1 / 15

Binary Regression Models

Binary Regression Models. Binary Models. In a number of contexts the dependent variable, Y, is nominal and binary Examples: Does a consumer Buy or Not Buy? Did the Dow go Up or down? Was a loan application accepted?. Binary Models.

marlee
Download Presentation

Binary Regression Models

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Binary Regression Models

  2. Binary Models • In a number of contexts the dependent variable, Y, is nominal and binary • Examples: • Does a consumer Buy or Not Buy? • Did the Dow go Up or down? • Was a loan application accepted?

  3. Binary Models • The problem with the linear regression is that it does not account for the fact that Y can only be 0 or 1 • Two popular models to deal with this are: • The Logit Model • The Probit Model

  4. The Binary Regression Logic • Think of the decision maker choosing Y based on the relative difference in utility she gets from Y=1 and Y=0 • If this difference is greater than some threshold (error) then Y=1 otherwise Y=0, so…

  5. The Probit and Logit Models • The Probit model assumes that the errors are standard normal • The Logit Model assumes that errors are Logistic NORMDIST in EXCEL

  6. Estimating the s • Two approaches: • A) Non-Linear Least Squares (NLLS) • Where we minimize • B) Maximum Likelihood • Where we maximize

  7. Fitted Probabilities/Values • Note that by plugging in the  you only get the fitted probabilities • To get predicted values you have to check if the fitted probabilities are above ½ • Lets try all of this in EXCEL… (maybe in GRETL?)

  8. Time Series Topics

  9. Time Series Topics • Topics to discuss: • Concepts and Terms • Autocorelation • Autoregression: [AR(p)] • Distributed Lag Models (ADL) • Conditional Heteroskedasticity • We will only have a basic introduction, if you are interested think about Bill Schwert’s APS 425 course.

  10. Concepts & Terms • Time Series: • A variable for which we have data over time • Lags: • First Lag: Yt-1 • s-th Lag: Yt-s • First Differences: Y = Yt – Yt-1 • Stationarity: • The time series Yt is stationary if the distribution of Yt does not change over time • Trend: • A persistent long term movement of a variable over time • Deterministic vs. Stochastic

  11. Autocorrelation • The correlation of Yt with its own past values (lags) • Also known as serial correlation • First Autocorrleation: Is the corrleation of Yt with Yt-1 • More generally: • The numerator in the above is a related construct called Autocovariance

  12. Autoregression • As the name suggests it is a regression of Yt on past values • Example: AR(1) • Special cases • Random Walk: • Random Walk with Drift

  13. Autoregression AR(p) • The AR(1) model can be generalized to include multiple lagged terms • This gives us the AR(p) model • How large should p be? • Use the Bayesian Information criterion number of coefficients including intercept

  14. Forecasts • Forecasts vs. Prediction • Generating a forecast: • Forecast Error • Root Mean Squared Forecast Error • Pseudo Out of Sample Forecasting • Simple Out-of Sample Forecasting • Iterated Multiperiod Forecasts

  15. Conditional Heteroskedasticity Models • We know that heteroskedasticity refers to the fact that the error variance is not constant • Conditional heteroskedasticity is when we can make this heteroskedasticity a function of something • ARCH: Autoregressive Conditional heteroskedasticity • GARCH: Generalized ARCH

More Related