semireg_tmb {predictmeans}

Fitting Semi Parametric Models Using glmmTMB

Description

Fit a semi parametric model based on glmmTMB.

Usage

semireg_tmb(formula, data, family = gaussian(), smoothZ = list(), ziformula = ~0, 
        dispformula = ~1, weights = NULL, offset = NULL, contrasts = NULL, na.action, 
		se = TRUE, verbose = FALSE, doFit = TRUE, control = glmmTMBControl(), 
		REML = TRUE, start = NULL, map = NULL, sparseX = NULL, prt=TRUE, 
		predict_info=TRUE)

Arguments

formula

A two-sided linear formula object describing both the fixed-effects and random-effects part of the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right. Random-effects terms are distinguished by vertical bars ("|") separating expressions for design matrices from grouping factors.

data

data frame (tibbles are OK) containing model variables. Not required, but strongly recommended; if data is not specified, downstream methods such as prediction with new data (predict(fitted_model, newdata = ...)) will fail. If it is necessary to call glmmTMB with model variables taken from the environment rather than from a data frame, specifying data=NULL will suppress the warning message.

family

a family function, a character string naming a family function, or the result of a call to a family function (variance/link function) information. See family for a generic discussion of families or family_glmmTMB for details of glmmTMB-specific families.

smoothZ

A list includes a set of smooth Z matrixs (called 'smooth term') used in the mixed effects model, the name of 'smooth term' should be different any variables in the model, each 'smooth term' is the result of function smZ. e.g. smoothZ=list(sm1=smZ(x1), sm2=smZ(x2, by=f1), sm3=smZ(x3, by=f2, group=TRUE), ...) where 'sm1' to 'sm3' should be new variable names in the data, and x1 to x3 are covariates, and f1, f2 are factors.

ziformula

a one-sided (i.e., no response variable) formula for zero-inflation combining fixed and random effects: the default ~0 specifies no zero-inflation. Specifying ~. sets the zero-inflation formula identical to the right-hand side of formula (i.e., the conditional effects formula); terms can also be added or subtracted. When using ~. as the zero-inflation formula in models where the conditional effects formula contains an offset term, the offset term will automatically be dropped. The zero-inflation model uses a logit link.

dispformula

a one-sided formula for dispersion containing only fixed effects: the default ~1 specifies the standard dispersion given any family. The argument is ignored for families that do not have a dispersion parameter. For an explanation of the dispersion parameter for each family, see sigma. The dispersion model uses a log link. In Gaussian mixed models, dispformula=~0 fixes the residual variance to be 0 (actually a small non-zero value), forcing variance into the random effects. The precise value can be controlled via control=glmmTMBControl(zero_dispval=...); the default value is sqrt(.Machine$double.eps).

weights

weights, as in glm. Not automatically scaled to have sum 1.

offset

offset for conditional model (only).

contrasts

an optional list, e.g., list(fac1="contr.sum"). See the contrasts.arg of model.matrix.default.

na.action

a function that specifies how to handle observations containing NAs. The default action (na.omit, inherited from the 'factory fresh' value of getOption("na.action")) strips any observations with any missing values in any variables. Using na.action = na.exclude will similarly drop observations with missing values while fitting the model, but will fill in NA values for the predicted and residual values for cases that were excluded during the fitting process because of missingness.

se

whether to return standard errors.

verbose

whether progress indication should be printed to the console.

doFit

whether to fit the full model, or (if FALSE) return the preprocessed data and parameter objects, without fitting the model.

control

control parameters, see glmmTMBControl.

