Lecture 2
inlabru workflow
Fitting a LGM with inlabru
The general workflow:
Fitting a LGM with inlabru
The general workflow:
Basic component features
Basic component features
The basic syntax for components is:
my_component_name: this is a user-chosen label for the model component. This is then used as input inpredict()andgenerate().main: here we define the input data for the component.model: The type of model component see?component, and?INLA::inla.list.models()$latent.
Examples
beta_0(1)orIntercept(1)define one intercept.cov_effect(altitude, model= "linear")defines the linear effect ofaltitudeon the predictor.time_effect(time, model= "rw2")defines the smooth effect oftimeon the predictor.
Shortcuts
Some inlabru shortcuts
In the slides we have fitted the model as:
but in the practical you have
Some inlabru shortcuts
In the slides we have fitted the model as:
but in the practical you have
- You don’t have to define a formula outside of the
bru_obs()function …it can also be defined inside the function!
- The expression
y ~ .just means “take all the components and sum them together”. It also tells thebru()function that your predictor is linear.
Why do we need the -1 in the formula?
inlabruprovides a dedicated term,Intercept(), for specifying an intercept that is shared across all data.When this term is omitted, a common intercept is added by default, unless the formula or component explicitly includes
-1. This will be come relevant later, when we look at models with multiple likelihoods.
One wrong way and two correct ways of coding
mean sd
beta0 0.281 22.361
beta1 1.038 0.333
Intercept 0.281 22.361 mean sd
Intercept 0.563 0.193
beta1 1.038 0.333 mean sd
beta0 0.563 0.193
beta1 1.038 0.333Categorical variables and interactions
Effects of categorical variables and Interactions
inlabru has a specific component type for this that is called fixed.
Let’s look at the iris dataset available in R
Sepal.Length Sepal.Width Petal.Length Petal.Width Species
1 5.1 3.5 1.4 0.2 setosa
2 4.9 3.0 1.4 0.2 setosa
3 4.7 3.2 1.3 0.2 setosa
4 4.6 3.1 1.5 0.2 setosa
5 5.0 3.6 1.4 0.2 setosa
6 5.4 3.9 1.7 0.4 setosaEffects of categorical variables in inlabru
We want to fit a model where Species is the only covariate.
Specieshas three categories:setosa,versicolorandvirginica.- We want to model it as a factor effect.
(Intercept) Speciesversicolor Speciesvirginica
5.006 0.930 1.582 Here I. setosa is our reference category!
How do we do this in inlabru?
Effects of categorical variables in inlabru
Option 1: Use the fixed model
ID mean sd
1 (Intercept) 5.0059868 0.07268916
2 Speciesversicolor 0.9300083 0.10279799
3 Speciesvirginica 1.5820048 0.10279799Note
spp(~ Species, model = "fixed")is anlm-style model definition! So an intercept is automatically included.- The results are stored in the
summary.randompart of the model, not thesummary.fixed.
Effects of categorical variables in inlabru
- Option 2: Fixed effect are just random effects with fixed precision 😄
[1] 5.005934 5.935922 6.587914What is happening here??
This is just a re-parametrization problem
Effects of categorical variables in inlabru
Alternative (and equivalent) coding options
Note
When using the fixed model, inlabru internally creates a model matrix using the function MatrixModels::model.Matrix(). The syntax
is equivalent to
Interactions of linear covariates in inlabru
Here the easiest option is to again use the fixed model type.
Say, we want to fit a model with interactions between (categorical) Species and (continuous) Petal.Length.
[1] 4.2116296 -1.8037483 -3.1512099 0.5433309 0.2848670 0.4522720[1] 0.4066572 0.5973291 0.6329061 0.2762484 0.2944994 0.2895902Interactions of linear covariates in inlabru
We can also use the idea that “fixed effects are just random effects with fixed precision” 😄
NOTE: This idea can be very useful in more complex contexts, where the fixed model does not work (for example if one wants to have spatially varying effect of a covariate!)
