GLMM_MCMC {mixAK} | R Documentation |
THIS FUNCTION IS BEING DEVELOPED AND ORDINARY USERS ARE NOT RECOMMENDED TO USE IT.
This function runs MCMC for a generalized linear mixed model with possibly several response variables and possibly normal mixtures in the distributions of random effects.
GLMM_MCMC(y, dist="gaussian", id, x, z, random.intercept, prior.beta, init.beta, scale.b, prior.b, init.b, prior.eps, init.eps, nMCMC=c(burn=10, keep=10, thin=1, info=10), tuneMCMC=list(beta=1, b=1), store=c(b=FALSE), keep.chains=TRUE) ## S3 method for class 'GLMM_MCMC': print(x, ...)
y |
vector, matrix or data frame with responses. If y is vector then
there is only one response in the model. If y is matrix or data frame then
each column gives values of one response. Missing values are allowed.
If there are several responses specified then continuous responses must be put in the first columns and discrete responses in the subsequent columns. |
dist |
character (vector) which determines distribution (and a link function) for each response variable. Possible values are: “gaussian” for gaussian (normal) distribution (with identity link), “binomial(logit)” for binomial (0/1) distribution with a logit link. “poisson(log)” for Poisson distribution with a log link. Single value is recycled if necessary. |
id |
vector which determines longitudinally or otherwise dependent observations. If not given then it is assumed that there are no clusters and all observations of one response are independent. |
x |
matrix or a list of matrices with covariates (intercept not included) for fixed effects.
If there is more than one response, this must always be a list. Note that intercept in included
in all models. Use a character value “empty” as a component of the list x
if there are no covariates for a particular response.
|
z |
matrix or a list of matrices with covariates (intercept not included) for random effects.
If there is more than one response, this must always be a list. Note that random intercept
is specified using the argument random.intercept .
REMARK: For a particular response, matrices x and z
may not have the same columns. That is, matrix x includes
covariates which are not involved among random effects and matrix
z includes covariates which are involved among random effects
(and implicitely among fixed effects as well).
|
random.intercept |
logical (vector) which determines for which responses random intercept should be included. |
prior.beta |
a list which specifies prior distribution for fixed
effects (not the means of random effects). The prior distribution is
normal and the user can specify the mean and variances.
The list prior.b can have the components listed below.
|
init.beta |
a numeric vector with initial values of fixed effects
(not the means of random effects). A sensible value is determined using the
maximum-likelihood fits (using lmer functions)
and does not have to be given by the user.
|
scale.b |
a list specifying how to scale the random effects during
the MCMC. A sensible value is determined using the
maximum-likelihood fits (using lmer functions)
and does not have to be given by the user.
If the user wishes to influence the shift and scale constants, these are given as components of the list scale.b . The components
are named:
|
prior.b |
a list which specifies prior distribution for (shifted
and scaled) random effects. The prior is in principle a normal
mixture (being a simple normal distribution if we restrict the
number of mixture components to be equal to one).
The list prior.b can have the components listed below. Their
meaning is analogous to the components of the same name of the
argument prior of function NMixMCMC (see
therein for details).
|
init.b |
a list with initial values for parameters related to the distribution of random effects and random effects themselves. Sensible initial values are determined by the function itself and do not have to be given by the user. |
prior.eps |
a list specifying prior distributions for
error terms for continuous responses. The list prior.eps can
have the components listed below. For all components, a sensible
value leading to weakly informative prior distribution can be
determined by the function.
|
init.eps |
a list with initial values for parameters related to the
distribution of error terms of continuous responses. The list
init.eps can have the components listed below. For all
components, a sensible value can be determined by the function.
|
nMCMC |
numeric vector of length 4 giving parameters of the MCMC
simulation. Its components may be named (ordering is then unimportant) as:
|
tuneMCMC |
a list with tuning scale parameters for proposal
distribution of fixed and random effects. It is used only when there
are some discrete response profiles. The components of the list have
the following meaning:
|
store |
logical vector indicating whether the chains of
parameters should be stored. Its components may be named (ordering
is then unimportant) as:
|
keep.chains |
logical. If FALSE , only summary statistics
are returned in the resulting object. This might be useful in the
model searching step to save some memory.
|
... |
additional arguments passed to the default print method. |
See accompanying paper (Komárek et al., 2010).
