Package 'glmmML' reference manual

Title:	Generalized Linear Models with Clustering
Description:	Binomial and Poisson regression for clustered data, fixed and random effects with bootstrapping.
Authors:	Göran Broström [aut, cre], Jianming Jin [ctb], Henrik Holmberg [ctb]
Maintainer:	Göran Broström <[email protected]>
License:	GPL (>= 3)
Version:	1.1.7
Built:	2024-11-20 06:59:00 UTC
Source:	CRAN

Gauss-Hermite

Description

Calculates the zeros and weights needed for Gauss-Hermite quadrature.

Usage

ghq(n.points = 1, modified = TRUE)
ghq(n.points = 1, modified = TRUE)

Arguments

`n.points`	Number of points.
`modified`	Multiply by exp(zeros**2)? Default is TRUE.

Details

Based on a Fortran 66 subroutine written by professor Jianming Jin.

Value

A list vith components

`zeros`	The zeros (abscissas).
`weights`	The weights

Note

The code is modified to suit the purpose of glmmML, with the permission of professor Jin.

Author(s)

Jianming Jin, Univ. of Illinois, Urbana-Campaign

References

Gauss-Hermite

Examples

ghq(15, FALSE)
ghq(15, FALSE)

Generalized Linear Models with fixed effects grouping

Description

Fits grouped GLMs with fixed group effects. The significance of the grouping is tested by simulation, with a bootstrap approach.

Usage

glmmboot(formula, family = binomial, data, cluster, weights, subset, na.action,
offset, contrasts = NULL, start.coef = NULL,
control = list(epsilon = 1e-08, maxit = 200, trace = FALSE), boot = 0)
glmmboot(formula, family = binomial, data, cluster, weights, subset, na.action,
offset, contrasts = NULL, start.coef = NULL,
control = list(epsilon = 1e-08, maxit = 200, trace = FALSE), boot = 0)

Arguments

`formula`	a symbolic description of the model to be fit. The details of model specification are given below.
`family`	Currently, the only valid values are `binomial` and `poisson`. The binomial family allows for the `logit` and `cloglog` links.
`data`	an optional data frame containing the variables in the model. By default the variables are taken from ‘environment(formula)’, typically the environment from which ‘glmmML’ is called.
`cluster`	Factor indicating which items are correlated.
`weights`	Case weights.
`subset`	an optional vector specifying a subset of observations to be used in the fitting process.
`na.action`	See glm.
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting.
`contrasts`	an optional list. See the 'contrasts.arg' of 'model.matrix.default'.
`start.coef`	starting values for the parameters in the linear predictor. Defaults to zero.
`control`	Controls the convergence criteria. See `glm.control` for details.
`boot`	number of bootstrap replicates. If equal to zero, no test of significance of the grouping factor is performed.

Details

The simulation is performed by simulating new response vectors from the fitted probabilities without clustering, and comparing the maximized log likelihoods. The maximizations are performed by profiling out the grouping factor. It is a very fast procedure, compared to glm, when the grouping factor has many levels.

Value

The return value is a list, an object of class 'glmmboot'.

`coefficients`	Estimated regression coefficients
`logLik`	the max log likelihood
`cluster.null.deviance`	Deviance without the clustering
`frail`	The estimated cluster effects
`bootLog`	The logLik values from the bootstrap samples
`bootP`	Bootstrap p value
`variance`	Variance covariance matrix
`sd`	Standard error of regression parameters
`boot_rep`	No. of bootstrap replicates
`mixed`	Logical
`deviance`	Deviance
`df.residual`	Its degrees of freedom
`aic`	AIC
`boot`	Logical
`call`	The function call

Note

There is no overall intercept for this model; each cluster has its own intercept. See frail

Author(s)

G\"oran Brostr\"om and Henrik Holmberg

References

Brostr\"om, G. and Holmberg, H. (2011). Generalized linear models with clustered data: Fixed and random effects models. Computational Statistics and Data Analysis 55:3123-3134.

Examples

## Not run:
id <- factor(rep(1:20, rep(5, 20)))
y <- rbinom(100, prob = rep(runif(20), rep(5, 20)), size = 1)
x <- rnorm(100)
dat <- data.frame(y = y, x = x, id = id)
res <- glmmboot(y ~ x, cluster = id, data = dat, boot = 5000)
## End(Not run)
##system.time(res.glm <- glm(y ~ x + id, family = binomial))
## Not run:
id <- factor(rep(1:20, rep(5, 20)))
y <- rbinom(100, prob = rep(runif(20), rep(5, 20)), size = 1)
x <- rnorm(100)
dat <- data.frame(y = y, x = x, id = id)
res <- glmmboot(y ~ x, cluster = id, data = dat, boot = 5000)
## End(Not run)
##system.time(res.glm <- glm(y ~ x + id, family = binomial))

Generalized Linear Models with fixed effects grouping

Description

'glmmbootFit' is the workhorse in the function glmmboot. It is suitable to call instead of 'glmmboot', e.g. in simulations.

