# Panel Data Models: Random Effects Models

Random effects models are of the form:

Density of observed dependent variable is f[y(I,t)|x(I,t),u(i)],

where x(I,t) is the vector of observed covariates and u(i) is a time invariant random variable. Random effects models are fit by two step generalized least squares for the linear model or by maximizing the unconditional likelihood for nonlinear models. The unconditional likelihood function is obtained by integrating u(i) out of the conditional likelihood. LIMDEP contains random effects estimators that use the familiar techniques in the literature for the following models.

- Binomial probit, logit, Gompertz, complementary log log
- Linear regression
- Tobit, truncated regression, categorical data regression
- Half- and truncated normal stochastic frontier
- Ordered probit, logit, Gompertz, complementary log log
- Poisson and negative binomial

Integration is done using closed forms, Gauss-Hermite quadrature (Butler-Moffitt) or maximum simulated likelihood with pseudorandom draws or Halton sequences.

In addition to the preceding models, you can also fit a ‘random effects’ model by fitting a random parameters model which contains only a random constant term. This adds about 50 models to the list above including the following.

- Probit, logit, Gompertz, complementary log log binary choice
- Tobit, truncated regression, categorical data
- Stochastic frontier
- Survival models: exponential, Weibull, lognormal, loglogistic
- Loglinear models: Weibull, gamma, exponential, inverse Gauss
- Bivariate probit, partial observability
- Ordered probit, ordered logit, ordered Gompertz, ordered complementary log log
- Sample selection Poisson, negative binomial, zero inflated Poisson
- Conditional logit (multinomial logit – discrete choice)

- Many others