1. Jefferson Davis Research Analytics
R Bootcamp Day 3
Jefferson Davis
Research Analytics

2. Day 2 stuff From yesterday and the day before
R values have types/classes such as numeric, character, logical, dataframes, and matrices.
Much of R functionality is in libraries
For help on a function run ? t.test() from the R console.
The plot() function will usually do something useful.

3. R: Common stats functions
Common statistical tests are very straightforward in R. Let's try one on yesterday's dataset cars of car speeds and stopping distances from the 1920s. head(cars) speed dist

4. R: Common stats functions
Here's a t-test that the mean of the speeds in cars is not 12. t.test(cars$speed, mu=12) One Sample t-test data: cars$speed t = , df = 49, p-value = 3.588e-05 alternative hypothesis: true mean is not equal to percent confidence interval: sample estimates: mean of x

5. R: Common stats functions
We can change the parameters of t-test. t.test(cars$speed, mu=12, alternative="less", conf.level=.99) One Sample t-test data: cars$speed t = , df = 49, p-value = 1 alternative hypothesis: true mean is less than percent confidence interval: Inf sample estimates: mean of x

6. R: Common stats functions
Anything you would see in a year long stats sequence will have an implentation in R. chisq.test() #Chi-squared prop.test() #Proportions test binom.test() #Exact binomial test ks.test() #Kolmogorov–Smirnov sd() #Standard deviation cor() #Correlation

7. R: Linear regression
Regression analysis is one of the most popular and important tools in statistics. If R goofed here, it would be worthless.
R uses the function lm() for linear models. The regression formula is given in Wilkinson-Rogers notation
Predictor terms
Wilkinson Notation
Intercept
1 (Default)
No intercept -1 x1
x1, x2
x1 + x2
x1, x2, x1x2
x1*x2 (or x1 + x2 + x1:x2)
x1x2
x1:x2
x12, x1
x1^2
x1 + x2
I(x1 + x2) (The letter I)

8. R: Linear regression
Regression analysis is one of the most important tools in statistics. R uses Wilkinson-Rogers notation to to specify linear models. So a model such as yi = β0 + β1 xi1 + εi
Shows up in the R syntax as
y ~ x1 Let's review this syntax. (Tables from

9. R: Linear regression Predictor terms Wilkinson Notation Intercept
1 (Default)
No intercept -1 x1
x1, x2
x1 + x2
x1, x2, x1x2
x1*x2
(or x1 + x2 + x1:x2)
x1x2
x1:x2
x12, x1
x1^2
x1 + x2
I(x1 + x2)

10. R: Linear regression yi = β0 + β1 xi1 + β2 xi2 + εi Two predictors
Model
Wilkinson Notation
yi = β0 + β1 xi1 + β2 xi2 + εi Two predictors
y ~ x1 + x2
yi = β1 xi1 + β2 xi2 + εi Two predictors and no intercept
y ~ x1 + x2 - 1
yi = β0 + β1 xi1 + β2 xi2 +
β3 xi1 xi2 + εi Two predictors with the interaction term
y ~ x1 * x2 y ~ x1 + x2 + x1:x2
yi = β0 + β1 (xi1 + xi2 ) + εi Regressing on the sum of predictors
y ~ I(x1 + x2)
yi = β0 + β1 xi1 + β2 xi2 + β3 xi β4 xi1 xi2 + εi
Three predictors with one interaction
y ~ x1 * x2 + x3

11. R: Linear regression
Model terms
Wilkinson Notation
yi = β1 xi1 + β2 xi2 + β3 xi1 xi2 + εi Two predictors, no intercept
yi = β0 + β1 xi1 + β2 xi2 + β3 xi β4 xi1 xi2 + β5 xi1 xi3 + β6 xi2 xi β7 xi1 xi2xi3+ εi Three predictors, all interaction terms
yi = β0 + β1 xi1 + β2 xi2 + β3 xi β4 xi1 xi2 + β5 xi1 xi3 + β6 xi2 xi εi
Three predictors, all two-way interaction terms.

12. R: Linear regression Model terms Wilkinson Notation
yi = β1 xi1 + β2 xi2 + β3 xi1 xi2 + εi Two predictors, no intercept
y ~ x1*x2 - 1
yi = β0 + β1 xi1 + β2 xi2 + β3 xi β4 xi1 xi2 + β5 xi1 xi3 + β6 xi2 xi β7 xi1 xi2xi3+ εi Three predictors, all interaction terms
y ~ x1 * x2 * x3
yi = β0 + β1 xi1 + β2 xi2 + β3 xi β4 xi1 xi2 + β5 xi1 xi3 + β6 xi2 xi εi
Three predictors, all two-way interaction terms
y ~ x1 * x2 * x3 – x1:x2:x3

13. R: Linear regression R uses the function lm() for linear models.
Generic syntax lm(DV ~ IV1, NAME_OF_DATAFRAME)
The above tells R that to regress the dependent variable (DV) onto independent variable IV1. We can include other variables and interaction effects. lm(DV ~ IV1 + IV2 + IV1*IV2, NAME_OF_DATAFRAME)

14. R: Linear regression
Let's do an example using the cars data set. How about regressing stopping distance on speed. lm(dist ~ speed, cars) Call:lm(formula = dist ~ speed, data = cars) Coefficients: (Intercept) speed
To work more let's store this in a variable car.fit <- lm(dist ~ speed, cars)

15. R: Linear regression
summary(car.fit) Call: lm(formula = dist ~ speed, data = cars) Residuals: Min Q Median Q Max Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) * speed e-12 ***

16. R: Linear regression
We can also look at individual fields of the lm object. car.fit$coefficients (Intercept) speed car.fit$residuals[1:3] car.fit$fitted.values[1:3]

17. R: Linear regression
Plot the fit plot(cars$speed, cars$dist, xlab = "distance", ylab = "speed") abline(car.fit, col="red")

18. R: Linear regression
Class lm object have their own overloaded plot() function plot(car.fit)

19. R: Linear regression
Class lm object have their own overloaded plot() function plot(car.fit)

20. R: Linear regression
Class lm object have their own overloaded plot() function plot(car.fit)

21. R: Mixed models
It doesn't seem crazy to fit a slope but use a random effect for intercept. fmOrthF <- lme( distance ~ age, data = OrthoFem, random = ~ 1 | Subject )

22. R: Linear regression
Class lm object have their own overloaded plot() function plot(car.fit)

23. R: Mixed models
Let's take a look at a mixed model. We need a more complex dataset. We use a subset of the Orthodont data set from the Nonlinear Mixed-Effects Models (nlme) library. library(nlme) head(Orthodont) Grouped Data: distance ~ age | Subject distance age Subject Sex M01 Male M01 Male M01 Male M01 Male

24. R: Mixed models
OrthoFem <- Orthodont[Orthodont$Sex == "Female", ] plot(OrthoFem)

25. R: Mixed models
In fact, it isn't crazy. summary(fmOrthF) Linear mixed-effects model fit by REML Data: OrthoFem AIC BIC logLik Random effects: Formula: ~1 | Subject (Intercept) Residual StdDev: Fixed effects: distance ~ age Value Std.Error DF t-value p-value (Intercept) age Correlation: (Intr)age

26. R: Conditional trees
At this point, I tag Olga in.