Usage

glmmbootFit(X, Y, weights = rep(1, NROW(Y)),
start.coef = NULL, cluster = rep(1, length(Y)),
offset = rep(0, length(Y)), family = binomial(),
control = list(epsilon = 1.e-8, maxit = 200, trace
= FALSE), boot = 0)
glmmbootFit(X, Y, weights = rep(1, NROW(Y)),
start.coef = NULL, cluster = rep(1, length(Y)),
offset = rep(0, length(Y)), family = binomial(),
control = list(epsilon = 1.e-8, maxit = 200, trace
= FALSE), boot = 0)

Arguments

`X`	The design matrix (n * p).
`Y`	The response vector of length n.
`weights`	Case weights.
`start.coef`	start values for the parameters in the linear predictor (except the intercept).
`cluster`	Factor indicating which items are correlated.
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting.
`family`	Currently, the only valid values are `binomial` and `poisson`. The binomial family allows for the `logit` and `cloglog` links.
`control`	A list. Controls the convergence criteria. See `glm.control` for details.
`boot`	number of bootstrap replicates. If equal to zero, no test of significance of the grouping factor is performed. If non-zero, it should be large, at least, say, 2000.

Value

A list with components

`coefficients`	Estimated regression coefficients (note: No intercept).
`logLik`	The maximised log likelihood.
`cluster.null.deviance`	deviance from a moddel without cluster.
`frail`	The estimated cluster effects.
`bootLog`	The maximised bootstrap log likelihood values. A vector of length `boot`.
`bootP`	The bootstrap p value.
`variance`	The variance-covariance matrix of the fixed effects (no intercept).
`sd`	The standard errors of the `coefficients`.
`boot_rep`	The number of bootstrap replicates.

Note

A profiling approach is used to estimate the cluster effects.

Author(s)

Göran Broström

Examples

## Not run
x <- matrix(rnorm(1000), ncol = 1)
id <- rep(1:100, rep(10, 100))
y <- rbinom(1000, size = 1, prob = 0.4)
fit <- glmmbootFit(x, y, cluster = id, boot = 200)
summary(fit)
## End(Not run)
## Should show no effects. And boot too small.
## Not run
x <- matrix(rnorm(1000), ncol = 1)
id <- rep(1:100, rep(10, 100))
y <- rbinom(1000, size = 1, prob = 0.4)
fit <- glmmbootFit(x, y, cluster = id, boot = 200)
summary(fit)
## End(Not run)
## Should show no effects. And boot too small.

Generalized Linear Models with random intercept

Description

Fits GLMs with random intercept by Maximum Likelihood and numerical integration via Gauss-Hermite quadrature.

Usage

glmmML(formula, family = binomial, data, cluster, weights,
cluster.weights, subset, na.action, 
offset, contrasts = NULL, prior = c("gaussian", "logistic", "cauchy"),
start.coef = NULL, start.sigma = NULL, fix.sigma = FALSE, x = FALSE, 
control = list(epsilon = 1e-08, maxit = 200, trace = FALSE),
method = c("Laplace", "ghq"), n.points = 8, boot = 0) 
glmmML(formula, family = binomial, data, cluster, weights,
cluster.weights, subset, na.action, 
offset, contrasts = NULL, prior = c("gaussian", "logistic", "cauchy"),
start.coef = NULL, start.sigma = NULL, fix.sigma = FALSE, x = FALSE, 
control = list(epsilon = 1e-08, maxit = 200, trace = FALSE),
method = c("Laplace", "ghq"), n.points = 8, boot = 0)

