment, e.g. 'self$parameters <- c(...)'.
The function calls check functions to automatically update linked matrices with the new parameters.
Public fields
dataData frame with data required to build covariance
formulaCovariance function formula.
parametersModel parameters specified in order of the functions in the formula.
ZDesign matrix
DCovariance matrix of the random effects
Methods
Public methods
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Method n()
Return the size of the design
Usage
Covariance$n()
Returns
Scalar
Method new()
Create a new Covariance object
Usage
Covariance$new(formula, data = NULL, parameters = NULL)
Arguments
formulaFormula describing the covariance function. See Details
data(Optional) Data frame with data required for constructing the covariance.
parameters(Optional) Vector with parameter values for the functions in the model
formula. See Details.
Returns
A Covariance object
Examples
\dontshow{
setParallel(FALSE) # for the CRAN check
}
df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.7),
data= df)
Method update_parameters()
Updates the covariance parameters
Usage
Covariance$update_parameters(parameters)
Arguments
parametersA vector of parameters for the covariance function(s). See Details.
Method print()
Show details of Covariance object
Usage
Covariance$print()
Arguments
...ignored
Examples
\dontshow{
setParallel(FALSE) # for the CRAN check
}
df <- nelder(~(cl(5)*t(5)) > ind(5))
Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
Method subset()
Keep specified indices and removes the rest
Usage
Covariance$subset(index)
Arguments
indexvector of indices to keep
Examples
\dontshow{
setParallel(FALSE) # for the CRAN check
}
df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
cov$subset(1:100)
Method chol_D()
Returns the Cholesky decomposition of the covariance matrix D
Usage
Covariance$chol_D()
Returns
A matrix
Method log_likelihood()
The function returns the values of the multivariate Gaussian log likelihood
with mean zero and covariance D for a given vector of random effect terms.
Usage
Covariance$log_likelihood(u)
Arguments
uVector of random effects
Returns
Value of the log likelihood
Method simulate_re()
Simulates a set of random effects from the multivariate Gaussian distribution
with mean zero and covariance D.
Usage
Covariance$simulate_re()
Returns
A vector of random effect values
Method sparse()
If this function is called then sparse matrix methods will be used for calculations involving D
Usage
Covariance$sparse(sparse = TRUE, amd = TRUE)
Arguments
sparseLogical. Whether to use sparse methods (TRUE) or not (FALSE)
amdLogical indicating whether to use and Approximate Minimum Degree algorithm to calculate an efficient permutation matrix so
that the Cholesky decomposition of PAP^T is calculated rather than A.
Returns
None. Called for effects.
Method parameter_table()
Returns a table showing which parameters are members of which covariance
function term.
Usage
Covariance$parameter_table()
Returns
A data frame
Method nngp()
Reports or sets the parameters for the nearest neighbour Gaussian process
Usage
Covariance$nngp(nn = NULL)
Arguments
nnInteger. Number of nearest neighbours. Optional - leave as NULL to return
details of the NNGP instead.
Returns
If 'nn' is NULL then the function will either return FALSE if not using a
Nearest neighbour approximation, or TRUE and the number of nearest neighbours, otherwise
it will return nothing.
Method hsgp()
Reports or sets the parameters for the Hilbert Space Gaussian process
Usage
Covariance$hsgp(m = NULL, L = NULL)
Arguments
mInteger or vector of integers. Number of basis functions per dimension. If only
a single number is provided and there is more than one dimension the same number will be applied
to all dimensions.
LDecimal. The boundary extension.
Returns
If 'm' and 'L' are NULL then the function will either return FALSE if not using a
Hilbert space approximation, or TRUE and the number of bases functions and boundary value, otherwise
it will return nothing.
Method clone()
The objects of this class are cloneable with this method.
Usage
Covariance$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
## ------------------------------------------------
## Method `Covariance$new`
## ------------------------------------------------
df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.7),
data= df)
## ------------------------------------------------
## Method `Covariance$print`
## ------------------------------------------------
df <- nelder(~(cl(5)*t(5)) > ind(5))
Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
## ------------------------------------------------
## Method `Covariance$subset`
## ------------------------------------------------
df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
cov$subset(1:100)
glmmrBase documentation built on April 3, 2025, 10:44 p.m.
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| Covariance | R Documentation |
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(\mu,\sigma)
\mu = h^-1(X\beta + Z\gamma)
\gamma \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 $new(). The class will generate the relevant matrices Z and D automatically. See glmmrBase for a detailed guide on model specification.
**Intitialisation**
A covariance function is specified as an additive formula made up of
components with structure (1|f(j)). The left side of the vertical bar
specifies the covariates in the model that have a random effects structure.
The right side of the vertical bar specify the covariance function 'f' for
that term using variable named in the data 'j'.
Covariance functions on the right side of the vertical bar are multiplied
together, i.e. (1|f(j)*g(t)).
There are several common functions included for a named variable in data x.
A non-exhaustive list (see glmmrBase for a full list):
* gr(x): Indicator function (1 parameter)
* fexp(x): Exponential function (2 parameters)
* ar(x): AR function (2 parameters)
* sqexp(x): Squared exponential (1 parameter)
* matern(x): Matern function (2 parameters)
* bessel(x): Modified Bessel function of the 2nd kind (1 parameter)
For many 2 parameter functions, such as 'ar' and 'fexp', alternative one parameter
versions are also available as 'ar0' and 'fexp0'. These function omit the variance
parameter and so can be used in combination with 'gr' functions such as 'gr(j)*ar0(t)'.
