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# Linear Regression PowerPoint PPT Presentation

Linear Regression. Hein Stigum Presentation, data and programs at: http://folk.uio.no/heins/ courses. Linear regression. Concepts. Outcome and regression types. Numerical data Discrete number of partners Continuous Weight Categorical data Nominal disease/ no disease Ordinal

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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### Outcome and regression types

• Numerical data

• Discrete

• number of partners

• Continuous

• Weight

• Categorical data

• Nominal

• disease/ no disease

• Ordinal

• small/ medium/ large

• Poisson regression

• Linear regression

• Logistic regression

• Ordinal regression

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### Measures and Assumptions

• 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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### 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

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Continuous outcome:Linear regression, Birth weight

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C2

parity

C1

sex

E

gest age

D

birth weight

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### 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

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Linear effects?

Yes

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### Bivariate analysis

Outcome: birthweight

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Continuous outcome:Linear regression, Birth weight

### Regression

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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

### Categorical covariates

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

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

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### Model estimation

Syntax:

regress weight gest sex Parity1 Parity2_7

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### 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

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### Test of assumptions

• Discuss

• Independent residuals?

• Plot residuals versus predicted y

• Linear effects?

• constantvariance?

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### Violations of assumptions

• Dependent residuals

Use linear mixed models

• Non linear effects

Or use piecewise linear

• Non-constant variance

Use robust variance estimation

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### Measures of influence

• Measure change in:

• Predicted outcome

• Deviance

• Coefficients (beta)

• Delta beta

Remove obs 1, see change

remove obs 2, see change

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### Delta beta for gestational age

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

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### Removing outlier

Full data

Outlier removed

One outlier affected two estimates

Final model

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### Summing up

• 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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