Methods for object of class "MixMod" for standard generic functions.
coef(object, ...)# S3 method for MixMod
coef(object, sub_model = c("main", "zero_part"),
...)
fixef(object, ...)
# S3 method for MixMod
fixef(object, sub_model = c("main", "zero_part"), ...)
ranef(object, ...)
# S3 method for MixMod
ranef(object, post_vars = FALSE, ...)
confint(object, parm, level = 0.95, ...)
# S3 method for MixMod
confint(object,
parm = c("fixed-effects", "var-cov","extra", "zero_part"),
level = 0.95, sandwich = FALSE, ...)
anova(object, ...)
# S3 method for MixMod
anova(object, object2, test = TRUE,
L = NULL, sandwich = FALSE, ...)
fitted(object, ...)
# S3 method for MixMod
fitted(object,
type = c("mean_subject", "subject_specific", "marginal"),
link_fun = NULL, ...)
residuals(object, ...)
# S3 method for MixMod
residuals(object,
type = c("mean_subject", "subject_specific", "marginal"),
link_fun = NULL, tasnf_y = function (x) x, ...)
predict(object, ...)
# S3 method for MixMod
predict(object, newdata, newdata2 = NULL,
type_pred = c("response", "link"),
type = c("mean_subject", "subject_specific", "marginal", "zero_part"),
se.fit = FALSE, M = 300, df = 10, scale = 0.3, level = 0.95,
seed = 1, return_newdata = FALSE, sandwich = FALSE, ...)
simulate(object, nsim = 1, seed = NULL, ...)
# S3 method for MixMod
simulate(object, nsim = 1, seed = NULL,
type = c("subject_specific", "mean_subject"), new_RE = FALSE,
acount_MLEs_var = FALSE, sim_fun = NULL,
sandwich = FALSE, ...)
terms(x, ...)
# S3 method for MixMod
terms(x, type = c("fixed", "random", "zi_fixed", "zi_random"), ...)
formula(x, ...)
# S3 method for MixMod
formula(x, type = c("fixed", "random", "zi_fixed", "zi_random"), ...)
model.frame(formula, ...)
# S3 method for MixMod
model.frame(formula, type = c("fixed", "random", "zi_fixed", "zi_random"), ...)
model.matrix(object, ...)
# S3 method for MixMod
model.matrix(object, type = c("fixed", "random", "zi_fixed", "zi_random"), ...)
nobs(object, ...)
# S3 method for MixMod
nobs(object, level = 1, ...)
VIF(object, ...)
# S3 method for MixMod
VIF(object, type = c("fixed", "zi_fixed"), ...)
cooks.distance(model, ...)
# S3 method for MixMod
cooks.distance(model, cores = max(parallel::detectCores() - 1, 1), ...)
The estimated fixed and random effects, coefficients (this is similar as in package nlme), confidence intervals fitted values (on the scale on the response) and residuals.
objects inheriting from class "MixMod". When object2
is also provided, then the model behind object must be nested within the model
behind object2.
character string indicating for which sub-model to extract the estimated coefficients; it is only relevant for zero-inflated models.
logical; if TRUE the posterior variances of the random effects
are returned as an extra attribute of the numeric matrix produced by ranef().
character string; for which type of parameters to calculate confidence
intervals. Option "var-cov" corresponds to the variance-covariance matrix of the
random effects. Option extra corresponds to extra (shape/dispersion)
parameters in the distribution of the outcome (e.g., the \(\theta\) parameter in
the negative binomial family). Option zero_inflated corresponds to the
coefficients of the zero-inflated sub-model.
numeric scalar between 0 and 1 denoting the level of the confidence interval.
