# Panel Data Models: Random Parameters – Mixed Models

LIMDEP’s wide variety of random parameters (mixed) models for panel data include ordered probit, logit, Poisson, loglinear, survival, mixed models and over 40 more. The random parameters model is defined in terms of the density of the observed random variable and the structural parameters in the model:

Density of observed y(i,t) = f[y(i,t), b(i), c(i), x(i,t)]

where b(i) and c(i) are parameter vectors and x(i,t) is a set of covariates observed at observation t.

Each distribution for group i is parameterized in terms of its own parameter vector, [b(i),c(i)]. The next level of the hierarchical (multilevel) model is specification of the means and variances of the random parameters.

The random effects model is a special case in which only the constant term is random. The random parameters model has been implemented in other software for the binary probit and logit, linear regression, and Poisson regression model. LIMDEP’s implementation supports about 50 different models.

## Wide Variety of Random Parameter Models with LIMDEP

- 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)

## Mixed Models and Other Features of the Estimator

- Mixture of fixed and random parameters - you specify which parameters are random and which are fixed
- Panel data or cross section implementation
- Distributions of random parameters may be normal, tent, uniform, lognormal
- Maximum simulated likelihood may use pseudorandom draws or Halton sequences
- Free correlation among random parameters (even with different distributions)
- Predictions
- Partial effects