• DenmarkMiniCourseSession1

Session 1: Linear and logistic regression

This session will cover the basics of linear and logistic regression. See below for a [#Topics list of topics]. Please make sure to do the readings and let me know in advance if there is terminology that you would like to be clarified. The goal of this session is to go through the basic steps of building linear or logistic regression model, understanding the output, and validating how good this model is.

I've also posted some [#assignments assignments] below. There is only one way to learn how to use the methods we will talk about and that is to apply them yourself to a data set that you understand. The tutorial is intended to get you to the level where you can do that.

Materials

• attachment:attention-r-data.csv
• attachment:attention-procedure.ppt
• attachment:attention-r-commands.R
• attachment:case-influence.ppt

Reading

Notes on the readings

If you'd like to follow along, the dataset used in the G&H07 reading can be found here: [http://www.stat.columbia.edu/~gelman/arm/examples/child.iq/]. To use the file, you will need to load the "foreign" package, then use the read.dta() function. Eg:

• library("foreign") BR kidiq <- read.dta(file="kidiq.dta")

Additional terminology

Feel free to add terms you want clarified in class:

Questions

• Q: On page 181, Baayen refers to one of the models, done via lm(), as a covariance model. Why is this considered a model of covariance rather than a regression?

• A: This refers to the fact that 'lm()' or any regression model allows the inclusion of continuous predictors (unlike ANOVA, aov() in R, but like ANCOVA - analysis of covariance). The idea is that, for a linear model, where the outcome is a continuous variable, a continuous predictor co-varies (to whatever extent) with the continuous outcome.
• Q: When doing a regression with a categorical variable (as Baayen does on page 182), is there an easy way to see which level is coded as 1 and which as 0?
• A: By default R codes the dependent variable so that the the outcome is the level that is 2nd in terms of alpha-numerically order.

Anchor(assignments)

Assignments

Please upload your solutions by Friday 3:30pm.

* (for Exercise 7, Baayen treats linear regression using lm or ols as the same as analysis of covariance (see section 4.4.1 (pp. 117-119))).

• attachment:APS-hw1.R

• attachment:BenVanDurme-hw1.R

• attachment:TingQian-hw1.R

Anchor(Topics)

Topics

• The Linear Model (LM)

  • Geometric interpretationBR Ordinary least squares (and how they are "optimal" for the purpose of predicting an outcome Y)BR

• Building a linear model (for data analysis)

  • lm(), ols()BR Structure and class of these objects

    • coef(), display(), summary()BR fitted(), resid()BR

    Standard output
• Interpreting the output of a linear model

  • What hypotheses are we testing?BR What are coefficients and how to read them?BR

    • anova(), drop()BR

    Coding?BR

    • contrasts()BR

    Transformations and other non-linearitiesBR

    • log(), sqrt()BR rcs(), pol()BR

• Using a model to predict unseen data

  • predict()BR

• Understanding the influence of individual cases, identifying outliers

  • boxplot()BR lm.influence()BR