Nonlinear models Hill et al Chapter 10

Types of nonlinear models Linear in the parameters. –Includes models that can be made linear by transformation: Nonlinear in the parameters –Require nonlinear least squares.

Polynomial terms in a regression For U-shaped curve we expect 2 0 U-shaped marginal cost curve 2 >0, 3 0

Interactions between continuous variables Is it reasonable that these effects are independent of income and age?

An alternative model

Empirical example

Nonlinear least squares Minimise sum of squared errors b = se(b) = Simple expressions for the value of beta that minimises S cannot be found. Similarly expressions for the se(beta) cannot be found. The problem is solved numerically.

A logistic growth curve

Example: proportion of steel produced with electric arc furnace

The poisson regression Number of visits to a lake: count data Does not have a normal distribution Poisson distribution is an alternative: is the average or mean number of visits per year, for all households Number of visits Frequency

Estimating the conditional mean function in the Poisson regression define the zero-mean error term

Computing probabilities in the Poisson regression What is the probability that a household located 50 miles from the Lake, with income of $60,000, and 3 family members, visits the park less than 3 times per year?