Linear Regression

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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

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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
• Categorical data
• Nominal
• disease/ no disease
• Ordinal
• small/ medium/ large
• Poisson regression
• Linear regression
• Logistic regression
• Ordinal regression

H.S.

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

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.

C2

parity

C1

sex

E

gest age

D

birth weight

DAGs

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.

Plot outcome by exposure, cont.

Linear effects?

Yes

H.S.

Bivariate analysis

Outcome: birthweight

H.S.

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<.

H.S.

Model estimation

Syntax:

regress weight gest sex Parity1 Parity2_7

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

Test of assumptions
• Discuss
• Independent residuals?
• Plot residuals versus predicted y
• Linear effects?
• constantvariance?

H.S.

Violations of assumptions
• Dependent residuals

Use linear mixed models

• Non linear effects

Or use piecewise linear

• Non-constant variance

Use robust variance estimation

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.

Delta beta for gestational age

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

H.S.

Removing outlier

Full data

Outlier removed

One outlier affected two estimates

Final model

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.