Assessment Option 1: Take-home exam Option 1: Take-home exam - - PowerPoint PPT Presentation

Assessment

• Option 1: Take-home exam

Option 1: Take-home exam

– Replicate an analysis we provide and answer questions – Will be uploaded by Friday, December 2, 2016

• Option 2: Essay involving data analysis

Option 2: Essay involving data analysis

– Replicate (or do) an analysis of your choice and write an essay – Consultation emails by Friday, December 9, 2016 (not required)

• Deadline for both

Deadline for both:

– 12:00 p.m. on Friday 27 January 2017 (HT Week 2) via Weblearn

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Drop-in sessions

• MT Week 8

MT Week 8 (Q-Step Lab):

• Tuesday, 10.00-12.00: Anna Petherick (Comp Gov)
• Wednesday, 10.00-12.00: Giacomo Arrighini (Pol Soc)
• Thursday, 10.00-12.00: Jeffrey Wright (IR)
• Friday, 10.00-12.00: Gerda Hooijer (Pol Soc)
• HT Week 1

HT Week 1 (Q-Step Lab):

• 15-min. slot bookings
• Alice E. will send you an email with a link to sign up

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Last week: influence

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Outlier = big residuals.

• Problem = limited, but can

increase standard error.

• Detect with studentized residuals.

High leverage = usually big or small value(s) of independent variable(s)

• Problem = can change coefficients
• Detect with hat values.

Influence = Outlierness * Leverage

If you find high-influence obs…

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• Don’t pretend it doesn’t exist
• Check for a coding mistake
• Investigate (think of Pat!)
• Dummy out + compare

Checking OLS:

Multicollinearity is the high correlation between two or more independent variables

• Problem: larger standard errors, unstable coefficients
• Detect: variance-inflation factor VIF

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What to check:

Heteroscedasticity Uncorrelated error Mean independence (And) Normality E lineaRity MulticollineaRity O R

Interpretation of Regression Results

anna.petherick@politics.ox.ac.uk

Political Analysis 2, Lab 6 (Just one more to go after this!)

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Linearity Linearity

• whether X is really big or really tiny in value, its relationship

with Y—its coefficient—is constant.

• “The predicted change in Y for a one-unit increase in X

holding the other variables in the model constant.”

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For example…

Predicting an incumbent party’s vote share in U.S. elections, using model C: = 48.24 + (0.57*Growth) + (0.67*Good News)

• Growth is “previous year’s

economic growth rate” (%)

• Good news is headlines – ‘no. of

consecutive quarters of growth’.

Kellstedt and Whitten, p203

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Interpreting coefficients

• Statistical significance: p-value
• Substantive significance: effect size
• Independent variables are measured in their own units

– Age (in years) – Gender (1=female, 0=male) – Income (in thousands $) à Calculate along the range (min-max) of X à Standardized coefficients (see homework section)

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Think sensibly Think sensibly

• Always think substantively.
• Sometimes predictions are

logically impossible or irrelevant.

Credit: Catherine de Vries 10

(non)-Linearity (non)-Linearity

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Transformations of X Transformations of X

• In OLS, the coefficients of the independent

variables are not squared, cubed, square- rooted or logged.

• But non-linear relationships between X and Y

can still be modelled by transforming X.

• For example, you could have something like:

Y= B0 + B1*X + B2*X2 + B3*logeZ

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Transformations of X cont… Transformations of X cont…

• Examples from the

literature: district magnitude is often logged; so is area and GDP per capita… age is

• ften squared.
• Predictions using logged
• r squared variables are

generated as before, just remember to transform your value of X before multiplying by the coefficient.

Brazil’s 5,570 municipalities:

• Altamira = 159 696 km²
• Santa Cruz de Minas = 2.8 km²

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Exponential exp(X)=ex

Risk War Geographic Proximity Note: number e = 2:718281.

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GDP Democracy

logarithmic

log(Y ) is defined as the power that you would need to raise e to in order to end up with Y ; i.e., elog(Y ) = Y . For example, log(7) = 1.945910149 because e1.945910149 = 7.

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Stretching and compressing data

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To make these data linear..

Either stretch out values of X: Or compress values of Y:

Over to you…

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?

When to transform X When to transform X

• Plot X against Y.
• Apply the 'bulging rule’:

Tukey and Mosteller

X X2

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When to transform X cont… When to transform X cont…

• Look for patterns in the residuals.

Hmm…that’s hardly a random distribution around zero!

Credit: statwing.com

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Fails and Krieckhaus (2010)

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