Let’s look at the interaction between (categorical) Species and (continuous) Petal.Length.
\[ \begin{aligned} \eta_i & = \beta_0 + \beta_{0,\text{Species}_i} + \beta_1x_i + \beta_{1,\text{Species}_i} x_i\\ &\class{fragment}{= \beta^*_{0,\text{Species}_i} + (\beta_1 + \beta_{1,\text{Species}_i}) x_i} \\ & \class{fragment}{= \beta^*_{0,\text{Species}_i} +\beta^*_{1,\text{Species}_i} x_i }\\ & \class{fragment}{=\underbrace{\beta^*_{0,\text{Species}_i}}_{\text{iid}} + \underbrace{\beta^*_{1,\text{Species}_i}}_{\text{iid}} \underbrace{x_i}_{\text{Petal.Length}}} \end{aligned} \]
Interactions of linear covariates in inlabru
The model for the linear predictor is:
ID mean
beta0.1 setosa 4.2115909
beta0.2 versicolor 2.4064718
beta0.3 virginica 1.0591448
beta1.1 setosa 0.5433553
beta1.2 versicolor 0.8285246
beta1.3 virginica 0.9958302Compare this with the lm results
Getting results from the fitted model
The result object
The fitted model is stored in an inlabru object
Let’s
# ask inlabru to compute DIC adn WAIC
bru_options_set(control.compute = list(dic = T, waic = T))
cmp = ~ -1 +
spp(Species, model = "iid", initial = -6, fixed = T) +
petal_length(Petal.Length, model = "linear") +
petal_width(Petal.Width, model = "linear")
lik = bru_obs(formula = Sepal.Length ~ .,
data = iris )
result = bru(cmp, lik)
summary(result)inlabru version: 2.15.0.9002
INLA version: 26.08.22
Latent components:
spp: main = iid(Species)
petal_length: main = linear(Petal.Length)
petal_width: main = linear(Petal.Width)
Observation models:
Model tag: <No tag>
Family: 'gaussian'
Data class: 'data.frame'
Response class: 'numeric'
Predictor: Sepal.Length ~ spp + petal_length + petal_width
Additive/Linear/Rowwise: TRUE/TRUE/TRUE
Used components: effect[spp, petal_length, petal_width], latent[]
Time used:
Pre = 2.97, Running = 0.401, Post = 0.178, Total = 3.54
Fixed effects:
mean sd 0.025quant 0.5quant 0.975quant mode kld
petal_length 0.906 0.074 0.761 0.906 1.052 0.906 0
petal_width -0.006 0.156 -0.312 -0.006 0.300 -0.006 0
Random effects:
Name Model
spp IID model
Model hyperparameters:
mean sd 0.025quant 0.5quant
Precision for the Gaussian observations 8.81 1.03 6.92 8.77
0.975quant mode
Precision for the Gaussian observations 10.94 8.69
Deviance Information Criterion (DIC) ...............: 108.27
Deviance Information Criterion (DIC, saturated) ....: 158.52
Effective number of parameters .....................: 6.01
Watanabe-Akaike information criterion (WAIC) ...: 108.56
Effective number of parameters .................: 6.02
Marginal log-Likelihood: -86.76
is computed
Posterior summaries for the linear predictor and the fitted values are computed
(Posterior marginals needs also 'control.compute=list(return.marginals.predictor=TRUE)')Getting results I
Some results are very easy to get as they are contained in the result object:
- Summaries for fixed effects
mean sd 0.025quant 0.5quant 0.975quant
petal_length 0.906159040 0.07417133 0.7605153 0.906157599 1.0518111
petal_width -0.005896374 0.15598558 -0.3121987 -0.005897043 0.3004097
mode kld
petal_length 0.906157613 3.799544e-09
petal_width -0.005897037 3.803449e-09- Summaries for random effects
ID mean sd 0.025quant 0.5quant 0.975quant mode
1 setosa 3.682625 0.1071961 3.472121 3.682627 3.893116 3.682627
2 versicolor 2.083569 0.2855943 1.522737 2.083576 2.644361 2.083576
3 virginica 1.568942 0.3815775 0.819624 1.568952 2.318206 1.568951
kld
1 3.798152e-09
2 3.795488e-09
3 3.795355e-09Getting results I
- Marginals for fixed effects
- Summaries for random effects
inlabru integration with tidy
As of now (version 2.14.1.9005.+) inlabru also provides broom-style tidiers for bru model objects.
