mice.impute.2l.hnb: Multiple Imputation of Zero-Inflated Two-Level Count Data

In kkleinke/countimp: Multiple Imputation of incomplete count data

Multiple Imputation of Zero-Inflated Two-Level Count Data

Description

The functions impute zero-inflated multilevel count data based on a two-level Poisson or negative binomial hurdle model, either using a Bayesian regression or a bootstrap regression approach (appendix: “.boot”). The .noint variants treat the intercept only as a fixed, but not as a random effect. It may be specified, if the intercept is excluded from the random part of the zero model (“.noint.zero”), the count model (“.noint.count”), or both models (“.noint.both”). Hurdle models are mixture models and consist of two model components: the zero model (a binomial generalized linear mixed effects model), determining, if the observational unit has a zero or non-zero value, and the count model (a zero-truncated two-level Poisson or NB model), determining, what non-zero value the observational unit has.

Usage

mice.impute.2l.hnb(y, ry, x, type, intercept.c = TRUE, intercept.z = TRUE,
  wy = NULL, EV = TRUE)

mice.impute.2l.hnb.boot(y, ry, x, type, intercept.c = TRUE,
  intercept.z = TRUE, wy = NULL, EV = TRUE)

mice.impute.2l.hnb.noint.both.boot(y, ry, x, type, intercept.c = FALSE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

mice.impute.2l.hnb.noint.both(y, ry, x, type, intercept.c = FALSE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

mice.impute.2l.hnb.noint.count.boot(y, ry, x, type, intercept.c = FALSE,
  intercept.z = TRUE, wy = NULL, EV = TRUE)

mice.impute.2l.hnb.noint.count(y, ry, x, type, intercept.c = FALSE,
  intercept.z = TRUE, wy = NULL, EV = TRUE)

mice.impute.2l.hnb.noint.zero.boot(y, ry, x, type, intercept.c = TRUE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

mice.impute.2l.hnb.noint.zero(y, ry, x, type, intercept.c = TRUE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

mice.impute.2l.hp(y, ry, x, type, intercept.c = TRUE, intercept.z = TRUE,
  wy = NULL, EV = TRUE)

mice.impute.2l.hp.boot(y, ry, x, type, intercept.c = TRUE,
  intercept.z = TRUE, wy = NULL, EV = TRUE)

mice.impute.2l.hp.noint.both.boot(y, ry, x, type, intercept.c = FALSE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

mice.impute.2l.hp.noint.both(y, ry, x, type, intercept.c = FALSE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

mice.impute.2l.hp.noint.count.boot(y, ry, x, type, intercept.c = FALSE,
  intercept.z = TRUE, wy = NULL, EV = TRUE)

mice.impute.2l.hp.noint.count(y, ry, x, type, intercept.c = FALSE,
  intercept.z = TRUE, wy = NULL, EV = TRUE)

mice.impute.2l.hp.noint.zero.boot(y, ry, x, type, intercept.c = TRUE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

mice.impute.2l.hp.noint.zero(y, ry, x, type, intercept.c = TRUE,
  intercept.z = FALSE, wy = NULL, EV = TRUE)

Arguments

y	Numeric vector with incomplete data in long format (i.e. the groups are stacked upon each other)
ry	Response pattern of y (TRUE=observed, FALSE=missing)
x	matrix with length(y) rows containing complete covariates; also in long format
type	vector of length ncol(x) identifying fixed, random, and class variables; type is automatically extracted from the predictorMatrix; see mice's user's manual for details about how to specify the imputation model; see also section “details”.
intercept.c	TRUE: model will include intercept as a random effect in the count model; FALSE: count model intercept will be treated as fixed.
intercept.z	TRUE: model will include intercept as a random effect in the zero model; FALSE: zero model intercept will be treated as fixed.
wy	Logical vector of length length(y). A TRUE value indicates locations in y for which imputations are created. Default is !ry
EV	should automatic outlier handling of imputed values be enabled? Default is TRUE: extreme imputations will be identified. These values will be replaced by imputations obtained by predictive mean matching (function mice.impute.midastouch())

Details

Model specification details:

• -2 = class variable (only one class variable is allowed!)

• 0 = variable not included in imputation model

• 1 = variable will be included as a fixed effect (zero and count model)

• 2 = variable will be included as a fixed and random effect (zero and count model)

• 3 = variable will be included as a fixed effect (count model only)

• 4 = variable will be included as a fixed and random effect (count model only)

• 5 = variable will be included as a fixed effect (zero model only)

• 6 = variable will be included as a fixed and random effect (zero model only)

The Bayesian regression variants (see Rubin 1987, p. 169-170) consist of the following steps:

1. Fit the zero model (a two-level binomial generalized linear mixed effects model), using the glmmTMB function from package glmmTMB; find bhat, the posterior mean, and V(bhat), the posterior variance of model parameters b

2. Draw b* from N(bhat,V(bhat))

3. Compute predicted probabilities for having a zero vs. non-zero count

4. Draw imputations (zeros and ones) from a binomial distribution with the respective individual probabilities obtained from step 3.

5. Fit the count model (a zero-truncated two-level Poisson or NB model) using the glmmTMB function from package glmmTMB; find bhat, the posterior mean, and V(bhat), the posterior variance of model parameters b.

6. Draw b* from N(bhat,V(bhat))

7. Compute predicted values using parameters b* and replace non-zero imputations (from step 4) by a draw from a zero-truncated NB distribution with mean parameter mu being the count predicted for the respective incomplete case.

The bootstrap functions draw a bootstrap sample from y[ry] and x[ry,] (Note: we resample clusters rather than individual cases) and consist of the following steps:

1. Fit the zero model to the bootstrap sample

2. Compute predicted probabilities for having a zero vs. non-zero count

3. Draw imputations from a binomial distribution.

4. Fit the count model to the boostrap sample

5. Compute predicted counts and draw non-zero imputations (from step 3) from a zero-truncated Poisson or NB distribution.

Value

Numeric vector of length sum(!ry) with imputations

Functions

• mice.impute.2l.hnb: Bayesian regression variant; random intercepts

• mice.impute.2l.hnb.boot: bootstrap regression variant; random intercepts

• mice.impute.2l.hnb.noint.both.boot: bootstrap regression variant; fixed intercepts

• mice.impute.2l.hnb.noint.both: Bayesian regression variant; fixed intercepts

• mice.impute.2l.hnb.noint.count.boot: bootstrap regression variant; fixed intercept in count model

• mice.impute.2l.hnb.noint.count: Bayesian regression variant; fixed intercept in count model

• mice.impute.2l.hnb.noint.zero.boot: bootstrap regression variant; fixed interceot in zero model

• mice.impute.2l.hnb.noint.zero: Bayesian regression variant; fixed intercept in zero model

• mice.impute.2l.hp: Bayesian regression variant; random intercepts

• mice.impute.2l.hp.boot: bootstrap regression variant; random intercepts

• mice.impute.2l.hp.noint.both.boot: bootstrap regression variant; fixed intercepts

• mice.impute.2l.hp.noint.both: Bayesian regression variant; fixed intercepts

• mice.impute.2l.hp.noint.count.boot: bootstrap regression variant; fixed intercept in count model

• mice.impute.2l.hp.noint.count: Bayesian regression variant; fixed intercept in count model

• mice.impute.2l.hp.noint.zero.boot: bootstrap regression variant; fixed interceot in zero model

• mice.impute.2l.hp.noint.zero: Bayesian regression variant; fixed intercept in zero model

Author(s)

Kristian Kleinke

kkleinke/countimp documentation built on Nov. 5, 2024, 11:51 a.m.