An object of class GLMM_MCMC
. It can have the following
components (some of them may be missing according to the context
of the model):
iter |
index of the last iteration performed. |
nMCMC |
used value of the argument nMCMC . |
dist |
a character vector of length R corresponding to the
dist argument. |
R |
a two component vector giving the number of continuous responses and the number of discrete responses. |
p |
a numeric vector of length R giving the number of non-intercept beta parameters for each response. |
q |
a numeric vector of length R giving the number of non-intercept random effects for each response. |
fixed.intercept |
a logical vector of length R which indicates inclusion of fixed intercept for each response. |
random.intercept |
a logical vector of length R which indicates inclusion of random intercept for each response. |
lbeta |
length of the vector of fixed effects. |
dimb |
dimension of the distribution of random effects. |
prior.beta |
a list containing the used value of the
argument prior.beta . |
prior.b |
a list containing the used value of the
argument prior.b . |
prior.eps |
a list containing the used value of the
argument prior.eps . |
init.beta |
a numeric vector with the used value of the
argument init.beta . |
init.b |
a list containing the used value of the
argument init.b . |
init.eps |
a list containing the used value of the
argument init.eps . |
state.beta |
a numeric vector with the last sampled value
of fixed effects beta. It can be used as argument
init.beta to restart MCMC. |
state.b |
a list with the last sampled values of parameters
related to the distribution of random effects. It has components
named b , K , w , mu , Sigma , Li , Q ,
gammaInv , r . It can be used as argument
init.b to restart MCMC. |
state.eps |
a list with the last sampled values of parameters
related to the distribution of residuals of continuous responses. It
has components named sigma , gammaInv . It can be used as argument
init.eps to restart MCMC. |
prop.accept.beta |
acceptance proportion from the Metropolis-Hastings algorithm for fixed effects (separately for each response type). Note that the acceptance proportion is equal to one for continuous responses since the Gibbs algorithm is used there. |
prop.accept.b |
acceptance proportion from the Metropolis-Hastings algorithm for random effects (separately for each cluster). Note that the acceptance proportion is equal to one for models with continuous responses only since the Gibbs algorithm is used there. |
scale.b |
a list containing the used value of the argument
scale.b . |
poster.mean.eta |
a data.frame with columns labeled
fixed and random holding posterior means for fixed
effect part of the linear predictor and the random effect part of
the linear predictor. In each column, there are first all values for
the first response, then all values for the second response etc. |
poster.mean.profile |
a data.frame with columns labeled
b1 , ..., bq , LogL , Logpb with
posterior means of random effects for each cluster and posterior
means of log(L) (log-likelihood given random effects)
and log(p(b)) for each cluster. |
poster.mean.w_b |
a numeric vector with posterior means of mixture weights after re-labeling. It is computed only if K[b] is fixed and even then I am not convinced that these are useful posterior summary statistics. In any case, they should be used with care. |
poster.mean.mu_b |
a matrix with posterior means of mixture means after re-labeling. It is computed only if K[b] is fixed and even then I am not convinced that these are useful posterior summary statistics. In any case, they should be used with care. |
poster.mean.Q_b |
a list with posterior means of mixture inverse variances after re-labeling. It is computed only if K[b] is fixed and even then I am not convinced that these are useful posterior summary statistics. In any case, they should be used with care. |
poster.mean.Sigma_b |
a list with posterior means of mixture variances after re-labeling. It is computed only if K[b] is fixed and even then I am not convinced that these are useful posterior summary statistics. In any case, they should be used with care. |
poster.mean.Li_b |
a list with posterior means of Cholesky decompositions of mixture inverse variances after re-labeling. It is computed only if K[b] is fixed and even then I am not convinced that these are useful posterior summary statistics. In any case, they should be used with care. |
poster.comp.prob1 |
a matrix which is present in the output object
if the number of mixture components in the distribution of random
effects is fixed and equal to K. In that case,
poster.comp.prob1 is a matrix with K columns and I
rows (I is the number of subjects defining the longitudinal
profiles or correlated observations) with estimated posterior component probabilities
– posterior means of the components of the underlying 0/1
allocation vector.