tidy()— one row per model term (fixed effects or hyperparameters)glance()— one row of model-level fit summariesaugment()— original data extended with posterior fitted values
inlabru integration with tidy
As of now (version 2.14.1.9005.+) inlabru also provides broom-style tidiers for bru model objects.
tidy()— one row per model term (fixed effects or hyperparameters)
tidy() returns a tibble with one row per fixed-effect term, including the posterior mean, standard deviation, and 95 % credible interval.
# A tibble: 2 × 5
term estimate std.error conf.low conf.high
<chr> <dbl> <dbl> <dbl> <dbl>
1 petal_length 0.906 0.0742 0.761 1.05
2 petal_width -0.00590 0.156 -0.312 0.300# A tibble: 1 × 5
term estimate std.error conf.low conf.high
<chr> <dbl> <dbl> <dbl> <dbl>
1 Precision for the Gaussian observations 8.81 1.03 6.91 10.9future versions will incorporate summaries for random effects
inlabru integration with tidy
As of now (version 2.14.1.9005.+) inlabru also provides broom-style tidiers for bru model objects.
tidy()— one row per model term (fixed effects or hyperparameters)
tidy() returns a tibble with one row per fixed-effect term, including the posterior mean, standard deviation, and 95 % credible interval.
Compatibility with ggplot
inlabru integration with tidy
As of now (version 2.14.1.9005.+) inlabru also provides broom-style tidiers for bru model objects.
glance()— one row of model-level fit summaries
returns a single-row tibble with the DIC, WAIC, marginal log-likelihood, the number of observations, and total wall-clock time.
# A tibble: 1 × 5
dic waic marginal_loglik nobs elapsed
<dbl> <dbl> <dbl> <int> <dbl>
1 108. 109. -86.4 150 3.84Useful for model comparison
cmp2 = ~ -1 +
spp(Species, model = "iid", initial = -6, fixed = T) +
petal_length(Petal.Length, model = "linear")
lik2 = bru_obs(formula = Sepal.Length ~ .,data = iris)
result2 = bru(cmp2, lik2)
bind_rows(
glance(result2) %>% mutate(model = "Species + Petal Length"),
glance(result) %>% mutate(model = "Species + Petal Length + Petal Width")
) %>%
select(model, dic, waic, marginal_loglik, nobs)# A tibble: 2 × 5
model dic waic marginal_loglik nobs
<chr> <dbl> <dbl> <dbl> <int>
1 Species + Petal Length 106. 106. -81.1 150
2 Species + Petal Length + Petal Width 108. 109. -86.4 150inlabru integration with tidy
As of now (version 2.14.1.9005.+) inlabru also provides broom-style tidiers for bru model objects.
augment()— original data extended with posterior fitted values
adds posterior summaries of the linear predictor to a data frame (or a prediction grid as we will see next). Note that you must supply a pred_formula that names what to predict
# A tibble: 6 × 9
Sepal.Length Sepal.Width Petal.Length Petal.Width Species .fitted .fitted_low
<dbl> <dbl> <dbl> <dbl> <fct> <dbl> <dbl>
1 5.1 3.5 1.4 0.2 setosa 4.95 4.86
2 4.9 3 1.4 0.2 setosa 4.95 4.86
3 4.7 3.2 1.3 0.2 setosa 4.86 4.77
4 4.6 3.1 1.5 0.2 setosa 5.04 4.95
5 5 3.6 1.4 0.2 setosa 4.95 4.86
6 5.4 3.9 1.7 0.4 setosa 5.22 5.13
# ℹ 2 more variables: .fitted_high <dbl>, .fitted_sd <dbl>.fitted: posterior mean.fitted_low.fitted_high: 2.5 % and 97.5 % quantiles.fitted_sd: posterior standard deviation.
