# Panel Data Models: Nonlinear Fixed Effects Models

We define fixed effects models in terms of the density of the observed random variable and an index function,

Density of observed y(i,t) = f[y(i,t), a(i) + b’x(i,t), other parameters)

There is one dummy variable coefficient for each individual or group. There may also be fixed ‘time’ effects for a two way model. LIMDEP’s implementation of this model is unconditional - for the models supported, the fixed effects cannot be conditioned out. All the dummy variable coefficients are actually estimated, with up to 50,000 groups, as well as the other model parameters. This is a new estimation method in LIMDEP that does not appear in any other software. This allows a far wider range of models than the conditional estimator.

## More Fixed Effects Models with LIMDEP’s Unconditional Estimators

- Linear regression model
- 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)

Compare the preceding list to the list of conditional fixed effects estimators in LIMDEP and other programs: linear regression, binary logit, Poisson, negative binomial.

## Enhanced Features of Unconditional Fixed Effects Estimators

- Full maximum likelihood estimation
- Automatic data check for groups of one and groups with no variation
- Dummy variable coefficients are retained
- Predictions
- Partial effects