In the nobs() method it denotes the level at which the number of observations is
counted. The value 0 corresponds to the number of independent sample units
determined by the number of levels of the grouping variable. If set to a value greater
than zero, it returns the total number of observations.
logical; should a p-value be calculated.
a numeric matrix representing a contrasts matrix. This is only used when in
anova() only object is provided, and it can only be specified for the fixed
effects. When L is used, a Wald test is performed.
logical; if TRUE the sandwich estimator is used in the calculation
of standard errors.
character string indicating the type of fitted values / residuals / predictions
/ variance inflation factors to calculate. Option "mean_subject" corresponds to only using the fixed-effects
part; option "subject_specific" corresponds to using both the fixed- and
random-effects parts; option "marginal" is based in multiplying the fixed
effects design matrix with the marginal coefficients obtained by
marginal_coefs.
the link_fun of marginal_coefs.
a function to transform the grouped / repeated measurements outcome before calculating the residuals; for example, relevant in two-part models for semi-continuous data, in which it is assumed that the log outcome follows a normal distribution.
a data frame based on which predictions are to be calculated.
newdata2 is only relevant when level = "subject_specific"; see
Details for more information.
character string indicating at which scale to calculate predictions.
Options are "link" indicating to calculate predictions at the link function /
linear predictor scale, and "response" indicating to calculate predictions at
the scale of the response variable.
logical, if TRUE standard errors of predictions are returned.
numeric scalar denoting the number of Monte Carlo samples; see Details for more information.
numeric scalar denoting the degrees of freedom for the Student's t proposal distribution; see Details for more information.
numeric scalar or vector denoting the scaling applied to the subject-specific covariance matrices of the random effects; see Details for more information.
numerical scalar giving the seed to be used in the Monte Carlo scheme.
logical; if TRUE the predict() method returns a copy
of the newdata and of newdata2 if the corresponding argument was not
NULL, with extra columns the predictions, and the lower and upper limits of
the cofidence intervals when type = "subject_specific".
numeric scalar giving the number of times to simulate the response variable.
logical; if TRUE, new random effects will be simulated, and new outcome
data will be simulated by simulate() using these new random effect. Otherwise,
the empirical Bayes estimates of the random effects from the fitted model will be used.
logical; if TRUE it accounts for the variability of the
maximum likelihood estimates (MLEs) by simulating a new value for the parameters from
a multivariate normal distribution with mean the MLEs and covariance matrix the
covariance matrix of the MLEs.
a function based on which to simulate the response variable. This is
relevant for non-standard models. The simulate() function also tries to extract
this function from the family component of object. The function should
have the following four arguments: n a numeric scalar denoting the number of
observations to simulate, mu a numeric vector of means, phis a numeric
vector of extra dispersion/scale parameters, and eta_zi a numeric vector for
the zero-part of the model, if this is relevant.
the number of cores to use in the computation.
further arguments; currently none is used.
Dimitris Rizopoulos d.rizopoulos@erasmusmc.nl
In generic terms, we assume that the mean of the outcome \(y_i\) (\(i = 1, ..., n\) denotes the subjects) conditional on the random effects is given by the equation: $$g{E(y_i | b_i)} = \eta_i = X_i \beta + Z_i b_i,$$ where \(g(.)\) denotes the link function, \(b_i\) the vector of random effects, \(\beta\) the vector of fixed effects, and \(X_i\) and \(Z_i\) the design matrices for the fixed and random effects, respectively.
Argument type_pred of predict() specifies whether predictions will be
calculated in the link / linear predictor scale, i.e., \(\eta_i\) or in the response
scale, i.e., \(g{E(y_i | b_i)}\).
When type = "mean_subject", predictions are calculated using only the fixed
effects, i.e., the \(X_i \beta\) part, where \(X_i\) is evaluated in newdata.
This corresponds to predictions for the 'mean' subjects, i.e., subjects who have
random effects value equal to 0. Note, that in the case of nonlinear link functions this
does not correspond to the averaged over the population predictions (i.e., marginal
predictions).
When type = "marginal", predictions are calculated using only the fixed
effects, i.e., the \(X_i \beta\) part, where \(X_i\) is evaluated in newdata,
but with \(\beta\) coefficients the marginalized coefficients obtain from
marginal_coefs. These predictions will be marginal / population averaged
predictions.
When type = "zero_part", predictions are calculated for the logistic regression of
the extra zero-part of the model (i.e., applicable for zero-inflated and hurdle models).