inlabru integration with tidy
As of now (version 2.14.1.9005.+) inlabru also provides broom-style tidiers for bru model objects.
augment()— original data extended with posterior fitted values
adds posterior summaries of the linear predictor to a data frame (or a prediction grid as we will see next). Note that you must supply a pred_formula that names what to predict
What can you put in the pred_formula?
covariate can be accessed as
.data$xthe effect as
xor.effect$xthe latent variable as
x_latentor.latent$xaugment()\(\rightarrow\)predict()\(\rightarrow\)generate()
We can use ggplot to plot the fitted line with credible bands:
Code
ggplot() +
geom_point(data = iris,
aes(Petal.Length,
Sepal.Length,
color=Species),
alpha = 0.4, size = 0.8) +
geom_ribbon(
data = augmented,
aes(Petal.Length,
ymin = .fitted_low,
ymax = .fitted_high,
fill=Species),
, alpha = 0.3
) +
geom_line(
data = augmented,
aes(Petal.Length,
.fitted,colour=Species),
, linewidth = 1
) +
labs(
title = "Posterior fitted line with 95 % CrI",
x = "Petal Length", y = "Sepal Length"
) +
facet_wrap(~Species,scales="free_x")
predict() and generate() functions
Often, one wants more “complex” results from the model.
For example if we fit the following model to the mtcar data
\[ \eta_i = \beta_{0,\text{Species}_i} + \beta_{1,\text{Species}_i}\text{Petal Length}_i,\ i =1,\dots,n \]
We might want to recover the three regression lines
\[ \beta_{0,\text{Species}_i} + \beta_{1,\text{Species}_i}\text{Petal Length}_i ,\ \text{Species} = 1,2,3 \]
To do this we can use the predict() and generate() functions.
predict()simulates from the fitted posterior distribution \(\pi(\mathbf{y}|\mathbf{u},\theta)\), computes what you ask and produces a summary of the samples (mean, sd, quantiles, etc)generate()simulates from the fitted posterior distribution \(\pi(\mathbf{y}|\mathbf{u},\theta)\), computes what you ask and returns the samples!
Example 1
cmp = ~ -1 + fixed_effects(~Species * Petal.Length, model = "fixed")
lik = bru_obs(formula = Sepal.Length ~ .,
data = iris)
fit = bru(cmp, lik)
pred_grid <- iris %>%
group_by(Species) %>%
reframe(Petal.Length = seq(min(Petal.Length),
max(Petal.Length), by = 0.1))
res = predict(fit, pred_grid, ~ fixed_effects)
res[1:5,] Species Petal.Length mean sd q0.025 q0.5 q0.975 median
1 setosa 1.0 4.755710 0.14919655 4.492748 4.745633 5.006521 4.745633
2 setosa 1.1 4.810650 0.12061724 4.592047 4.804754 5.025146 4.804754
3 setosa 1.2 4.865590 0.09337071 4.701537 4.866891 5.046524 4.866891
4 setosa 1.3 4.920530 0.06905303 4.798226 4.920336 5.060580 4.920336
5 setosa 1.4 4.975469 0.05195395 4.890673 4.973738 5.089349 4.973738
mean.mc_std_err sd.mc_std_err
1 0.017311884 0.011961146
2 0.013996808 0.009675420
3 0.010834620 0.007487745
4 0.008003619 0.005491577
5 0.005967543 0.003860738Example 1
Notice that we predict only within the range of the covariate for each species:
Example 2
Species Petal.Length mean sd q0.025 q0.5 q0.975 median
1 setosa 1.0 4.754516 0.14747815 4.492408 4.744297 5.057362 4.744297
2 setosa 1.1 4.808086 0.12008517 4.597748 4.800461 5.057235 4.800461
3 setosa 1.2 4.861657 0.09364703 4.692505 4.854236 5.065953 4.854236
4 setosa 1.3 4.915227 0.06926585 4.794829 4.910235 5.067040 4.910235
