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## PowerPoint Slideshow about ' Linear Regression' - nathan-mcneil

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### Linear Regression

Hein Stigum

Presentation, data and programs at:

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

H.S.

Outcome and regression types

- 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

H.S.

Regression idea

H.S.

Measures and Assumptions

- 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

H.S.

Workflow

- 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

H.S.

parity

C1

sex

E

gest age

D

birth weight

DAGsAssociations Bivariate (unadjusted)

Causal effects Multivariable (adjusted)

Draw your assumptions before your conclusions

H.S.

Plot outcome by exposure

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

H.S.

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

Categorical covariatesgenerate Parity1 = (parity==1) if parity<.

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

H.S.

Create meaningful constant

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

Model results

H.S.

Test of assumptions Plot residuals versus predicted y

- Discuss
- Independent residuals?

- Linear effects?
- constantvariance?

H.S.

Violations of assumptions

- Dependent residuals
Use linear mixed models

- Non linear effects
Add square term

Or use piecewise linear

- Non-constant variance
Use robust variance estimation

H.S.

Influence

H.S.

Measures of influence

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

Remove obs 1, see change

remove obs 2, see change

H.S.

Summing up

- DAGs
- Guide analysis

- Plots
- Unequal variance, non-linearity, outliers

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

H.S.

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