# Expression (CovariateModel)

Define relationship between parameters and covariates

## Description

The `Expression` property is a string or cell array of strings, where each string represents the relationship between a parameter and one or more covariates. The `Expression` property denotes fixed effects with the prefix `theta`, and random effects with the prefix `eta`.

Each expression string must be in the form:

 `parameterName = relationship`

This example of an expression string defines the relationship between a parameter (`volume`) and a covariate (`weight`), with fixed effects, but no random effects:

 `CovModelObj.Expression = {'volume = theta1 + theta2*weight'};`

This table illustrates expression formats for some common parameter-covariate relationships.

Parameter-Covariate RelationshipExpression Format
Linear with random effect`Cl = theta1 + theta2*WEIGHT + eta1`
Exponential without random effect`Cl = exp(theta_Cl + theta_Cl_WT*WEIGHT)`
Exponential, WEIGHT centered by mean, has random effect```Cl = exp(theta1 + theta2*(WEIGHT - mean(WEIGHT)) + eta1)```
Exponential, log(WEIGHT), which is equivalent to power model`Cl = exp(theta1 + theta2*log(WEIGHT) + eta1)`
Exponential, dependent on WEIGHT and AGE, has random effect`Cl = exp(theta1 + theta2*WEIGHT + theta3*AGE + eta1)`
Inverse of probit, dependent on WEIGHT and AGE, has random effect```Cl = probitinv(theta1 + theta2*WEIGHT + theta3*AGE + eta1)```
Inverse of logit, dependent on WEIGHT and AGE, has random effect```Cl = logitinv(theta1 + theta2*WEIGHT + theta3*AGE + eta1)```

 Tip   To simultaneously fit data from multiple dose levels, use a `CovariateModel` object as an input argument to `sbiofitmixed`, and omit the random effect (`eta`) from the `Expression` property in the `CovariateModel` object.

The `Expression` property must meet the following requirements:

• The expression strings are valid MATLAB® code.

• Each expression string is linear with a transformation.

• There is exactly one expression string for each parameter.

• In each expression string, a covariate is used in at most one term.

• In each expression string, there is at most one random effect (`eta`)

• Fixed effect (`theta`) and random effect (`eta`) names are unique within and across expression strings. That is, each covariate has its own fixed effect.

 Tip   Use the `getCovariateData` method to view the covariate data when writing equations for the `Expression` property of a `CovariateModel` object.
 Tip   Use the `verify` method to check that the `Expression` property of a `CovariateModel` object meets the conditions described previously.

## Characteristics

 Applies to Object: `CovariateModel` Data type String or cell array of strings Data values `parameterName = relationship` Access Read/write