5 setosa 1.4 4.968798 0.05004422 4.885144 4.972742 5.078605 4.972742
mean.mc_std_err sd.mc_std_err
1 0.016772140 0.010121623
2 0.013649102 0.008202926
3 0.010635221 0.006352590
4 0.007857976 0.004656955
5 0.005679451 0.003375142Example 2
Yet another example
Let’s fit the model for the Tokyo rainfall data
\[ \begin{aligned} y_t|\eta_t&\sim\text{Bin}(n_t, p_t),\qquad i = 1,\dots,366\\ \eta_t &= \text{logit}(p_t)= \beta_0 + f(\text{time}_t) \end{aligned} \]
We now want to extract results…what do we want?
- The time effect \(f(\text{time}_t)\) ?
- The linear predictor \(\eta_t = \beta_0 + f(\text{time}_t)\)?
- The estimated probability offit precipitation \(p_t = \text{inv_logit}(\eta_t)\) ?
We can get all of them with the predict() or generate() functions!
Example - predict()
or
y n time mean sd q0.025 q0.5 q0.975 median mean.mc_std_err sd.mc_std_err
1 0 2 1 0.176 0.083 0.063 0.163 0.369 0.163 0.003 0.003
2 0 2 2 0.174 0.078 0.066 0.161 0.360 0.161 0.003 0.002
3 1 2 3 0.172 0.073 0.068 0.160 0.353 0.160 0.002 0.002Example - predict()
Example - generate()
time_eff lin_pred probs
1 -0.3753867 -1.720212 0.1518438
2 -0.3621072 -1.706933 0.1535620
3 -0.3508974 -1.695723 0.1550247Example - generate()
The _latent suffix
Sometimes, one wants to sample directly from latent parameters without specifying any new input data (or, in other words, to sample with an identity projection matrix).
The keyword
_latentcan be appended to a latent component name to retrieve that.
For example, the following code recovers the intercept and the time effect at day 13
NOTE Here newdata is just an empty object.
Manipulating posterior marginals
Manipulating posterior marginals
We might be interested in functions of the posterior marginals that are computed by the bru() function.
For example, we might want to:
- compute the mean of a posterior marginal
- compute the median of a posterior marginal
- sample from the posterior marginal
- …
All this can be done with the help of the inla.*marginal() family of functions
Example from the Tokyo example
Obtain the posterior marginal for the standard deviation of the random effect, compute its mean and median and sample from it.
The inla.*marginal() family
| Function Name | Usage |
|---|---|
inla.dmarginal(x, marginal, ...) |
Density at a vector of evaluation points \(x\) |
inla.pmarginal(q, marginal, ...) |
Distribution function at a vector of quantiles q |
inla.qmarginal(p, marginal, ...) |
Quantile function at a vector of probabilities p |
inla.rmarginal(n, marginal) |
Generate n random deviates |
inla.hpdmarginal(p, marginal, ...) |
Compute the highest posterior density interval at level p |
inla.emarginal(fun, marginal, ...) |
Compute the expected value assuming transformation given by fun |
inla.mmarginal(marginal) |
Computes the mode |
inla.smarginal(marginal, ...) |
Smoothed density (returns x-values and interpolated y-values) |
inla.tmarginal(fun, marginal, ...) |
Transform the marginal using function fun |
inla.zmarginal(marginal) |
Summary statistics for the marginal |
NAs in inlabru
Missing values in inlabru
The bru() function treats missing values in the dataset differently depending on their role in the model.
