Panel Data Models: Random Parameters – Multilevel Models

The random parameters model is defined in terms of the density of the observed random variable and the structural parameters in the model:

           

That is, each distribution for group i is parameterized in terms of its own parameter vector, qi.  The next level of the hierarchical (multilevel) model is:

           

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 logit, linear regression, and Poisson regression model. LIMDEP’s implementation supports a far wider variety of models.

• 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)
  

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
• ui may be a single random draw or AR(1)
• Free correlation among random parameters (even with different distributions)
• Predictions computed
• Marginal effects