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Linear Regression

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Linear Regression

Hein Stigum

Presentation, data and programs at:

http://folk.uio.no/heins/courses

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Linear regression

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- Numerical data
- Discrete
- number of partners

- Continuous
- Weight

- Discrete
- Categorical data
- Nominal
- disease/ no disease

- Ordinal
- small/ medium/ large

- Nominal

- Poisson regression
- Linear regression
- Logistic regression
- Ordinal regression

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- Adjusted effects
- b1 is the increase in weight per day of gestational age
- b1 is adjusted for b2

- Assumptions
- Independent errors
- Linear effects
- Constant error variance

- Robustness
- influence

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- DAG
- Plots: distribution and scatter
- Bivariate analysis
- Regression
- Model estimation
- Test of assumptions
- Independent errors
- Linear effects
- Constant error variance

- Robustness
- Influence

Discuss

Plot

Plot

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Continuous outcome:Linear regression, Birth weight

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C2

parity

C1

sex

E

gest age

D

birth weight

AssociationsBivariate (unadjusted)

Causal effectsMultivariable (adjusted)

Draw your assumptions before your conclusions

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Effects on linear regression:

OK

Be clear on the research question:

overall birth weight: linear regression

low birth weight:logistic regression

linear and logistic can give opposite results

May lead to non-constant error variance

May have high influential outliers

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Linear effects?

Yes

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Outcome: birthweight

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Continuous outcome:Linear regression, Birth weight

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2 categories

OK, but know the coding

3+ categories

Use “dummies”

“Dummies” are 0/1 variables used to create contrasts

Want 3 categories for parity: 0, 1 and 2-7 children

Choose 0 as reference

Make dummies for the two other categories

generate Parity1 =(parity==1) if parity<.

generate Parity2_7 =(parity>=2) if parity<.

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Syntax:

regress weight gest sex Parity1 Parity2_7

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Expected birth weight at:

gest= 0, sex=0, parity=0

gest=280, sex=1, parity=0

Alternative: center variables

gen gest280=gest-280gest280 has a meaningful zero at 280 days

gen sex0=sex-1 sex0 has a meaningful zero at boys

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- Discuss
- Independent residuals?

- Linear effects?
- constantvariance?

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- Dependent residuals
Use linear mixed models

- Non linear effects
Add square term

Or use piecewise linear

- Non-constant variance
Use robust variance estimation

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- Measure change in:
- Predicted outcome
- Deviance
- Coefficients (beta)
- Delta beta

Remove obs 1, see change

remove obs 2, see change

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If obs nr 539 is removed, beta will change from 6 to 16

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Full data

Outlier removed

One outlier affected two estimates

Final model

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- DAGs
- Guide analysis

- Plots
- Unequal variance, non-linearity, outliers

- Bivariate analysis
- Linear regression
- Fit model
- Check assumptions
- Check robustness
- Make meaningful constant

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