Take the model definition:
NA’s in the responseyIf
y[i] = NA, this means that y[i] is not observed, hence gives no contribution to the likelihood.NA’s in fixed effectxIf
x[i] = NAthis means thatx[i]is not part of the linear predictor fory[i]. For fixed effects, this is equivalent tox[i]=0, hence internally we make this change:x[is.na(x)] = 0NA’s in random effectzIf
z[i] = NA, this means that the random effect does not contribute to the linear predictor fory[i].
Can inlabru deal with missing covariates?
No, inlabru has no way to `impute’ or integrate-out missing covariates.
You have to adjust your model to account for missing covariates.
Sometimes, you can formulate a joint model for the data and the covariates, but this is case-specific.
Getting help while using inlabru
Which priors have I used?
You might wonder which priors have you used in your model..
NB inla.priors.used is a function of the INLA package, so you need to load it explicitly.
Getting help!
The inla.doc() function provides help on the different prior, latent models and likelihood.
Which models are implemented?
Likelihoods
Section [likelihood]
0binomial New 0-inflated Binomial
0binomialS New 0-inflated Binomial Swap
0nbinomial New 0-inflated nBinomial
0nbinomialS New 0-inflated nBinomialS
0poisson New 0-inflated Poisson
0poissonS New 0-inflated Poisson Swap
1poisson New 1-inflated Poisson
1poissonS New 1-inflated Poisson Swap
agaussian The aggregated Gaussian likelihoood
bcgaussian The Box-Cox Gaussian likelihoood
bell The Bell likelihood
beta The Beta likelihood
betabinomial The Beta-Binomial likelihood
betabinomialna The Beta-Binomial Normal approximation likelihood
bgev The blended Generalized Extreme Value likelihood
binomial The Binomial likelihood
binomialmix Binomial mixture
cbinomial The clustered Binomial likelihood
cennbinomial2 The CenNegBinomial2 likelihood (similar to cenpoisson2)
cenpoisson Then censored Poisson likelihood
cenpoisson2 Then censored Poisson likelihood (version 2)
circularnormal The circular Gaussian likelihoood
cloglike User-defined likelihood
coxph Cox-proportional hazard likelihood
dgompertzsurv destructive gompertz (survival) distribution
dgp Discrete generalized Pareto likelihood
egp Exteneded Generalized Pareto likelihood
exponential The Exponential likelihood
exponentialsurv The Exponential likelihood (survival)
exppower The exponential power likelihoood
fl The fl likelihood
fmri fmri distribution (special nc-chi)
fmrisurv fmri distribution (special nc-chi)
gamma The Gamma likelihood
gammacount A Gamma generalisation of the Poisson likelihood
gammacountmean Another Gamma generalisation of the Poisson likelihood
gammajw A special case of the Gamma likelihood
gammajwsurv A special case of the Gamma likelihood (survival)
gammasurv The Gamma likelihood (survival)
gammasv The Gamma likelihood with constant rate
gaussian The Gaussian likelihoood
gaussianjw The GaussianJW likelihoood
gev The Generalized Extreme Value likelihood
ggaussian Generalized Gaussian
ggaussianS Generalized GaussianS
gompertz gompertz distribution
gompertzsurv gompertz distribution