These can be used for possible clustering of the subjects based on the longitudinal profiles. |
poster.comp.prob2 |
a matrix which is present in the output object
if the number of mixture components in the distribution of random
effects is fixed and equal to K. In that case,
poster.comp.prob2 is a matrix with K columns and I
rows (I is the number of subjects defining the longitudinal
profiles or correlated observations)
with estimated posterior component probabilities
– posterior mean over model parameters including random effects.
These can be used for possible clustering of the subjects based on the longitudinal profiles. |
summ.beta |
a matrix with posterior summary statistics for fixed effects. |
summ.b.Mean |
a matrix with posterior summary statistics for means of random effects. |
summ.b.SDCorr |
a matrix with posterior summary statistics for standard deviations of random effects and correlations of each pair of random effects. |
summ.sigma_eps |
a matrix with posterior summary statistics for standard deviations of the error terms in the (mixed) models of continuous responses. |
freqK_b |
frequency table for the MCMC sample of the number of mixture components in the distribution of the random effects. |
propK_b |
posterior probabilities for the numbers of mixture components in the distribution of random effects. |
K_b |
numeric vector with a chain for K[b] (number of mixture components in the distribution of random effects). |
w_b |
numeric vector or matrix with a chain for w[b] (mixture weights for the distribution of random effects). It is a matrix with K[b] columns when K[b] is fixed. Otherwise, it is a vector with weights put sequentially after each other. |
mu_b |
numeric vector or matrix with a chain for mu[b] (mixture means for the distribution of random effects). It is a matrix with dimb*K[b] columns when K[b] is fixed. Otherwise, it is a vector with means put sequentially after each other. |
Q_b |
numeric vector or matrix with a chain for lower triangles of Q[b] (mixture inverse variances for the distribution of random effects). It is a matrix with (dimb*(dimb+1)2)*K[b] columns when K[b] is fixed. Otherwise, it is a vector with lower triangles of Q[b] matrices put sequentially after each other. |
Sigma_b |
numeric vector or matrix with a chain for lower triangles of Sigma[b] (mixture variances for the distribution of random effects). It is a matrix with (dimb*(dimb+1)2)*K[b] columns when K[b] is fixed. Otherwise, it is a vector with lower triangles of Sigma[b] matrices put sequentially after each other. |
Li_b |
numeric vector or matrix with a chain for lower triangles of Cholesky decompositions of Q[b] matrices. It is a matrix with (dimb*(dimb+1)2)*K[b] columns when K[b] is fixed. Otherwise, it is a vector with lower triangles put sequentially after each other. |
gammaInv_b |
matrix with dimb columns with a chain for inverses of the hyperparameter gamma[b]. |
order_b |
numeric vector or matrix with order indeces of mixture components in the distribution of random effects. It is a matrix with K[b] columns when K[b] is fixed. Otherwise it is a vector with orders put sequentially after each other. |
rank_b |
numeric vector or matrix with rank indeces of mixture components in the distribution of random effects. It is a matrix with K[b] columns when K[b] is fixed. Otherwise it is a vector with ranks put sequentially after each other. |
mixture_b |
data.frame with columns labeled
b.Mean.* , b.SD.* , b.Corr.*.*
containing the chains for the means, standard deviations and correlations of the
distribution of the random effects based on a normal mixture at each
iteration. |
b |
a matrix with the MCMC chains for random effects. It is
included only if store[b] is TRUE . |
beta |
numeric vector or matrix with the MCMC chain(s) for fixed effects. |
sigma_eps |
numeric vector or matrix with the MCMC chain(s) for standard deviations of the error terms in the (mixed) models for continuous responses. |
gammaInv_eps |
matrix with dimb columns with MCMC chain(s) for inverses of the hyperparameter gamma[b]. |
Arnošt Komárek arnost.komarek[AT]mff.cuni.cz
Komárek, A., Hansen, B. E., Kuiper, E. M. M., van Buuren, H. R., and Lesaffre, E. (2010). Discriminant analysis using a multivariate linear mixed model with a normal mixture in the random effects distribution. Statistics in Medicine. To appear.
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