Parameter Estimation, Dummies, &amp; Model Fit

1 / 13

# Parameter Estimation, Dummies, & Model Fit - PowerPoint PPT Presentation

Parameter Estimation, Dummies, &amp; Model Fit. We know mechanically how to “run a regression”…but how are the parameters actually estimated? How can we handle “categorical” explanatory (independent) variables? What is a measure of “goodness of fit” of a statistical model to data?.

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.

## PowerPoint Slideshow about ' Parameter Estimation, Dummies, & Model Fit' - jorn

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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Parameter Estimation, Dummies, & Model Fit
• We know mechanically how to “run a regression”…but how are the parameters actually estimated?
• How can we handle “categorical” explanatory (independent) variables?
• What is a measure of “goodness of fit” of a statistical model to data?
Example: Alien Species
• Exotic species cause economic and ecological damage
• Not all countries equally invaded
• Want to understand characteristics of country that make it more likely to be “invaded”.
Understanding Invasive Species

Steps to improving our understanding:

• Generate a set of hypotheses (so they can be “accepted” or “rejected”)
• Develop a statistical model. Interpret hypotheses in context of statistical model.
• Collect data. Estimate parameters of model.
• Test hypotheses.
2 Hypotheses (in words)
• We’ll measure “invasiveness” as proportion of Alien/Native species (article by Dalmazzone).
• Population density plays a role in a country’s invasiveness.
• Island nations are more invaded than mainland nations.
Variables
• Variables:
• Dependent: Proportion of number of alien species to native species in each country.
• Independent:
• Island?
• Population Density
• GDP per capita
• Agricultural activity
Computer Minimizes Sei2
• Remember, OLS finds coefficients that minimize sum squared residuals
• Graphical representation
• Why is this appropriate?
• Can show that this criterion leads to estimates that are most precise unbiased estimates.
Dummy Variable
• Generally:
• Male/Female; Pre-regulation/Post-regulation; etc..
• Use a “Dummy Variable”. Value = 1 if country is Island, 0 otherwise.
• More generally, if n categories, use n-1 dummies.
• E.g. if want to distinguish between 6 continents
• Problem: Lose “degrees of freedom”.
A Simple Model
• A simple linear model looks like this:
• Dummy changes intercept (explain).
• Interaction dummy variable?
• E.g. Invasions of island nations more strongly affected by agricultural activity.
Translating our Hypotheses
• 2 Hypotheses
• Hypothesis 1: Population: Focus on a3
• Hypothesis 2: Island: Focus on a2
• “Hypothesis Testing”… forthcoming in course.
• Parameter Estimates:

Value Std.Error t value Pr(>|t|)

(Intercept) -0.0184 0.0859 -0.2141 0.8326

Island 0.0623 0.0821 0.7588 0.4564

Pop.dens 0.0010 0.0002 6.2330 0.0000

GDP 0.0000 0.0000 3.3249 0.0032

Agr -0.0014 0.0015 -0.9039 0.3763

“Goodness of Fit”: R2
• “Coefficient of Determination”
• R2=Squared correlation between Y and OLS prediction of Y
• R2=% of total variation that is explained by regression, [0,1]
• OLS maximizes R2.
• Adding independent cannot  R2
• Adjusted R2 penalizes for # vars.