Derive the posterior distribution for a model.
Arguments
- object
A
bage_modobject, created withmod_pois(),mod_binom(), ormod_norm().- method
Estimation method. Current choices are
"standard"(the default) and"inner-outer". See below for details.- vars_inner
Names of variables to use for inner model when
methodis"inner-outer". IfNULL(the default)vars_inner` is the age, sex/gender, and time variables.- optimizer
Which optimizer to use. Current choices are
"multi","nlminb","BFGS", and"CG". Default is"multi". See below for details.- quiet
Whether to suppress messages from optimizer. Default is
TRUE.- max_jitter
Maximum quantity to add to diagonal of precision matrix, if Cholesky factorization is failing. Default is 0.0001.
- start_oldpar
Whether the optimizer should start at previous estimates. Used only when
fit()is being called on a fitted model. Default isFALSE.- ...
Not currently used.
Estimation methods
When method is "standard" (the default),
all parameters, other than
the lowest-level rates, probabilities, or
means are jointly estimated within TMB.
When method is "inner-outer", estimation is
carried out in multiple steps, which, in large models,
can sometimes reduce computation times.
In Step 1, the data is aggregated across all dimensions other
than those specified in var_inner, and a model
for the inner variables is fitted to the data.
In Step 2, the data is aggregated across the
remaining variables, and a model for the
outer variables is fitted to the data.
In Step 3, values for dispersion are calculated.
Parameter estimates from steps 1, 2, and 3
are then combined. "inner-outer" methods are
still experimental, and may change in future.
Optimizer
The choices for the optimizer argument are:
"multi"Try"nlminb", and if that fails, restart from the parameter values where"nlminb"stopped, using"BFGS". The default."nlminb"stats::nlminb()"BFGS"stats::optim()using method"BFGS"."GC"stats::optim()using method"CG"(conjugate gradient).
Cholesky factorization and max_jitter
Sampling from the posterior distribution requires
performing a Cholesky factorization of the precision
matrix returned by TMB. This factorization sometimes
fails because of numerical problems. Adding a small
quantity to the diagonal of the precision matrix
can alleviate numerical problems, though potentially
at the cost of reduced accuracy. If the Cholesky factorization
initially fails, bage will try again with progressively
largeer quantities added to the diagonal, up to the
maximum set by max_jitter. Increasing the value of
max_jitter can help suppress numerical problems
further. A safer strategy, however, is to simplify
the model, or to use more informative priors.
See also
mod_pois()Specify a Poisson modelmod_binom()Specify a binomial modelmod_norm()Specify a normal modelaugment()Extract values for rates, probabilities, or means, together with original datacomponents()Extract values for hyper-parametersforecast()Forecast, based on a modelreport_sim()Simulation study of a modelunfit()Reset a modelis_fitted()Check if a model has been fittedMathematical Details vignette
Examples
## specify model
mod <- mod_pois(injuries ~ age + sex + year,
data = nzl_injuries,
exposure = popn)
## examine unfitted model
mod
#>
#> ------ Unfitted Poisson model ------
#>
#> injuries ~ age + sex + year
#>
#> exposure: popn
#>
#> term prior along n_par n_par_free
#> (Intercept) NFix() - 1 1
#> age RW() age 12 12
#> sex NFix() - 2 2
#> year RW() year 19 19
#>
#> disp: mean = 1
#>
#> n_draw var_time var_age var_sexgender
#> 1000 year age sex
#>
## fit model
mod <- fit(mod)
#> Building log-posterior function...
#> Finding maximum...
#> Drawing values for hyper-parameters...
## examine fitted model
mod
#>
#> ------ Fitted Poisson model ------
#>
#> injuries ~ age + sex + year
#>
#> exposure: popn
#>
#> term prior along n_par n_par_free std_dev
#> (Intercept) NFix() - 1 1 -
#> age RW() age 12 12 0.76
#> sex NFix() - 2 2 0.72
#> year RW() year 19 19 0.08
#>
#> disp: mean = 1
#>
#> n_draw var_time var_age var_sexgender optimizer
#> 1000 year age sex nlminb
#>
#> time_total time_max time_draw iter converged message
#> 0.27 0.12 0.12 13 TRUE relative convergence (4)
#>
## extract rates
aug <- augment(mod)
aug
#> # A tibble: 912 × 9
#> age sex ethnicity year injuries popn .observed
#> <fct> <chr> <chr> <int> <int> <int> <dbl>
#> 1 0-4 Female Maori 2000 12 35830 0.000335
#> 2 5-9 Female Maori 2000 6 35120 0.000171
#> 3 10-14 Female Maori 2000 3 32830 0.0000914
#> 4 15-19 Female Maori 2000 6 27130 0.000221
#> 5 20-24 Female Maori 2000 6 24380 0.000246
#> 6 25-29 Female Maori 2000 6 24160 0.000248
#> 7 30-34 Female Maori 2000 12 22560 0.000532
#> 8 35-39 Female Maori 2000 3 22230 0.000135
#> 9 40-44 Female Maori 2000 6 18130 0.000331
#> 10 45-49 Female Maori 2000 6 13770 0.000436
#> # ℹ 902 more rows
#> # ℹ 2 more variables: .fitted <rdbl<1000>>, .expected <rdbl<1000>>
## extract hyper-parameters
comp <- components(mod)
comp
#> # A tibble: 37 × 4
#> term component level .fitted
#> <chr> <chr> <chr> <rdbl<1000>>
#> 1 (Intercept) effect (Intercept) -2.5 (-4.1, -0.83)
#> 2 age effect 0-4 -2.5 (-4.3, -0.93)
#> 3 age effect 5-9 -3.8 (-5.6, -2.2)
#> 4 age effect 10-14 -3.3 (-5.2, -1.7)
#> 5 age effect 15-19 -1.6 (-3.4, -0.076)
#> 6 age effect 20-24 -1.5 (-3.3, 0.099)
#> 7 age effect 25-29 -1.6 (-3.4, -0.053)
#> 8 age effect 30-34 -1.7 (-3.5, -0.12)
#> 9 age effect 35-39 -1.7 (-3.5, -0.12)
#> 10 age effect 40-44 -1.7 (-3.5, -0.14)
#> # ℹ 27 more rows