When type = "subject_specific", predictions are calculated using both the fixed-
and random-effects parts, i.e., \(X_i \beta + Z_i b_i\), where \(X_i\) and \(Z_i\)
are evaluated in newdata. Estimates for the random effects of each subject are
obtained as modes from the posterior distribution \([b_i | y_i; \theta]\) evaluated in
newdata and with \(theta\) (denoting the parameters of the model, fixed effects
and variance components) replaced by their maximum likelihood estimates.
Notes: (i) When se.fit = TRUE and type_pred = "response", the
standard errors returned are on the linear predictor scale, not the response scale.
(ii) When se.fit = TRUE and the model contains an extra zero-part, no standard
errors are computed when type = "mean_subject". (iii) When the model contains an
extra zero-part, type = "marginal" predictions are not yet implemented.
When se.fit = TRUE and type = "subject_specific", standard errors and
confidence intervals for the subject-specific predictions are obtained by a Monte Carlo
scheme entailing three steps repeated M times, namely
Account for the variability of maximum likelihood estimates (MLES) by simulating a new value \(\theta^*\) for the parameters \(\theta\) from a multivariate normal distribution with mean the MLEs and covariance matrix the covariance matrix of the MLEs.
Account for the variability in the random effects estimates by
simulating a new value \(b_i^*\) for the random effects \(b_i\) from the posterior
distribution \([b_i | y_i; \theta^*]\). Because the posterior distribution does not
have a closed-form, a Metropolis-Hastings algorithm is used to sample the new value
\(b_i^*\) using as proposal distribution a multivariate Student's-t distribution
with degrees of freedom df, centered at the mode of the posterior distribution
\([b_i | y_i; \theta]\) with \(\theta\) the MLEs, and scale matrix the inverse
Hessian matrix of the log density of \([b_i | y_i; \theta]\) evaluated at the modes,
but multiplied by scale. The scale and df parameters can be used
to adjust the acceptance rate.
The predictions are calculated using \(X_i \beta^* + Z_i b_i^*\).
Argument newdata2 can be used to calculate dynamic subject-specific predictions.
I.e., using the observed responses \(y_i\) in newdata, estimates of the random
effects of each subject are obtained. For the same subjects we want to obtain predictions
in new covariates settings for which no response data are yet available. For example,
in a longitudinal study, for a subject we have responses up to a follow-up \(t\)
(newdata) and we want the prediction at \(t + \Delta t\) (newdata2).
mixed_model,
marginal_coefs
# \donttest{
# simulate some data
set.seed(123L)
n <- 500
K <- 15
t.max <- 25
betas <- c(-2.13, -0.25, 0.24, -0.05)
D <- matrix(0, 2, 2)
D[1:2, 1:2] <- c(0.48, -0.08, -0.08, 0.18)
times <- c(replicate(n, c(0, sort(runif(K-1, 0, t.max)))))
group <- sample(rep(0:1, each = n/2))
DF <- data.frame(year = times, group = factor(rep(group, each = K)))
X <- model.matrix(~ group * year, data = DF)
Z <- model.matrix(~ year, data = DF)
b <- cbind(rnorm(n, sd = sqrt(D[1, 1])), rnorm(n, sd = sqrt(D[2, 2])))
id <- rep(1:n, each = K)
eta.y <- as.vector(X %*% betas + rowSums(Z * b[id, ]))
DF$y <- rbinom(n * K, 1, plogis(eta.y))
DF$id <- factor(id)
################################################
fm1 <- mixed_model(fixed = y ~ year + group, random = ~ year | id, data = DF,
family = binomial())
head(coef(fm1))
fixef(fm1)
head(ranef(fm1))
confint(fm1)
confint(fm1, "var-cov")
head(fitted(fm1, "subject_specific"))
head(residuals(fm1, "marginal"))
fm2 <- mixed_model(fixed = y ~ year * group, random = ~ year | id, data = DF,
family = binomial())
# likelihood ratio test between fm1 and fm2
anova(fm1, fm2)
# the same but with a Wald test
anova(fm2, L = rbind(c(0, 0, 0, 1)))
# }
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