Parameters are provided to the covariance function as a vector. The parameters in the vector for each function should be provided in the order the covariance functions are written are written. For example, * Formula: '~(1|gr(j))+(1|gr(j*t))'; parameters: 'c(0.05,0.01)' * Formula: '~(1|gr(j)*fexp0(t))'; parameters: 'c(0.05,0.5)'
Updating of parameters is automatic if using the 'update_parameters()' member function.
Using 'update_parameters()' is the preferred way of updating the parameters of the mean or covariance objects as opposed to direct assignment, e.g. 'self$parameters <- c(...)'. The function calls check functions to automatically update linked matrices with the new parameters.
Public fields
dataData frame with data required to build covariance
formulaCovariance function formula.
parametersModel parameters specified in order of the functions in the formula.
ZDesign matrix
DCovariance matrix of the random effects
Methods
Public methods
Method n()
Return the size of the design
Usage
Covariance$n()
Returns
Scalar
Method new()
Create a new Covariance object
Usage
Covariance$new(formula, data = NULL, parameters = NULL)
Arguments
formulaFormula describing the covariance function. See Details
data(Optional) Data frame with data required for constructing the covariance.
parameters(Optional) Vector with parameter values for the functions in the model formula. See Details.
Returns
A Covariance object
Examples
\dontshow{
setParallel(FALSE) # for the CRAN check
}
df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.7),
data= df)
Method update_parameters()
Updates the covariance parameters
Usage
Covariance$update_parameters(parameters)
Arguments
parametersA vector of parameters for the covariance function(s). See Details.
Method print()
Show details of Covariance object
Usage
Covariance$print()
Arguments
...ignored
Examples
\dontshow{
setParallel(FALSE) # for the CRAN check
}
df <- nelder(~(cl(5)*t(5)) > ind(5))
Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
Method subset()
Keep specified indices and removes the rest
Usage
Covariance$subset(index)
Arguments
indexvector of indices to keep
Examples
\dontshow{
setParallel(FALSE) # for the CRAN check
}
df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
cov$subset(1:100)
Method chol_D()
Returns the Cholesky decomposition of the covariance matrix D
Usage
Covariance$chol_D()
Returns
A matrix
Method log_likelihood()
The function returns the values of the multivariate Gaussian log likelihood with mean zero and covariance D for a given vector of random effect terms.
Usage
Covariance$log_likelihood(u)
Arguments
uVector of random effects
Returns
Value of the log likelihood
Method simulate_re()
Simulates a set of random effects from the multivariate Gaussian distribution with mean zero and covariance D.
Usage
Covariance$simulate_re()
Returns
A vector of random effect values
Method sparse()
If this function is called then sparse matrix methods will be used for calculations involving D
Usage
Covariance$sparse(sparse = TRUE, amd = TRUE)
Arguments
sparseLogical. Whether to use sparse methods (TRUE) or not (FALSE)
amdLogical indicating whether to use and Approximate Minimum Degree algorithm to calculate an efficient permutation matrix so that the Cholesky decomposition of PAP^T is calculated rather than A.
Returns
None. Called for effects.
Method parameter_table()
Returns a table showing which parameters are members of which covariance function term.
Usage
Covariance$parameter_table()
Returns
A data frame
Method nngp()
Reports or sets the parameters for the nearest neighbour Gaussian process
Usage
Covariance$nngp(nn = NULL)
Arguments
nnInteger. Number of nearest neighbours. Optional - leave as NULL to return details of the NNGP instead.
Returns
If 'nn' is NULL then the function will either return FALSE if not using a Nearest neighbour approximation, or TRUE and the number of nearest neighbours, otherwise it will return nothing.
Method hsgp()
Reports or sets the parameters for the Hilbert Space Gaussian process
Usage
Covariance$hsgp(m = NULL, L = NULL)
Arguments
mInteger or vector of integers. Number of basis functions per dimension. If only a single number is provided and there is more than one dimension the same number will be applied to all dimensions.
LDecimal. The boundary extension.
Returns
If 'm' and 'L' are NULL then the function will either return FALSE if not using a Hilbert space approximation, or TRUE and the number of bases functions and boundary value, otherwise it will return nothing.
Method clone()
The objects of this class are cloneable with this method.
Usage
Covariance$clone(deep = FALSE)
Arguments
deepWhether to make a deep clone.
Examples
## ------------------------------------------------
## Method `Covariance$new`
## ------------------------------------------------
df <- nelder(~(cl(5)*t(5)) > ind(5))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.7),
data= df)
## ------------------------------------------------
## Method `Covariance$print`
## ------------------------------------------------
df <- nelder(~(cl(5)*t(5)) > ind(5))
Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
## ------------------------------------------------
## Method `Covariance$subset`
## ------------------------------------------------
df <- nelder(~(cl(10)*t(5)) > ind(10))
cov <- Covariance$new(formula = ~(1|gr(cl)*ar0(t)),
parameters = c(0.05,0.8),
data= df)
cov$subset(1:100)
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