Linear Model. Formal Definition General Linear Model.

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Presentation transcript:

Linear Model

Formal Definition

General Linear Model

General Linear Model Can transform the predictor values to linearize the relationship between the predictors and the response Also changes the variance so it only should be done if the variance is not uniform and is made uniform by the transform

Polynomial Regression

Need More Not all phenomenon follow linear response Not all residuals are normally distributed This leads: –GLMs: Single function, specified regression distribution –GAMs: Multiple functions –“Non-parametric” approaches: function is determined by the computer

GLM

Generalized Linear Models

Common Functions in R Probability Distribution (Link Function) Binomial (link = "logit") –True/false, alive/dead Gaussian (link = "identity") –Continuous, normal Gamma (link = "inverse") –Seed distribution, distance from… Poisson (link = "log") –Counts

Normal Distribution WikipediaAKA “Gaussian” Distribution

Binomial Number of successes of yes/no experimentsWikipedia

Poisson Number of events in time T, k=number of occurrences Wikipedia

Gamma Distribution Wait times, seed distribution, etc. Wikipedia

Deviance

Degrees of Freedom