glmmTMB | R Documentation |

Fit a generalized linear mixed model (GLMM) using Template Model Builder (TMB).

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

`formula` |
combined fixed and random effects formula, following lme4 syntax. |

`data` |
data frame (tibbles are OK) containing model variables. Not required, but strongly recommended; if |

`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 |

`ziformula` |
a |

`dispformula` |
a |

`weights` |
weights, as in |

`offset` |
offset for conditional model (only). |

`contrasts` |
an optional list, e.g., |

`na.action` |
a function that specifies how to handle observations
containing |

`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 |

`REML` |
whether to use REML estimation rather than maximum likelihood. |

`start` |
starting values, expressed as a list with possible components |

`map` |
a list specifying which parameter values should be fixed to a constant value rather than estimated. |

`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. |

Binomial models with more than one trial (i.e., not binary/Bernoulli) can either be specified in the form

`prob ~ ..., weights = N`

, or in the more typical two-column matrix`cbind(successes,failures)~...`

form.Behavior of

`REML=TRUE`

for Gaussian responses matches`lme4::lmer`

. It may also be useful in some cases with non-Gaussian responses (Millar 2011). Simulations should be done first to verify.Because the

`df.residual`

method for`glmmTMB`

currently counts the dispersion parameter, users should multiply this value by`sqrt(nobs(fit) / (1+df.residual(fit)))`

when comparing with`lm`

.Although models can be fitted without specifying a

`data`

argument, its use is strongly recommended; drawing model components from the global environment, or using`df$var`

notation within model formulae, can lead to confusing (and sometimes hard-to-detect) errors.By default, vector-valued random effects are fitted with unstructured (general symmetric positive definite) variance-covariance matrices. Structured variance-covariance matrices can be specified in the form

`struc(terms|group)`

, where`struc`

is one of-
`diag`

(diagonal, heterogeneous variance) -
`ar1`

(autoregressive order-1, homogeneous variance) -
`cs`

(compound symmetric, heterogeneous variance) -
`ou`

(* Ornstein-Uhlenbeck, homogeneous variance) -
`exp`

(* exponential autocorrelation) -
`gau`

(* Gaussian autocorrelation) -
`mat`

(* Matérn process correlation) -
`toep`

(* Toeplitz) -
`rr`

(reduced rank/factor-analytic model) -
`homdiag`

(diagonal, homogeneous variance)

Structures marked with * are experimental/untested. See

`vignette("covstruct", package = "glmmTMB")`

for more information.-
For backward compatibility, the

`family`

argument can also be specified as a list comprising the name of the distribution and the link function (e.g.`list(family="binomial", link="logit")`

). However,**this alternative is now deprecated**; it produces a warning and will be removed at some point in the future. Furthermore, certain capabilities such as Pearson residuals or predictions on the data scale will only be possible if components such as`variance`

and`linkfun`

are present, see`family`

.Smooths taken from the

`mgcv`

package can be included in`glmmTMB`

formulas using`s`

; these terms will appear as additional components in both the fixed and the random-effects terms. This functionality is*experimental*for now. We recommend using`REML=TRUE`

. See`s`

for details of specifying smooths (and`smooth2random`

and the appendix of Wood (2004) for technical details).

For more information about the glmmTMB package, see Brooks et al. (2017) and the `vignette(package="glmmTMB")`

collection. For the underlying TMB package that performs the model estimation, see Kristensen et al. (2016).

Brooks, M. E., Kristensen, K., van Benthem, K. J., Magnusson, A., Berg, C. W., Nielsen, A., Skaug, H. J., Mächler, M. and Bolker, B. M. (2017). glmmTMB balances speed and flexibility among packages for zero-inflated generalized linear mixed modeling. *The R Journal*, **9**(2), 378–400.

Kristensen, K., Nielsen, A., Berg, C. W., Skaug, H. and Bell, B. (2016). TMB: Automatic differentiation and Laplace approximation. *Journal of Statistical Software*, **70**, 1–21.

Millar, R. B. (2011). *Maximum Likelihood Estimation and Inference: With Examples in R, SAS and ADMB.* Wiley, New York.
Wood, S. N. (2004) Stable and Efficient Multiple Smoothing Parameter Estimation for Generalized Additive Models. *Journal of the American Statistical Association* **99**(467): 673–86. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/016214504000000980")}

```
(m1 <- glmmTMB(count ~ mined + (1|site),
zi=~mined,
family=poisson, data=Salamanders))
summary(m1)
##' ## Zero-inflated negative binomial model
(m2 <- glmmTMB(count ~ spp + mined + (1|site),
zi=~spp + mined,
family=nbinom2, data=Salamanders))
## Hurdle Poisson model
(m3 <- glmmTMB(count ~ spp + mined + (1|site),
zi=~spp + mined,
family=truncated_poisson, data=Salamanders))
## Binomial model
data(cbpp, package="lme4")
(bovine <- glmmTMB(cbind(incidence, size-incidence) ~ period + (1|herd),
family=binomial, data=cbpp))
## Dispersion model
sim1 <- function(nfac=40, nt=100, facsd=0.1, tsd=0.15, mu=0, residsd=1)
{
dat <- expand.grid(fac=factor(letters[1:nfac]), t=1:nt)
n <- nrow(dat)
dat$REfac <- rnorm(nfac, sd=facsd)[dat$fac]
dat$REt <- rnorm(nt, sd=tsd)[dat$t]
dat$x <- rnorm(n, mean=mu, sd=residsd) + dat$REfac + dat$REt
dat
}
set.seed(101)
d1 <- sim1(mu=100, residsd=10)
d2 <- sim1(mu=200, residsd=5)
d1$sd <- "ten"
d2$sd <- "five"
dat <- rbind(d1, d2)
m0 <- glmmTMB(x ~ sd + (1|t), dispformula=~sd, data=dat)
fixef(m0)$disp
c(log(5^2), log(10^2)-log(5^2)) # expected dispersion model coefficients
## Using 'map' to fix random-effects SD to 10
m1_map <- update(m1, map=list(theta=factor(NA)),
start=list(theta=log(10)))
VarCorr(m1_map)
## smooth terms
data("Nile")
ndat <- data.frame(time = c(time(Nile)), val = c(Nile))
sm1 <- glmmTMB(val ~ s(time), data = ndat,
REML = TRUE, start = list(theta = 5))
plot(val ~ time, data = ndat)
lines(ndat$time, predict(sm1))
```

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