gp Generalized Pareto likelihood
gpoisson The generalized Poisson likelihood
iidgamma (experimental)
iidlogitbeta (experimental)
lavm Link adjusted von Mises circular distribution
loggammafrailty (experimental)
logistic The Logistic likelihoood
loglogistic The loglogistic likelihood
loglogisticsurv The loglogistic likelihood (survival)
lognormal The log-Normal likelihood
lognormalsurv The log-Normal likelihood (survival)
logperiodogram Likelihood for the log-periodogram
mgamma The modal Gamma likelihood
mgammasurv The modal Gamma likelihood (survival)
nbinomial The negBinomial likelihood
nbinomial2 The negBinomial2 likelihood
nmix Binomial-Poisson mixture
nmixnb NegBinomial-Poisson mixture
npoisson The Normal approximation to the Poisson likelihood
nvm Normal approx of the von Mises circular distribution
nzpoisson The nzPoisson likelihood
obeta The ordered Beta likelihood
occupancy Occupancy likelihood
poisson The Poisson likelihood
poisson.special1 The Poisson.special1 likelihood
pom Likelihood for the proportional odds model
qkumar A quantile version of the Kumar likelihood
qloglogistic A quantile loglogistic likelihood
qloglogisticsurv A quantile loglogistic likelihood (survival)
rcpoisson Randomly censored Poisson
sem The SEM likelihoood
simplex The simplex likelihood
sn The Skew-Normal likelihoood
stdgaussian The stdGaussian likelihoood
stochvol The Gaussian stochvol likelihood
stochvolln The Log-Normal stochvol likelihood
stochvolnig The Normal inverse Gaussian stochvol likelihood
stochvolsn The SkewNormal stochvol likelihood
stochvolt The Student-t stochvol likelihood
t Student-t likelihood
tpoisson Thinned Poisson
tstrata A stratified version of the Student-t likelihood
tweedie Tweedie distribution
vm von Mises circular distribution
weibull The Weibull likelihood
weibullsurv The Weibull likelihood (survival)
wrappedcauchy The wrapped Cauchy likelihoood
xbinomial The Binomial likelihood (experimental version)
xpoisson The Poisson likelihood (expert version)
zeroinflatedbetabinomial0 Zero-inflated Beta-Binomial, type 0
zeroinflatedbetabinomial1 Zero-inflated Beta-Binomial, type 1
zeroinflatedbetabinomial2 Zero inflated Beta-Binomial, type 2
zeroinflatedbinomial0 Zero-inflated Binomial, type 0
zeroinflatedbinomial1 Zero-inflated Binomial, type 1
zeroinflatedbinomial2 Zero-inflated Binomial, type 2
zeroinflatedcenpoisson0 Zero-inflated censored Poisson, type 0
zeroinflatedcenpoisson1 Zero-inflated censored Poisson, type 1
zeroinflatednbinomial0 Zero inflated negBinomial, type 0
zeroinflatednbinomial1 Zero inflated negBinomial, type 1
zeroinflatednbinomial1strata2 Zero inflated negBinomial, type 1, strata 2
zeroinflatednbinomial1strata3 Zero inflated negBinomial, type 1, strata 3
zeroinflatednbinomial2 Zero inflated negBinomial, type 2
zeroinflatedpoisson0 Zero-inflated Poisson, type 0
zeroinflatedpoisson1 Zero-inflated Poisson, type 1
zeroinflatedpoisson2 Zero-inflated Poisson, type 2
zeroninflatedbinomial2 Zero and N inflated binomial, type 2
zeroninflatedbinomial3 Zero and N inflated binomial, type 3 Which models are implemented?
