Model Variables - The Unknowns

When we ask Dismod-AT to do a fit, what unknowns will it solve for? If we do a fit to a linear regression, \(y ~ b_0 + b_1 x\), then it tells us the parameters \(b_i\). It also tells us the uncertainty, as determined by residuals between predicted and actual \(y\). In the case of Dismod-AT, the model variables are equivalent to those parameters \(b_i\). Dismod-AT documentation lists all of the model variables, but let’s cover the most common ones here.

First are the five disease rates, which are inputs to the ODE. Each rate is a continuous function of age and time, specified by an interpolation among points on an age-time grid. Therefore, the model variables from a rate are its value at each of the age-time points.

The covariate multipliers are also continuous functions of age and time. Each of the covariate multipliers has model variables for every point in its smoothing. There can be a covariate multiplier for each combination of covariate column and application to rate value, measurement value, or measurement standard deviation, so that’s a possible \(3c\) covariate multipliers, where \(c\) is the number of covariate columns.

The child rate effects also are variables. Because there is one for each location, and there is a smoothing grid for child rate effects, this creates many model variables.