Arguments

`formula`	a symbolic description of the model to be fit. The details of model specification are given below.
`family`	Currently, the only valid values are `binomial` and `poisson`. The binomial family allows for the `logit` and `cloglog` links.
`data`	an optional data frame containing the variables in the model. By default the variables are taken from ‘environment(formula)’, typically the environment from which ‘glmmML’ is called.
`cluster`	Factor indicating which items are correlated.
`weights`	Case weights. Defaults to one.
`cluster.weights`	Cluster weights. Defaults to one.
`subset`	an optional vector specifying a subset of observations to be used in the fitting process.
`na.action`	See glm.
`start.coef`	starting values for the parameters in the linear predictor. Defaults to zero.
`start.sigma`	starting value for the mixing standard deviation. Defaults to 0.5.
`fix.sigma`	Should sigma be fixed at start.sigma?
`x`	If TRUE, the design matrix is returned (as x).
`offset`	this can be used to specify an a priori known component to be included in the linear predictor during fitting.
`contrasts`	an optional list. See the 'contrasts.arg' of 'model.matrix.default'.
`prior`	Which "prior" distribution (for the random effects)? Possible choices are "gaussian" (default), "logistic", and "cauchy".
`control`	Controls the convergence criteria. See `glm.control` for details.
`method`	There are two choices "Laplace" (default) and "ghq" (Gauss-Hermite).
`n.points`	Number of points in the Gauss-Hermite quadrature. If n.points == 1, the Gauss-Hermite is the same as Laplace approximation. If `method` is set to "Laplace", this parameter is ignored.
`boot`	Do you want a bootstrap estimate of cluster effect? The default is No (`boot = 0`). If you want to say yes, enter a positive integer here. It should be equal to the number of bootstrap samples you want to draw. A recomended absolute minimum value is `boot = 2000`.

Details

The integrals in the log likelihood function are evaluated by the Laplace approximation (default) or Gauss-Hermite quadrature. The latter is now fully adaptive; however, only approximate estimates of variances are available for the Gauss-Hermite (n.points > 1) method.

For the binomial families, the response can be a two-column matrix, see the help page for glm for details.

Value

The return value is a list, an object of class 'glmmML'. The components are:

`boot`	No. of boot replicates
`converged`	Logical
`coefficients`	Estimated regression coefficients
`coef.sd`	Their standard errors
`sigma`	The estimated random effects' standard deviation
`sigma.sd`	Its standard error
`variance`	The estimated variance-covariance matrix. The last column/row corresponds to the standard deviation of the random effects (`sigma`)
`aic`	AIC
`bootP`	Bootstrap p value from testing the null hypothesis of no random effect (sigma = 0)
`deviance`	Deviance
`mixed`	Logical
`df.residual`	Degrees of freedom
`cluster.null.deviance`	Deviance from a glm with no clustering. Subtracting `deviance` gives a test statistic for the null hypothesis of no clustering. Its asymptotic distribution is a symmetric mixture a constant at zero and a chi-squared distribution with one df. The printed p-value is based on this.
`cluster.null.df`	Its degrees of freedom
`posterior.modes`	Estimated posterior modes of the random effects
`terms`	The terms object
`info`	From hessian inversion. Should be 0. If not, no variances could be estimated. You could try fixing sigma at the estimated value and rerun.
`prior`	Which prior was used?
`call`	The function call
`x`	The design matrix if asked for, otherwise not present

Note

The optimization may not converge with the default value of start.sigma. In that case, try different start values for sigma. If still no convergence, consider the possibility to fix the value of sigma at several values and study the profile likelihood.

Author(s)

G\"oran Brostr\"om

References

Brostr\"om, G. and Holmberg, H. (2011). Generalized linear models with clustered data: Fixed and random effects models. Computational Statistics and Data Analysis 55:3123-3134.

Examples

id <- factor(rep(1:20, rep(5, 20)))
y <- rbinom(100, prob = rep(runif(20), rep(5, 20)), size = 1)
x <- rnorm(100)
dat <- data.frame(y = y, x = x, id = id)
glmmML(y ~ x, data = dat, cluster = id)
id <- factor(rep(1:20, rep(5, 20)))
y <- rbinom(100, prob = rep(runif(20), rep(5, 20)), size = 1)
x <- rnorm(100)
dat <- data.frame(y = y, x = x, id = id)
glmmML(y ~ x, data = dat, cluster = id)

Generalized Linear Model with random intercept

Description

This function is called by glmmML, but it can also be called directly by the user.