REML

whether to use REML estimation rather than maximum likelihood.

start

starting values, expressed as a list with possible components beta, betazi, betad (fixed-effect parameters for conditional, zero-inflation, dispersion models); b, bzi (conditional modes for conditional and zero-inflation models); theta, thetazi (random-effect parameters, on the standard deviation/Cholesky scale, for conditional and z-i models); psi (extra family parameters, e.g., shape for Tweedie models).

map

a list specifying which parameter values should be fixed to a constant value rather than estimated. map should be a named list containing factors corresponding to a subset of the internal parameter names (see start parameter). Distinct factor values are fitted as separate parameter values, NA values are held fixed: e.g., map=list(beta=factor(c(1,2,3,NA))) would fit the first three fixed-effect parameters of the conditional model and fix the fourth parameter to its starting value. In general, users will probably want to use start to specify non-default starting values for fixed parameters. See MakeADFun for more details.

sparseX

a named logical vector containing (possibly) elements named "cond", "zi", "disp" to indicate whether fixed-effect model matrices for particular model components should be generated as sparse matrices, e.g. c(cond=TRUE). Default is all FALSE

prt

Logical scalar - Should the info to be print on screen in the middle of the process or not?

predict_info

Logical scalar - Should provide the info for function semipred or not? In case of there is a correlation theta parameter appearing, you may set predict=FALSE.

Details

A semi parametric model can be parameterized as a linear (or generalized linear) mixed model in which its random effects are smooth functions of some covariates (named ‘smooth term’). semireg_tmb follows the approach suggested by Wand and Ormerod (2008) and represents the 'smooth term' using O'Sullivan-type of Z.

Value

semer

A glmmTMB model used in the fitting.

data

A data.frame with generated variables in the fitting.

fomul_vars

Name of variables in the formula of semireg_tmb model.

sm_vars

Name of variables in the smoothZ list.

smoothZ_call

A call used to produce smooth terms in the fitting.

knots_lst

Knots used in each smooth term in the fitting.

range_lst

Range of covariate used in each smooth term in the fitting.

cov_lst

Covariance matrix list for each smooth term.

u_lst

Random effects list for each smooth term.

type_lst

Smooth type list of smooth terms.

CovMat

Covariance matrix for all smooth terms.

Cov_ind

Covariance matrix index for each smooth term.

Cov_indN

Covariance matrix index for each smooth term when group=TRUE in smoothZ argument.

df

Degree of freedom of all random terms.

tmbf

The glmmTMB model result using doFit=FALSE.

Author(s)

Dongwen Luo, Siva Ganesh and John Koolaard

References

Wand, M.P. and Ormerod, J.T. (2008). On semiparametric regression with O'Sullivan penalized splines. Australian and New Zealand Journal of Statistics. 50, 179-198.

Examples

## Not run
# library(predictmeans)
# library(HRW) 
# data(WarsawApts)
# help(WarsawApts)
# str(WarsawApts)
# fit1 <- semireg_tmb(areaPerMzloty ~ construction.date,
#                smoothZ=list(
#                  grp=smZ(construction.date, k=25)
#                ),
#                data = WarsawApts)
# sp_out1 <- semipred(fit1, "construction.date", "construction.date")
# 
# WarsawApts$district <- factor(WarsawApts$district)
# fit2 <- semireg_tmb(areaPerMzloty ~ construction.date*district, resp_scale = TRUE,
#                 smoothZ=list(group=smZ(construction.date, k=15,
#                                        by = district, group=TRUE)), 
#                 data=WarsawApts)
# sp_out2_1 <- semipred(fit2, "district", "construction.date")
# sp_out2_2 <- semipred(fit2, "district", "construction.date", contr=c(2,1))
# 
# data(indonRespir)
# help(indonRespir)
# str(indonRespir)
# fit3 <- semireg_tmb(respirInfec ~ age+vitAdefic + female + height
#                + stunted + visit2 + visit3 + visit4  + visit5 + visit6+(1|idnum),
#                smoothZ=list(
#                  grp=smZ(age)
#                ),
#                family = binomial,
#                data = indonRespir)
# sp_out3 <- semipred(fit3, "age", "age")
# library(ggplot2)
# sp_out3$plt+
#   geom_rug(data = subset(indonRespir, respirInfec==0), sides = "b", col="deeppink") +
#   geom_rug(data = subset(indonRespir, respirInfec==1), sides = "t", col="deeppink")+
#   ylim(0, 0.2)