Observe_statement_for_Gaussian_Residual

Observe statement for Gaussian Residual models

The observe statement is used to define a residual error model for a continuous observed variable, where the observe variable is defined to be a function of the prediction and a Gaussian/normal error variable. The syntax for the observe statement is given as follows:

    observe(observedVariable([independentVariable]) = expression
       [, bql][, action code])

If there are no differential equations in the model, the independentVariable for the observations can be specified.

This allows the Maximum Likelihood Models object to produce the appropriate output plots and worksheets. For example, a Michaelis-Menten model of reaction kinetics can be written as:

   observe(RxnRate(C)=Vmax*C/(C+Km)+eps)

If the bql option is specified, then it indicates that the input dataset contains BQL values for the observed variable, and the occurrence of observations below the lower limit of quantification is automatically incorporated into the likelihood calculations.

If action code is given, it indicates actions to be performed before or after each observation. See “Action code” and “Observation statement action codes” sections for more information.

The corresponding Gaussian error variable is declared through the error statement with its syntax given as follows:

    error (ErrorVariable[(freeze)][ = StandardDeviationOfErrorVariable])

Supplying the initial value for the standard deviation of the error variable is optional. If it is not provided, a value of 1 is used. The freeze is used to specify whether the standard deviation of the error variable is fixed or not during the estimation process. This is similar to the fixef and ranef statements. The model can include multiple error statements.

It is worth pointing out that the observe statement can only contain a single error variable. Compound residual error models for any given observed variable, such as mixed additive and proportional, must be built using a combination of fixed effects and a single error variable rather than multiple error variables. See the “Additional residual error model details” section in the Structure tab description for Maximum Likelihood models for details.