Usage

glmmML.fit(X, Y, weights = rep(1, NROW(Y)), cluster.weights = rep(1, NROW(Y)),
start.coef = NULL, start.sigma = NULL,
fix.sigma = FALSE,
cluster = NULL, offset = rep(0, nobs), family = binomial(),
method = 1, n.points = 1,
control = list(epsilon = 1.e-8, maxit = 200, trace = FALSE),
intercept = TRUE, boot = 0, prior = 0) 
glmmML.fit(X, Y, weights = rep(1, NROW(Y)), cluster.weights = rep(1, NROW(Y)),
start.coef = NULL, start.sigma = NULL,
fix.sigma = FALSE,
cluster = NULL, offset = rep(0, nobs), family = binomial(),
method = 1, n.points = 1,
control = list(epsilon = 1.e-8, maxit = 200, trace = FALSE),
intercept = TRUE, boot = 0, prior = 0)

Arguments

`X`	Design matrix of covariates.
`Y`	Response vector. Or two-column matrix.
`weights`	Case weights. Defaults to one.
`cluster.weights`	Cluster weights. Defaults to one.
`start.coef`	Starting values for the coefficients.
`start.sigma`	Starting value for the mixing standard deviation.
`fix.sigma`	Should sigma be fixed at start.sigma?
`cluster`	The clustering variable.
`offset`	The offset in the model.
`family`	Family of distributions. Defaults to binomial with logit link. Other possibilities are binomial with cloglog link and poisson with log link.
`method`	Laplace (1) or Gauss-hermite (0)?
`n.points`	Number of points in the Gauss-Hermite quadrature. Default is `n.points = 1`, which is equivalent to Laplace approximation.
`control`	Control of the iterations. See `glm.control`.
`intercept`	Logical. If TRUE, an intercept is fitted.
`boot`	Integer. If > 0, bootstrapping with `boot` replicates.
`prior`	Which prior distribution? 0 for "gaussian", 1 for "logistic", 2 for "cauchy".

Details

In the optimisation, "vmmin" (in C code) is used.

Value

A list. For details, see the code, and glmmML.

Author(s)

Göran Broström

References

Broström (2003)

Examples

x <- cbind(rep(1, 14), rnorm(14))
y <- rbinom(14, prob = 0.5, size = 1)
id <- rep(1:7, 2)

glmmML.fit(x, y, cluster = id)


x <- cbind(rep(1, 14), rnorm(14))
y <- rbinom(14, prob = 0.5, size = 1)
id <- rep(1:7, 2)

glmmML.fit(x, y, cluster = id)

Prints a 'glmmML' object.

Description

A glmmboot object is the output of glmmboot.

Usage

## S3 method for class 'glmmboot'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)
## S3 method for class 'glmmboot'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)

Arguments

`x`	The glmmboot object
`digits`	Number of printed digits.
`na.print`	How to print NAs
`...`	Additional parameters, which are ignored.

Details

Nothing in particular.

Value

A short summary of the object is printed.

Note

This is the only summary method available for the moment.

Author(s)

Göran Broström

Prints a 'glmmML' object.

Description

A glmmML object is the output of glmmML.

Usage

## S3 method for class 'glmmML'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)
## S3 method for class 'glmmML'
print(x, digits = max(3, getOption("digits") - 3), na.print = "", ...)

Arguments

`x`	The glmmML object
`digits`	Number of printed digits.
`na.print`	How to print NAs
`...`	Additional parameters, which are ignored.

Details

Nothing in particular.

Value

A short summary of the object is printed.

Note

This is the only summary method available for the moment.

Author(s)

Göran Broström

Summary of a glmmboot object

Description

It simply calls print.glmmboot

Usage

## S3 method for class 'glmmboot'
summary(object, ...)
## S3 method for class 'glmmboot'
summary(object, ...)

Arguments

`object`	A glmmboot object
`...`	Additional arguments

Details

A summary method will be written soon.

Value

Nothing is returned.

Note

Preliminary

Author(s)

Göran Broström

Summary of a glmmML object

Description

It simply calls print.glmmML

Usage

## S3 method for class 'glmmML'
summary(object, ...)
## S3 method for class 'glmmML'
summary(object, ...)

Arguments

`object`	A glmmML object
`...`	Additional arguments

Value

Nothing is returned.

Note

Preliminary

Author(s)

Göran Broström

Package 'glmmML'

Help Index

Gauss-Hermite

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Generalized Linear Models with fixed effects grouping

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Generalized Linear Models with fixed effects grouping

Description

Usage

Arguments

Value

Note

Author(s)

See Also

Examples

Generalized Linear Models with random intercept

Description

Usage

Arguments

Details

Value

Note

Author(s)

References

See Also

Examples

Generalized Linear Model with random intercept

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Prints a 'glmmML' object.

Description

Usage

Arguments

Details

Value

Note

Author(s)

See Also

Prints a 'glmmML' object.

Description

Usage

Arguments

Details

Value

Note

Author(s)

See Also

Summary of a glmmboot object

Description

Usage

Arguments

Details

Value

Note

Author(s)