Components
Section [latent]
2diid (This model is obsolute)
ar Auto-regressive model of order p (AR(p))
ar1 Auto-regressive model of order 1 (AR(1))
ar1c Auto-regressive model of order 1 w/covariates
besag The Besag area model (CAR-model)
besag2 The shared Besag model
besagproper A proper version of the Besag model
besagproper2 An alternative proper version of the Besag model
bym The BYM-model (Besag-York-Mollier model)
bym2 The BYM-model with the PC priors
cgeneric Generic latent model specified using C
clinear Constrained linear effect
copy Create a copy of a model component
crw2 Exact solution to the random walk of order 2
dmatern Dense Matern field
fgn Fractional Gaussian noise model
fgn2 Fractional Gaussian noise model (alt 2)
generic A generic model
generic0 A generic model (type 0)
generic1 A generic model (type 1)
generic2 A generic model (type 2)
generic3 A generic model (type 3)
iid Gaussian random effects in dim=1
iid1d Gaussian random effect in dim=1 with Wishart prior
iid2d Gaussian random effect in dim=2 with Wishart prior
iid3d Gaussian random effect in dim=3 with Wishart prior
iid4d Gaussian random effect in dim=4 with Wishart prior
iid5d Gaussian random effect in dim=5 with Wishart prior
iidkd Gaussian random effect in dim=k with Wishart prior
intslope Intecept-slope model with Wishart-prior
linear Alternative interface to an fixed effect
log1exp A nonlinear model of a covariate
logdist A nonlinear model of a covariate
matern2d Matern covariance function on a regular grid
meb Berkson measurement error model
mec Classical measurement error model
ou The Ornstein-Uhlenbeck process
prw2 Proper random walk of order 2
revsigm Reverse sigmoidal effect of a covariate
rgeneric Generic latent model specified using R
rw1 Random walk of order 1
rw2 Random walk of order 2
rw2d Thin-plate spline model
rw2diid Thin-plate spline with iid noise
scopy Create a scopy of a model component
seasonal Seasonal model for time series
sigm Sigmoidal effect of a covariate
slm Spatial lag model
spde A SPDE model
spde2 A SPDE2 model
spde3 A SPDE3 model
z The z-model in a classical mixed model formulationWhich models are implemented?
Priors
Section [prior]
betacorrelation Beta prior for the correlation
dirichlet Dirichlet prior
expression: A generic prior defined using expressions
flat A constant prior
gamma Gamma prior
gaussian Gaussian prior
invalid Void prior
jeffreystdf Jeffreys prior for the doc
laplace Laplace prior
linksnintercept Skew-normal-link intercept-prior
logflat A constant prior for log(theta)
loggamma Log-Gamma prior
logiflat A constant prior for log(1/theta)
logitbeta Logit prior for a probability
logtgaussian Truncated Gaussian prior
logtnormal Truncated Normal prior
minuslogsqrtruncnormal (obsolete)
mvnorm A multivariate Normal prior
none No prior
normal Normal prior
pc Generic PC prior
pc.alphaw PC prior for alpha in Weibull
pc.ar PC prior for the AR(p) model
pc.cor0 PC prior correlation, basemodel cor=0
pc.cor1 PC prior correlation, basemodel cor=1
pc.dof PC prior for log(dof-2)
pc.egptail PC prior for the tail in the EGP likelihood
pc.fgnh PC prior for the Hurst parameter in FGN
pc.gamma PC prior for a Gamma parameter
pc.gammacount PC prior for the GammaCount likelihood
pc.gevtail PC prior for the tail in the GEV likelihood
pc.matern PC prior for the Matern SPDE
pc.mgamma PC prior for a Gamma parameter
pc.prec PC prior for log(precision)
pc.prw2.range PCprior for the range in PRW2
pc.range PC prior for the range in the Matern SPDE
pc.sn PC prior for the skew-normal
pc.spde.GA (experimental)
pom #classes-dependent prior for the POM model
ref.ar Reference prior for the AR(p) model, p<=3
rprior: A R-function defining the prior
table: A generic tabulated prior
wishart1d Wishart prior dim=1
wishart2d Wishart prior dim=2
wishart3d Wishart prior dim=3
wishart4d Wishart prior dim=4
wishart5d Wishart prior dim=5
wishartkd Wishart prior Take home message
Take home message
Linear models with interactions
inlabruhas a special model to implement thisbut it is also worth to understand that “fixed effects are just random effects with fixed precision 😄
inlabruintegrates with widely used broom-style tidiers (more features might be addedd soon)
predict()andgenerate()functions are powerful tools (based on sampling from the posterior distribution) to obtain many interesting results!missing values are usually not a problem but in some cases have to be treated carefully.
