make_model_object function takes a disag_data object created by prepare_data
and creates a TMB model object to be used in fitting.
make_model_object(
data,
priors = NULL,
family = "gaussian",
link = "identity",
field = TRUE,
iid = TRUE,
silent = TRUE
)The TMB model object returned by MakeADFun.
disag_data object returned by prepare_data function that contains all the necessary objects for the model fitting
list of prior values
likelihood function: gaussian, binomial or poisson
link function: logit, log or identity
logical. Flag the spatial field on or off
logical. Flag the iid effect on or off
logical. Suppress verbose output.
The model definition
The disaggregation model make predictions at the pixel level: $$link(pred_i) = \beta_0 + \beta X + GP(s_i) + u_i$$
And then aggregates these predictions to the polygon level using the weighted sum (via the aggregation raster, \(agg_i\)): $$cases_j = \sum_{i \epsilon j} pred_i \times agg_i$$ $$rate_j = \frac{\sum_{i \epsilon j} pred_i \times agg_i}{\sum_{i \epsilon j} agg_i}$$
The different likelihood correspond to slightly different models (\(y_j\) is the response count data):
Gaussian: If \(\sigma\) is the dispersion of the pixel data, \(\sigma_j\) is the dispersion of the polygon data, where \(\sigma_j = \sigma \sqrt{\sum agg_i^2} / \sum agg_i \) $$dnorm(y_j/\sum agg_i, rate_j, \sigma_j)$$ - predicts incidence rate.
Binomial: For a survey in polygon j, \(y_j\) is the number positive and \(N_j\) is the number tested. $$dbinom(y_j, N_j, rate_j)$$ - predicts prevalence rate.
Poisson: $$dpois(y_j, cases_j)$$ - predicts incidence count.
Specify priors for the regression parameters, field and iid effect as a single named list. Hyperpriors for the field are given as penalised complexity priors you specify \(\rho_{min}\) and \(\rho_{prob}\) for the range of the field where \(P(\rho < \rho_{min}) = \rho_{prob}\), and \(\sigma_{min}\) and \(\sigma_{prob}\) for the variation of the field where \(P(\sigma > \sigma_{min}) = \sigma_{prob}\). Also, specify pc priors for the iid effect.
The precise names and default values for these priors are:
priormean_intercept: 0
priorsd_intercept: 10.0
priormean_slope: 0.0
priorsd_slope: 0.5
prior_rho_min: A third the length of the diagonal of the bounding box.
prior_rho_prob: 0.1
prior_sigma_max: sd(response/mean(response))
prior_sigma_prob: 0.1
prior_iideffect_sd_max: 0.1
prior_iideffect_sd_prob: 0.01
The family and link arguments are used to specify the likelihood and link function respectively. The likelihood function can be one of gaussian, poisson or binomial. The link function can be one of logit, log or identity. These are specified as strings.
The field and iid effect can be turned on or off via the field and iid logical flags. Both are default TRUE.
The iterations argument specifies the maximum number of iterations the model can run for to find an optimal point.
The silent argument can be used to publish/supress verbose output. Default TRUE.