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# Nonlinear panel-data models

Stata now fits nonlinear models with random effects. This means that when your science says that the model should be nonlinear in the parameters, as in the constant elasticity of substitution (CES) production function or in a growth curve for adoption of a new technology, you can now fit that model even when you have panel data. Parameters in the fixed portion of the model and random effects can both enter the model nonlinearly.

Now instead of fitting a linear model with random effects $$U_j$$, such as

$$y_{ij} = \beta_0+\beta_1 x_{ij}+U_j+\epsilon_{ij}$$

we can fit a nonlinear model with random effects, such as

$$y_{ij} = (\beta_1+ U_{j})/[1+\exp\{-(time_{ij}-\beta_2)/\beta_3\}]+\epsilon_{ij}$$

The new menl command fits these models. The command is discussed in detail here. In particular, an example with random intercepts is presented under Random intercepts. You can also fit models with random coefficients as shown in the Random coefficients and random-effects covariance structures example. You can even fit models with additional levels. See the Nonlinear three-level model: CES production function.

## Highlights

• Nonlinear models: Fixed and random effects enter nonlinearly
• Random effects
• Random intercepts
• Random coefficients
• Flexible residual correlation structures
• Predict random effects and their standard errors